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// Copyright 2018 Dolphin Emulator Project
// SPDX-License-Identifier: GPL-2.0-or-later
#include "Common/FloatUtils.h"
#include <bit>
#include <cmath>
namespace Common
{
u32 ClassifyDouble(double dvalue)
{
const u64 ivalue = std::bit_cast<u64>(dvalue);
const u64 sign = ivalue & DOUBLE_SIGN;
const u64 exp = ivalue & DOUBLE_EXP;
if (exp > DOUBLE_ZERO && exp < DOUBLE_EXP)
{
// Nice normalized number.
return sign ? PPC_FPCLASS_NN : PPC_FPCLASS_PN;
}
const u64 mantissa = ivalue & DOUBLE_FRAC;
if (mantissa)
{
if (exp)
return PPC_FPCLASS_QNAN;
// Denormalized number.
return sign ? PPC_FPCLASS_ND : PPC_FPCLASS_PD;
}
if (exp)
{
// Infinite
return sign ? PPC_FPCLASS_NINF : PPC_FPCLASS_PINF;
}
// Zero
return sign ? PPC_FPCLASS_NZ : PPC_FPCLASS_PZ;
}
u32 ClassifyFloat(float fvalue)
{
const u32 ivalue = std::bit_cast<u32>(fvalue);
const u32 sign = ivalue & FLOAT_SIGN;
const u32 exp = ivalue & FLOAT_EXP;
if (exp > FLOAT_ZERO && exp < FLOAT_EXP)
{
// Nice normalized number.
return sign ? PPC_FPCLASS_NN : PPC_FPCLASS_PN;
}
const u32 mantissa = ivalue & FLOAT_FRAC;
if (mantissa)
{
if (exp)
return PPC_FPCLASS_QNAN; // Quiet NAN
// Denormalized number.
return sign ? PPC_FPCLASS_ND : PPC_FPCLASS_PD;
}
if (exp)
{
// Infinite
return sign ? PPC_FPCLASS_NINF : PPC_FPCLASS_PINF;
}
// Zero
return sign ? PPC_FPCLASS_NZ : PPC_FPCLASS_PZ;
}
const std::array<BaseAndDec, 32> frsqrte_expected = {{
{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},
{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},
}};
double ApproximateReciprocalSquareRoot(double val)
{
s64 integral = std::bit_cast<s64>(val);
s64 mantissa = integral & ((1LL << 52) - 1);
const s64 sign = integral & (1ULL << 63);
s64 exponent = integral & (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 MakeQuiet(val);
}
// 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;
}
const s64 exponent_lsb = exponent & (1LL << 52);
exponent = ((0x3FFLL << 52) - ((exponent - (0x3FELL << 52)) / 2)) & (0x7FFLL << 52);
integral = sign | exponent;
const int i = static_cast<int>((exponent_lsb | mantissa) >> 37);
const auto& entry = frsqrte_expected[i / 2048];
integral |= static_cast<s64>(entry.m_base + entry.m_dec * (i % 2048)) << 26;
return std::bit_cast<double>(integral);
}
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)
{
s64 integral = std::bit_cast<s64>(val);
const s64 mantissa = integral & ((1LL << 52) - 1);
const s64 sign = integral & (1ULL << 63);
s64 exponent = integral & (0x7FFLL << 52);
// Special case 0
if (mantissa == 0 && exponent == 0)
return std::copysign(std::numeric_limits<double>::infinity(), val);
// Special case NaN-ish numbers
if (exponent == (0x7FFLL << 52))
{
if (mantissa == 0)
return std::copysign(0.0, val);
return MakeQuiet(val);
}
// Special case small inputs
if (exponent < (895LL << 52))
return std::copysign(std::numeric_limits<float>::max(), val);
// Special case large inputs
if (exponent >= (1149LL << 52))
return std::copysign(0.0, val);
exponent = (0x7FDLL << 52) - exponent;
const int i = static_cast<int>(mantissa >> 37);
const auto& entry = fres_expected[i / 1024];
integral = sign | exponent;
integral |= static_cast<s64>(entry.m_base - (entry.m_dec * (i % 1024) + 1) / 2) << 29;
return std::bit_cast<double>(integral);
}
} // namespace Common
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