dolphin/Source/Core/Common/FloatUtils.cpp

// Copyright 2018 Dolphin Emulator Project
// Licensed under GPLv2+
// Refer to the license.txt file included.

#include "Common/FloatUtils.h"

#include <cmath>

#include "Common/BitUtils.h"

namespace Common
{
u32 ClassifyDouble(double dvalue)
{
  const u64 ivalue = BitCast<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 = BitCast<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 = {{
    {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)
{
  s64 integral = BitCast<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 0.0 + 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 bool odd_exponent = !(exponent & (1LL << 52));
  exponent = ((0x3FFLL << 52) - ((exponent - (0x3FELL << 52)) / 2)) & (0x7FFLL << 52);
  integral = sign | exponent;

  const int i = static_cast<int>(mantissa >> 37);
  const int index = i / 2048 + (odd_exponent ? 16 : 0);
  const auto& entry = frsqrte_expected[index];
  integral |= static_cast<s64>(entry.m_base - entry.m_dec * (i % 2048)) << 26;

  return BitCast<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 = BitCast<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 0.0 + 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 BitCast<double>(integral);
}

}  // namespace Common