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// Copyright 2018 Dolphin Emulator Project
// Licensed under GPLv2+
// Refer to the license.txt file included.
#include "Common/FloatUtils.h"
#include <cmath>
namespace Common
{
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 std::array<BaseAndDec, 32> frsqrte_expected = {{
{0x3ffa000, 0x7a4}, {0x3c29000, 0x700}, {0x38aa000, 0x670}, {0x3572000, 0x5f2},
{0x3279000, 0x584}, {0x2fb7000, 0x524}, {0x2d26000, 0x4cc}, {0x2ac0000, 0x47e},
{0x2881000, 0x43a}, {0x2665000, 0x3fa}, {0x2468000, 0x3c2}, {0x2287000, 0x38e},
{0x20c1000, 0x35e}, {0x1f12000, 0x332}, {0x1d79000, 0x30a}, {0x1bf4000, 0x2e6},
{0x1a7e800, 0x568}, {0x17cb800, 0x4f3}, {0x1552800, 0x48d}, {0x130c000, 0x435},
{0x10f2000, 0x3e7}, {0x0eff000, 0x3a2}, {0x0d2e000, 0x365}, {0x0b7c000, 0x32e},
{0x09e5000, 0x2fc}, {0x0867000, 0x2d0}, {0x06ff000, 0x2a8}, {0x05ab800, 0x283},
{0x046a000, 0x261}, {0x0339800, 0x243}, {0x0218800, 0x226}, {0x0105800, 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);
const auto& entry = frsqrte_expected[index];
vali |= (s64)(entry.m_base - entry.m_dec * (i % 2048)) << 26;
return valf;
}
const std::array<BaseAndDec, 32> fres_expected = {{
{0x7ff800, 0x3e1}, {0x783800, 0x3a7}, {0x70ea00, 0x371}, {0x6a0800, 0x340}, {0x638800, 0x313},
{0x5d6200, 0x2ea}, {0x579000, 0x2c4}, {0x520800, 0x2a0}, {0x4cc800, 0x27f}, {0x47ca00, 0x261},
{0x430800, 0x245}, {0x3e8000, 0x22a}, {0x3a2c00, 0x212}, {0x360800, 0x1fb}, {0x321400, 0x1e5},
{0x2e4a00, 0x1d1}, {0x2aa800, 0x1be}, {0x272c00, 0x1ac}, {0x23d600, 0x19b}, {0x209e00, 0x18b},
{0x1d8800, 0x17c}, {0x1a9000, 0x16e}, {0x17ae00, 0x15b}, {0x14f800, 0x15b}, {0x124400, 0x143},
{0x0fbe00, 0x143}, {0x0d3800, 0x12d}, {0x0ade00, 0x12d}, {0x088400, 0x11a}, {0x065000, 0x11a},
{0x041c00, 0x108}, {0x020c00, 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);
const auto& entry = fres_expected[i / 1024];
vali = sign | exponent;
vali |= (s64)(entry.m_base - (entry.m_dec * (i % 1024) + 1) / 2) << 29;
return valf;
}
} // namespace Common
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