dolphin/Source/Core/Common/MathUtil.cpp

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// Copyright 2008 Dolphin Emulator Project
2015-05-17 23:08:10 +00:00
// Licensed under GPLv2+
// Refer to the license.txt file included.
#include <cmath>
#include <cstring>
#include <limits>
#include <numeric>
#include "Common/CommonTypes.h"
#include "Common/MathUtil.h"
namespace MathUtil
{
u32 ClassifyDouble(double dvalue)
{
// TODO: Optimize the below to be as fast as possible.
IntDouble value(dvalue);
u64 sign = value.i & DOUBLE_SIGN;
u64 exp = value.i & DOUBLE_EXP;
if (exp > DOUBLE_ZERO && exp < DOUBLE_EXP)
{
// Nice normalized number.
return sign ? PPC_FPCLASS_NN : PPC_FPCLASS_PN;
}
else
{
u64 mantissa = value.i & DOUBLE_FRAC;
if (mantissa)
{
if (exp)
{
return PPC_FPCLASS_QNAN;
}
else
{
// Denormalized number.
return sign ? PPC_FPCLASS_ND : PPC_FPCLASS_PD;
}
}
else if (exp)
{
// Infinite
return sign ? PPC_FPCLASS_NINF : PPC_FPCLASS_PINF;
}
else
{
// Zero
return sign ? PPC_FPCLASS_NZ : PPC_FPCLASS_PZ;
}
}
}
u32 ClassifyFloat(float fvalue)
{
// TODO: Optimize the below to be as fast as possible.
IntFloat value(fvalue);
u32 sign = value.i & FLOAT_SIGN;
u32 exp = value.i & FLOAT_EXP;
if (exp > FLOAT_ZERO && exp < FLOAT_EXP)
{
// Nice normalized number.
return sign ? PPC_FPCLASS_NN : PPC_FPCLASS_PN;
}
else
{
u32 mantissa = value.i & FLOAT_FRAC;
if (mantissa)
{
if (exp)
{
return PPC_FPCLASS_QNAN; // Quiet NAN
}
else
{
// Denormalized number.
return sign ? PPC_FPCLASS_ND : PPC_FPCLASS_PD;
}
}
else if (exp)
{
// Infinite
return sign ? PPC_FPCLASS_NINF : PPC_FPCLASS_PINF;
}
else
{
// Zero
return sign ? PPC_FPCLASS_NZ : PPC_FPCLASS_PZ;
}
}
}
const int frsqrte_expected_base[] = {
0x3ffa000, 0x3c29000, 0x38aa000, 0x3572000, 0x3279000, 0x2fb7000, 0x2d26000, 0x2ac0000,
0x2881000, 0x2665000, 0x2468000, 0x2287000, 0x20c1000, 0x1f12000, 0x1d79000, 0x1bf4000,
0x1a7e800, 0x17cb800, 0x1552800, 0x130c000, 0x10f2000, 0x0eff000, 0x0d2e000, 0x0b7c000,
0x09e5000, 0x0867000, 0x06ff000, 0x05ab800, 0x046a000, 0x0339800, 0x0218800, 0x0105800,
};
const int frsqrte_expected_dec[] = {
0x7a4, 0x700, 0x670, 0x5f2, 0x584, 0x524, 0x4cc, 0x47e, 0x43a, 0x3fa, 0x3c2,
0x38e, 0x35e, 0x332, 0x30a, 0x2e6, 0x568, 0x4f3, 0x48d, 0x435, 0x3e7, 0x3a2,
0x365, 0x32e, 0x2fc, 0x2d0, 0x2a8, 0x283, 0x261, 0x243, 0x226, 0x20b,
};
double ApproximateReciprocalSquareRoot(double val)
{
union
{
double valf;
s64 vali;
};
valf = val;
s64 mantissa = vali & ((1LL << 52) - 1);
s64 sign = vali & (1ULL << 63);
s64 exponent = vali & (0x7FFLL << 52);
// Special case 0
if (mantissa == 0 && exponent == 0)
return sign ? -std::numeric_limits<double>::infinity() :
std::numeric_limits<double>::infinity();
// Special case NaN-ish numbers
if (exponent == (0x7FFLL << 52))
{
if (mantissa == 0)
{
if (sign)
return std::numeric_limits<double>::quiet_NaN();
return 0.0;
}
return 0.0 + valf;
}
// Negative numbers return NaN
if (sign)
return std::numeric_limits<double>::quiet_NaN();
if (!exponent)
{
// "Normalize" denormal values
do
{
exponent -= 1LL << 52;
mantissa <<= 1;
} while (!(mantissa & (1LL << 52)));
mantissa &= (1LL << 52) - 1;
exponent += 1LL << 52;
}
bool odd_exponent = !(exponent & (1LL << 52));
exponent = ((0x3FFLL << 52) - ((exponent - (0x3FELL << 52)) / 2)) & (0x7FFLL << 52);
int i = (int)(mantissa >> 37);
vali = sign | exponent;
int index = i / 2048 + (odd_exponent ? 16 : 0);
vali |= (s64)(frsqrte_expected_base[index] - frsqrte_expected_dec[index] * (i % 2048)) << 26;
return valf;
}
const int fres_expected_base[] = {
0x7ff800, 0x783800, 0x70ea00, 0x6a0800, 0x638800, 0x5d6200, 0x579000, 0x520800,
0x4cc800, 0x47ca00, 0x430800, 0x3e8000, 0x3a2c00, 0x360800, 0x321400, 0x2e4a00,
0x2aa800, 0x272c00, 0x23d600, 0x209e00, 0x1d8800, 0x1a9000, 0x17ae00, 0x14f800,
0x124400, 0x0fbe00, 0x0d3800, 0x0ade00, 0x088400, 0x065000, 0x041c00, 0x020c00,
};
const int fres_expected_dec[] = {
0x3e1, 0x3a7, 0x371, 0x340, 0x313, 0x2ea, 0x2c4, 0x2a0, 0x27f, 0x261, 0x245,
0x22a, 0x212, 0x1fb, 0x1e5, 0x1d1, 0x1be, 0x1ac, 0x19b, 0x18b, 0x17c, 0x16e,
0x15b, 0x15b, 0x143, 0x143, 0x12d, 0x12d, 0x11a, 0x11a, 0x108, 0x106,
};
// Used by fres and ps_res.
double ApproximateReciprocal(double val)
{
// We are using namespace std scoped here because the Android NDK is complete trash as usual
// For 32bit targets(mips, ARMv7, x86) it doesn't provide an implementation of std::copysign
// but instead provides just global namespace copysign implementations.
// The workaround for this is to just use namespace std within this function's scope
// That way on real toolchains it will use the std:: variant like normal.
using namespace std;
union
{
double valf;
s64 vali;
};
valf = val;
s64 mantissa = vali & ((1LL << 52) - 1);
s64 sign = vali & (1ULL << 63);
s64 exponent = vali & (0x7FFLL << 52);
// Special case 0
if (mantissa == 0 && exponent == 0)
return copysign(std::numeric_limits<double>::infinity(), valf);
// Special case NaN-ish numbers
if (exponent == (0x7FFLL << 52))
{
if (mantissa == 0)
return copysign(0.0, valf);
return 0.0 + valf;
}
// Special case small inputs
if (exponent < (895LL << 52))
return copysign(std::numeric_limits<float>::max(), valf);
// Special case large inputs
if (exponent >= (1149LL << 52))
return copysign(0.0, valf);
exponent = (0x7FDLL << 52) - exponent;
int i = (int)(mantissa >> 37);
vali = sign | exponent;
vali |= (s64)(fres_expected_base[i / 1024] - (fres_expected_dec[i / 1024] * (i % 1024) + 1) / 2)
<< 29;
return valf;
}
} // namespace
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inline void MatrixMul(int n, const float* a, const float* b, float* result)
{
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < n; ++j)
{
float temp = 0;
for (int k = 0; k < n; ++k)
{
temp += a[i * n + k] * b[k * n + j];
}
result[i * n + j] = temp;
}
}
}
// Calculate sum of a float list
float MathFloatVectorSum(const std::vector<float>& Vec)
{
return std::accumulate(Vec.begin(), Vec.end(), 0.0f);
}
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void Matrix33::LoadIdentity(Matrix33& mtx)
{
memset(mtx.data, 0, sizeof(mtx.data));
mtx.data[0] = 1.0f;
mtx.data[4] = 1.0f;
mtx.data[8] = 1.0f;
}
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void Matrix33::RotateX(Matrix33& mtx, float rad)
{
float s = sin(rad);
float c = cos(rad);
memset(mtx.data, 0, sizeof(mtx.data));
mtx.data[0] = 1;
mtx.data[4] = c;
mtx.data[5] = -s;
mtx.data[7] = s;
mtx.data[8] = c;
}
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void Matrix33::RotateY(Matrix33& mtx, float rad)
{
float s = sin(rad);
float c = cos(rad);
memset(mtx.data, 0, sizeof(mtx.data));
mtx.data[0] = c;
mtx.data[2] = s;
mtx.data[4] = 1;
mtx.data[6] = -s;
mtx.data[8] = c;
}
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void Matrix33::Multiply(const Matrix33& a, const Matrix33& b, Matrix33& result)
{
MatrixMul(3, a.data, b.data, result.data);
}
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void Matrix33::Multiply(const Matrix33& a, const float vec[3], float result[3])
{
for (int i = 0; i < 3; ++i)
{
result[i] = 0;
for (int k = 0; k < 3; ++k)
{
result[i] += a.data[i * 3 + k] * vec[k];
}
}
}
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void Matrix44::LoadIdentity(Matrix44& mtx)
{
memset(mtx.data, 0, sizeof(mtx.data));
mtx.data[0] = 1.0f;
mtx.data[5] = 1.0f;
mtx.data[10] = 1.0f;
mtx.data[15] = 1.0f;
}
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void Matrix44::LoadMatrix33(Matrix44& mtx, const Matrix33& m33)
{
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 3; ++j)
{
mtx.data[i * 4 + j] = m33.data[i * 3 + j];
}
}
for (int i = 0; i < 3; ++i)
{
mtx.data[i * 4 + 3] = 0;
mtx.data[i + 12] = 0;
}
mtx.data[15] = 1.0f;
}
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void Matrix44::Set(Matrix44& mtx, const float mtxArray[16])
{
for (int i = 0; i < 16; ++i)
{
mtx.data[i] = mtxArray[i];
}
}
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void Matrix44::Translate(Matrix44& mtx, const float vec[3])
{
LoadIdentity(mtx);
mtx.data[3] = vec[0];
mtx.data[7] = vec[1];
mtx.data[11] = vec[2];
}
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void Matrix44::Shear(Matrix44& mtx, const float a, const float b)
{
LoadIdentity(mtx);
mtx.data[2] = a;
mtx.data[6] = b;
}
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void Matrix44::Multiply(const Matrix44& a, const Matrix44& b, Matrix44& result)
{
MatrixMul(4, a.data, b.data, result.data);
}