dolphin/Source/Core/Common/MathUtil.h

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// Copyright 2008 Dolphin Emulator Project
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// Licensed under GPLv2+
// Refer to the license.txt file included.
#pragma once
#include <algorithm>
#include <array>
#include <cstdlib>
#include <vector>
#include "Common/CommonTypes.h"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace MathUtil
{
template <typename T>
constexpr T SNANConstant()
{
return std::numeric_limits<T>::signaling_NaN();
}
#ifdef _MSC_VER
// MSVC needs a workaround, because its std::numeric_limits<double>::signaling_NaN()
// will use __builtin_nans, which is improperly handled by the compiler and generates
// a bad constant. Here we go back to the version MSVC used before the builtin.
// TODO: Remove this and use numeric_limits directly whenever this bug is fixed.
template <>
constexpr double SNANConstant()
{
return (_CSTD _Snan._Double);
}
template <>
constexpr float SNANConstant()
{
return (_CSTD _Snan._Float);
}
#endif
template <class T>
constexpr T Clamp(const T val, const T& min, const T& max)
{
return std::max(min, std::min(max, val));
}
template <typename T>
constexpr bool IsPow2(T imm)
{
return imm > 0 && (imm & (imm - 1)) == 0;
}
// The most significant bit of the fraction is an is-quiet bit on all architectures we care about.
static const u64 DOUBLE_SIGN = 0x8000000000000000ULL, DOUBLE_EXP = 0x7FF0000000000000ULL,
DOUBLE_FRAC = 0x000FFFFFFFFFFFFFULL, DOUBLE_ZERO = 0x0000000000000000ULL,
DOUBLE_QBIT = 0x0008000000000000ULL;
static const u32 FLOAT_SIGN = 0x80000000, FLOAT_EXP = 0x7F800000, FLOAT_FRAC = 0x007FFFFF,
FLOAT_ZERO = 0x00000000;
union IntDouble
{
double d;
u64 i;
explicit IntDouble(u64 _i) : i(_i) {}
explicit IntDouble(double _d) : d(_d) {}
};
union IntFloat
{
float f;
u32 i;
explicit IntFloat(u32 _i) : i(_i) {}
explicit IntFloat(float _f) : f(_f) {}
};
inline bool IsQNAN(double d)
{
IntDouble x(d);
return ((x.i & DOUBLE_EXP) == DOUBLE_EXP) && ((x.i & DOUBLE_QBIT) == DOUBLE_QBIT);
}
inline bool IsSNAN(double d)
{
IntDouble x(d);
return ((x.i & DOUBLE_EXP) == DOUBLE_EXP) && ((x.i & DOUBLE_FRAC) != DOUBLE_ZERO) &&
((x.i & DOUBLE_QBIT) == DOUBLE_ZERO);
}
inline float FlushToZero(float f)
{
IntFloat x(f);
if ((x.i & FLOAT_EXP) == 0)
{
x.i &= FLOAT_SIGN; // turn into signed zero
}
return x.f;
}
inline double FlushToZero(double d)
{
IntDouble x(d);
if ((x.i & DOUBLE_EXP) == 0)
{
x.i &= DOUBLE_SIGN; // turn into signed zero
}
return x.d;
}
enum PPCFpClass
{
PPC_FPCLASS_QNAN = 0x11,
PPC_FPCLASS_NINF = 0x9,
PPC_FPCLASS_NN = 0x8,
PPC_FPCLASS_ND = 0x18,
PPC_FPCLASS_NZ = 0x12,
PPC_FPCLASS_PZ = 0x2,
PPC_FPCLASS_PD = 0x14,
PPC_FPCLASS_PN = 0x4,
PPC_FPCLASS_PINF = 0x5,
};
// Uses PowerPC conventions for the return value, so it can be easily
// used directly in CPU emulation.
u32 ClassifyDouble(double dvalue);
// More efficient float version.
u32 ClassifyFloat(float fvalue);
struct BaseAndDec
{
int m_base;
int m_dec;
};
extern const std::array<BaseAndDec, 32> frsqrte_expected;
extern const std::array<BaseAndDec, 32> fres_expected;
// PowerPC approximation algorithms
double ApproximateReciprocalSquareRoot(double val);
double ApproximateReciprocal(double val);
template <class T>
struct Rectangle
{
T left{};
T top{};
T right{};
T bottom{};
constexpr Rectangle() = default;
constexpr Rectangle(T theLeft, T theTop, T theRight, T theBottom)
: left(theLeft), top(theTop), right(theRight), bottom(theBottom)
{
}
constexpr bool operator==(const Rectangle& r) const
{
return left == r.left && top == r.top && right == r.right && bottom == r.bottom;
}
T GetWidth() const { return abs(right - left); }
T GetHeight() const { return abs(bottom - top); }
// If the rectangle is in a coordinate system with a lower-left origin, use
// this Clamp.
void ClampLL(T x1, T y1, T x2, T y2)
{
left = Clamp(left, x1, x2);
right = Clamp(right, x1, x2);
top = Clamp(top, y2, y1);
bottom = Clamp(bottom, y2, y1);
}
// If the rectangle is in a coordinate system with an upper-left origin,
// use this Clamp.
void ClampUL(T x1, T y1, T x2, T y2)
{
left = Clamp(left, x1, x2);
right = Clamp(right, x1, x2);
top = Clamp(top, y1, y2);
bottom = Clamp(bottom, y1, y2);
}
};
} // namespace MathUtil
float MathFloatVectorSum(const std::vector<float>&);
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// Rounds down. 0 -> undefined
inline int IntLog2(u64 val)
{
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#if defined(__GNUC__)
return 63 - __builtin_clzll(val);
#elif defined(_MSC_VER)
unsigned long result = ULONG_MAX;
_BitScanReverse64(&result, val);
return result;
#else
int result = -1;
while (val != 0)
{
val >>= 1;
++result;
}
return result;
#endif
}
// Tiny matrix/vector library.
// Used for things like Free-Look in the gfx backend.
class Matrix33
{
public:
static void LoadIdentity(Matrix33& mtx);
// set mtx to be a rotation matrix around the x axis
static void RotateX(Matrix33& mtx, float rad);
// set mtx to be a rotation matrix around the y axis
static void RotateY(Matrix33& mtx, float rad);
// set result = a x b
static void Multiply(const Matrix33& a, const Matrix33& b, Matrix33& result);
static void Multiply(const Matrix33& a, const float vec[3], float result[3]);
float data[9];
};
class Matrix44
{
public:
static void LoadIdentity(Matrix44& mtx);
static void LoadMatrix33(Matrix44& mtx, const Matrix33& m33);
static void Set(Matrix44& mtx, const float mtxArray[16]);
static void Translate(Matrix44& mtx, const float vec[3]);
static void Shear(Matrix44& mtx, const float a, const float b = 0);
static void Multiply(const Matrix44& a, const Matrix44& b, Matrix44& result);
float data[16];
};