// Copyright 2008 Dolphin Emulator Project // Licensed under GPLv2+ // Refer to the license.txt file included. #include #include #include #include #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 std::array 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::infinity() : std::numeric_limits::infinity(); // Special case NaN-ish numbers if (exponent == (0x7FFLL << 52)) { if (mantissa == 0) { if (sign) return std::numeric_limits::quiet_NaN(); return 0.0; } return 0.0 + valf; } // Negative numbers return NaN if (sign) return std::numeric_limits::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 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::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::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 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& Vec) { return std::accumulate(Vec.begin(), Vec.end(), 0.0f); } 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; } 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; } 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; } void Matrix33::Multiply(const Matrix33& a, const Matrix33& b, Matrix33& result) { MatrixMul(3, a.data, b.data, result.data); } 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]; } } } 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; } 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; } void Matrix44::Set(Matrix44& mtx, const float mtxArray[16]) { for (int i = 0; i < 16; ++i) { mtx.data[i] = mtxArray[i]; } } 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]; } void Matrix44::Shear(Matrix44& mtx, const float a, const float b) { LoadIdentity(mtx); mtx.data[2] = a; mtx.data[6] = b; } void Matrix44::Multiply(const Matrix44& a, const Matrix44& b, Matrix44& result) { MatrixMul(4, a.data, b.data, result.data); }