using ARMeilleure.State; using System; using System.Diagnostics; namespace ARMeilleure.Instructions { static class SoftFloat { static SoftFloat() { RecipEstimateTable = BuildRecipEstimateTable(); RecipSqrtEstimateTable = BuildRecipSqrtEstimateTable(); } internal static readonly byte[] RecipEstimateTable; internal static readonly byte[] RecipSqrtEstimateTable; private static byte[] BuildRecipEstimateTable() { byte[] tbl = new byte[256]; for (int idx = 0; idx < 256; idx++) { uint src = (uint)idx + 256u; Debug.Assert(256u <= src && src < 512u); src = (src << 1) + 1u; uint aux = (1u << 19) / src; uint dst = (aux + 1u) >> 1; Debug.Assert(256u <= dst && dst < 512u); tbl[idx] = (byte)(dst - 256u); } return tbl; } private static byte[] BuildRecipSqrtEstimateTable() { byte[] tbl = new byte[384]; for (int idx = 0; idx < 384; idx++) { uint src = (uint)idx + 128u; Debug.Assert(128u <= src && src < 512u); if (src < 256u) { src = (src << 1) + 1u; } else { src = (src >> 1) << 1; src = (src + 1u) << 1; } uint aux = 512u; while (src * (aux + 1u) * (aux + 1u) < (1u << 28)) { aux = aux + 1u; } uint dst = (aux + 1u) >> 1; Debug.Assert(256u <= dst && dst < 512u); tbl[idx] = (byte)(dst - 256u); } return tbl; } } static class SoftFloat16_32 { public static float FPConvert(ushort valueBits) { ExecutionContext context = NativeInterface.GetContext(); double real = valueBits.FPUnpackCv(out FPType type, out bool sign, context); float result; if (type == FPType.SNaN || type == FPType.QNaN) { if ((context.Fpcr & FPCR.Dn) != 0) { result = FPDefaultNaN(); } else { result = FPConvertNaN(valueBits); } if (type == FPType.SNaN) { FPProcessException(FPException.InvalidOp, context); } } else if (type == FPType.Infinity) { result = FPInfinity(sign); } else if (type == FPType.Zero) { result = FPZero(sign); } else { result = FPRoundCv(real, context); } return result; } private static float FPDefaultNaN() { return -float.NaN; } private static float FPInfinity(bool sign) { return sign ? float.NegativeInfinity : float.PositiveInfinity; } private static float FPZero(bool sign) { return sign ? -0f : +0f; } private static float FPMaxNormal(bool sign) { return sign ? float.MinValue : float.MaxValue; } private static double FPUnpackCv( this ushort valueBits, out FPType type, out bool sign, ExecutionContext context) { sign = (~(uint)valueBits & 0x8000u) == 0u; uint exp16 = ((uint)valueBits & 0x7C00u) >> 10; uint frac16 = (uint)valueBits & 0x03FFu; double real; if (exp16 == 0u) { if (frac16 == 0u) { type = FPType.Zero; real = 0d; } else { type = FPType.Nonzero; // Subnormal. real = Math.Pow(2d, -14) * ((double)frac16 * Math.Pow(2d, -10)); } } else if (exp16 == 0x1Fu && (context.Fpcr & FPCR.Ahp) == 0) { if (frac16 == 0u) { type = FPType.Infinity; real = Math.Pow(2d, 1000); } else { type = (~frac16 & 0x0200u) == 0u ? FPType.QNaN : FPType.SNaN; real = 0d; } } else { type = FPType.Nonzero; // Normal. real = Math.Pow(2d, (int)exp16 - 15) * (1d + (double)frac16 * Math.Pow(2d, -10)); } return sign ? -real : real; } private static float FPRoundCv(double real, ExecutionContext context) { const int minimumExp = -126; const int e = 8; const int f = 23; bool sign; double mantissa; if (real < 0d) { sign = true; mantissa = -real; } else { sign = false; mantissa = real; } int exponent = 0; while (mantissa < 1d) { mantissa *= 2d; exponent--; } while (mantissa >= 2d) { mantissa /= 2d; exponent++; } if ((context.Fpcr & FPCR.Fz) != 0 && exponent < minimumExp) { context.Fpsr |= FPSR.Ufc; return FPZero(sign); } uint biasedExp = (uint)Math.Max(exponent - minimumExp + 1, 0); if (biasedExp == 0u) { mantissa /= Math.Pow(2d, minimumExp - exponent); } uint intMant = (uint)Math.Floor(mantissa * Math.Pow(2d, f)); double error = mantissa * Math.Pow(2d, f) - (double)intMant; if (biasedExp == 0u && (error != 0d || (context.Fpcr & FPCR.Ufe) != 0)) { FPProcessException(FPException.Underflow, context); } bool overflowToInf; bool roundUp; switch (context.Fpcr.GetRoundingMode()) { default: case FPRoundingMode.ToNearest: roundUp = (error > 0.5d || (error == 0.5d && (intMant & 1u) == 1u)); overflowToInf = true; break; case FPRoundingMode.TowardsPlusInfinity: roundUp = (error != 0d && !sign); overflowToInf = !sign; break; case FPRoundingMode.TowardsMinusInfinity: roundUp = (error != 0d && sign); overflowToInf = sign; break; case FPRoundingMode.TowardsZero: roundUp = false; overflowToInf = false; break; } if (roundUp) { intMant++; if (intMant == 1u << f) { biasedExp = 1u; } if (intMant == 1u << (f + 1)) { biasedExp++; intMant >>= 1; } } float result; if (biasedExp >= (1u << e) - 1u) { result = overflowToInf ? FPInfinity(sign) : FPMaxNormal(sign); FPProcessException(FPException.Overflow, context); error = 1d; } else { result = BitConverter.Int32BitsToSingle( (int)((sign ? 1u : 0u) << 31 | (biasedExp & 0xFFu) << 23 | (intMant & 0x007FFFFFu))); } if (error != 0d) { FPProcessException(FPException.Inexact, context); } return result; } private static float FPConvertNaN(ushort valueBits) { return BitConverter.Int32BitsToSingle( (int)(((uint)valueBits & 0x8000u) << 16 | 0x7FC00000u | ((uint)valueBits & 0x01FFu) << 13)); } private static void FPProcessException(FPException exc, ExecutionContext context) { int enable = (int)exc + 8; if ((context.Fpcr & (FPCR)(1 << enable)) != 0) { throw new NotImplementedException("Floating-point trap handling."); } else { context.Fpsr |= (FPSR)(1 << (int)exc); } } } static class SoftFloat32_16 { public static ushort FPConvert(float value) { ExecutionContext context = NativeInterface.GetContext(); double real = value.FPUnpackCv(out FPType type, out bool sign, out uint valueBits, context); bool altHp = (context.Fpcr & FPCR.Ahp) != 0; ushort resultBits; if (type == FPType.SNaN || type == FPType.QNaN) { if (altHp) { resultBits = FPZero(sign); } else if ((context.Fpcr & FPCR.Dn) != 0) { resultBits = FPDefaultNaN(); } else { resultBits = FPConvertNaN(valueBits); } if (type == FPType.SNaN || altHp) { FPProcessException(FPException.InvalidOp, context); } } else if (type == FPType.Infinity) { if (altHp) { resultBits = (ushort)((sign ? 1u : 0u) << 15 | 0x7FFFu); FPProcessException(FPException.InvalidOp, context); } else { resultBits = FPInfinity(sign); } } else if (type == FPType.Zero) { resultBits = FPZero(sign); } else { resultBits = FPRoundCv(real, context); } return resultBits; } private static ushort FPDefaultNaN() { return (ushort)0x7E00u; } private static ushort FPInfinity(bool sign) { return sign ? (ushort)0xFC00u : (ushort)0x7C00u; } private static ushort FPZero(bool sign) { return sign ? (ushort)0x8000u : (ushort)0x0000u; } private static ushort FPMaxNormal(bool sign) { return sign ? (ushort)0xFBFFu : (ushort)0x7BFFu; } private static double FPUnpackCv( this float value, out FPType type, out bool sign, out uint valueBits, ExecutionContext context) { valueBits = (uint)BitConverter.SingleToInt32Bits(value); sign = (~valueBits & 0x80000000u) == 0u; uint exp32 = (valueBits & 0x7F800000u) >> 23; uint frac32 = valueBits & 0x007FFFFFu; double real; if (exp32 == 0u) { if (frac32 == 0u || (context.Fpcr & FPCR.Fz) != 0) { type = FPType.Zero; real = 0d; if (frac32 != 0u) { FPProcessException(FPException.InputDenorm, context); } } else { type = FPType.Nonzero; // Subnormal. real = Math.Pow(2d, -126) * ((double)frac32 * Math.Pow(2d, -23)); } } else if (exp32 == 0xFFu) { if (frac32 == 0u) { type = FPType.Infinity; real = Math.Pow(2d, 1000); } else { type = (~frac32 & 0x00400000u) == 0u ? FPType.QNaN : FPType.SNaN; real = 0d; } } else { type = FPType.Nonzero; // Normal. real = Math.Pow(2d, (int)exp32 - 127) * (1d + (double)frac32 * Math.Pow(2d, -23)); } return sign ? -real : real; } private static ushort FPRoundCv(double real, ExecutionContext context) { const int minimumExp = -14; const int e = 5; const int f = 10; bool sign; double mantissa; if (real < 0d) { sign = true; mantissa = -real; } else { sign = false; mantissa = real; } int exponent = 0; while (mantissa < 1d) { mantissa *= 2d; exponent--; } while (mantissa >= 2d) { mantissa /= 2d; exponent++; } uint biasedExp = (uint)Math.Max(exponent - minimumExp + 1, 0); if (biasedExp == 0u) { mantissa /= Math.Pow(2d, minimumExp - exponent); } uint intMant = (uint)Math.Floor(mantissa * Math.Pow(2d, f)); double error = mantissa * Math.Pow(2d, f) - (double)intMant; if (biasedExp == 0u && (error != 0d || (context.Fpcr & FPCR.Ufe) != 0)) { FPProcessException(FPException.Underflow, context); } bool overflowToInf; bool roundUp; switch (context.Fpcr.GetRoundingMode()) { default: case FPRoundingMode.ToNearest: roundUp = (error > 0.5d || (error == 0.5d && (intMant & 1u) == 1u)); overflowToInf = true; break; case FPRoundingMode.TowardsPlusInfinity: roundUp = (error != 0d && !sign); overflowToInf = !sign; break; case FPRoundingMode.TowardsMinusInfinity: roundUp = (error != 0d && sign); overflowToInf = sign; break; case FPRoundingMode.TowardsZero: roundUp = false; overflowToInf = false; break; } if (roundUp) { intMant++; if (intMant == 1u << f) { biasedExp = 1u; } if (intMant == 1u << (f + 1)) { biasedExp++; intMant >>= 1; } } ushort resultBits; if ((context.Fpcr & FPCR.Ahp) == 0) { if (biasedExp >= (1u << e) - 1u) { resultBits = overflowToInf ? FPInfinity(sign) : FPMaxNormal(sign); FPProcessException(FPException.Overflow, context); error = 1d; } else { resultBits = (ushort)((sign ? 1u : 0u) << 15 | (biasedExp & 0x1Fu) << 10 | (intMant & 0x03FFu)); } } else { if (biasedExp >= 1u << e) { resultBits = (ushort)((sign ? 1u : 0u) << 15 | 0x7FFFu); FPProcessException(FPException.InvalidOp, context); error = 0d; } else { resultBits = (ushort)((sign ? 1u : 0u) << 15 | (biasedExp & 0x1Fu) << 10 | (intMant & 0x03FFu)); } } if (error != 0d) { FPProcessException(FPException.Inexact, context); } return resultBits; } private static ushort FPConvertNaN(uint valueBits) { return (ushort)((valueBits & 0x80000000u) >> 16 | 0x7E00u | (valueBits & 0x003FE000u) >> 13); } private static void FPProcessException(FPException exc, ExecutionContext context) { int enable = (int)exc + 8; if ((context.Fpcr & (FPCR)(1 << enable)) != 0) { throw new NotImplementedException("Floating-point trap handling."); } else { context.Fpsr |= (FPSR)(1 << (int)exc); } } } static class SoftFloat32 { public static float FPAdd(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out uint op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out uint op2, context); float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if (inf1 && inf2 && sign1 == !sign2) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else if ((inf1 && !sign1) || (inf2 && !sign2)) { result = FPInfinity(false); } else if ((inf1 && sign1) || (inf2 && sign2)) { result = FPInfinity(true); } else if (zero1 && zero2 && sign1 == sign2) { result = FPZero(sign1); } else { result = value1 + value2; if ((context.Fpcr & FPCR.Fz) != 0 && float.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0f); } } } return result; } public static int FPCompare(float value1, float value2, bool signalNaNs) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out _, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out _, context); int result; if (type1 == FPType.SNaN || type1 == FPType.QNaN || type2 == FPType.SNaN || type2 == FPType.QNaN) { result = 0b0011; if (type1 == FPType.SNaN || type2 == FPType.SNaN || signalNaNs) { FPProcessException(FPException.InvalidOp, context); } } else { if (value1 == value2) { result = 0b0110; } else if (value1 < value2) { result = 0b1000; } else { result = 0b0010; } } return result; } public static float FPCompareEQ(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out _, out _, context); value2 = value2.FPUnpack(out FPType type2, out _, out _, context); float result; if (type1 == FPType.SNaN || type1 == FPType.QNaN || type2 == FPType.SNaN || type2 == FPType.QNaN) { result = ZerosOrOnes(false); if (type1 == FPType.SNaN || type2 == FPType.SNaN) { FPProcessException(FPException.InvalidOp, context); } } else { result = ZerosOrOnes(value1 == value2); } return result; } public static float FPCompareGE(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out _, out _, context); value2 = value2.FPUnpack(out FPType type2, out _, out _, context); float result; if (type1 == FPType.SNaN || type1 == FPType.QNaN || type2 == FPType.SNaN || type2 == FPType.QNaN) { result = ZerosOrOnes(false); FPProcessException(FPException.InvalidOp, context); } else { result = ZerosOrOnes(value1 >= value2); } return result; } public static float FPCompareGT(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out _, out _, context); value2 = value2.FPUnpack(out FPType type2, out _, out _, context); float result; if (type1 == FPType.SNaN || type1 == FPType.QNaN || type2 == FPType.SNaN || type2 == FPType.QNaN) { result = ZerosOrOnes(false); FPProcessException(FPException.InvalidOp, context); } else { result = ZerosOrOnes(value1 > value2); } return result; } public static float FPCompareLE(float value1, float value2) { return FPCompareGE(value2, value1); } public static float FPCompareLT(float value1, float value2) { return FPCompareGT(value2, value1); } public static float FPDiv(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out uint op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out uint op2, context); float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if ((inf1 && inf2) || (zero1 && zero2)) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else if (inf1 || zero2) { result = FPInfinity(sign1 ^ sign2); if (!inf1) { FPProcessException(FPException.DivideByZero, context); } } else if (zero1 || inf2) { result = FPZero(sign1 ^ sign2); } else { result = value1 / value2; if ((context.Fpcr & FPCR.Fz) != 0 && float.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0f); } } } return result; } public static float FPMax(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out uint op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out uint op2, context); float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { if (value1 > value2) { if (type1 == FPType.Infinity) { result = FPInfinity(sign1); } else if (type1 == FPType.Zero) { result = FPZero(sign1 && sign2); } else { result = value1; } } else { if (type2 == FPType.Infinity) { result = FPInfinity(sign2); } else if (type2 == FPType.Zero) { result = FPZero(sign1 && sign2); } else { result = value2; if ((context.Fpcr & FPCR.Fz) != 0 && float.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0f); } } } } return result; } public static float FPMaxNum(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1.FPUnpack(out FPType type1, out _, out _, context); value2.FPUnpack(out FPType type2, out _, out _, context); if (type1 == FPType.QNaN && type2 != FPType.QNaN) { value1 = FPInfinity(true); } else if (type1 != FPType.QNaN && type2 == FPType.QNaN) { value2 = FPInfinity(true); } return FPMax(value1, value2); } public static float FPMin(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out uint op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out uint op2, context); float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { if (value1 < value2) { if (type1 == FPType.Infinity) { result = FPInfinity(sign1); } else if (type1 == FPType.Zero) { result = FPZero(sign1 || sign2); } else { result = value1; } } else { if (type2 == FPType.Infinity) { result = FPInfinity(sign2); } else if (type2 == FPType.Zero) { result = FPZero(sign1 || sign2); } else { result = value2; if ((context.Fpcr & FPCR.Fz) != 0 && float.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0f); } } } } return result; } public static float FPMinNum(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1.FPUnpack(out FPType type1, out _, out _, context); value2.FPUnpack(out FPType type2, out _, out _, context); if (type1 == FPType.QNaN && type2 != FPType.QNaN) { value1 = FPInfinity(false); } else if (type1 != FPType.QNaN && type2 == FPType.QNaN) { value2 = FPInfinity(false); } return FPMin(value1, value2); } public static float FPMul(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out uint op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out uint op2, context); float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if ((inf1 && zero2) || (zero1 && inf2)) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else if (inf1 || inf2) { result = FPInfinity(sign1 ^ sign2); } else if (zero1 || zero2) { result = FPZero(sign1 ^ sign2); } else { result = value1 * value2; if ((context.Fpcr & FPCR.Fz) != 0 && float.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0f); } } } return result; } public static float FPMulAdd(float valueA, float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); valueA = valueA.FPUnpack(out FPType typeA, out bool signA, out uint addend, context); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out uint op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out uint op2, context); bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; float result = FPProcessNaNs3(typeA, type1, type2, addend, op1, op2, out bool done, context); if (typeA == FPType.QNaN && ((inf1 && zero2) || (zero1 && inf2))) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } if (!done) { bool infA = typeA == FPType.Infinity; bool zeroA = typeA == FPType.Zero; bool signP = sign1 ^ sign2; bool infP = inf1 || inf2; bool zeroP = zero1 || zero2; if ((inf1 && zero2) || (zero1 && inf2) || (infA && infP && signA != signP)) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else if ((infA && !signA) || (infP && !signP)) { result = FPInfinity(false); } else if ((infA && signA) || (infP && signP)) { result = FPInfinity(true); } else if (zeroA && zeroP && signA == signP) { result = FPZero(signA); } else { // TODO: When available, use: T MathF.FusedMultiplyAdd(T, T, T); // https://github.com/dotnet/corefx/issues/31903 result = valueA + (value1 * value2); if ((context.Fpcr & FPCR.Fz) != 0 && float.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0f); } } } return result; } public static float FPMulSub(float valueA, float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPNeg(); return FPMulAdd(valueA, value1, value2); } public static float FPMulX(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out uint op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out uint op2, context); float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if ((inf1 && zero2) || (zero1 && inf2)) { result = FPTwo(sign1 ^ sign2); } else if (inf1 || inf2) { result = FPInfinity(sign1 ^ sign2); } else if (zero1 || zero2) { result = FPZero(sign1 ^ sign2); } else { result = value1 * value2; if ((context.Fpcr & FPCR.Fz) != 0 && float.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0f); } } } return result; } public static float FPRecipEstimate(float value) { ExecutionContext context = NativeInterface.GetContext(); value.FPUnpack(out FPType type, out bool sign, out uint op, context); float result; if (type == FPType.SNaN || type == FPType.QNaN) { result = FPProcessNaN(type, op, context); } else if (type == FPType.Infinity) { result = FPZero(sign); } else if (type == FPType.Zero) { result = FPInfinity(sign); FPProcessException(FPException.DivideByZero, context); } else if (MathF.Abs(value) < MathF.Pow(2f, -128)) { bool overflowToInf; switch (context.Fpcr.GetRoundingMode()) { default: case FPRoundingMode.ToNearest: overflowToInf = true; break; case FPRoundingMode.TowardsPlusInfinity: overflowToInf = !sign; break; case FPRoundingMode.TowardsMinusInfinity: overflowToInf = sign; break; case FPRoundingMode.TowardsZero: overflowToInf = false; break; } result = overflowToInf ? FPInfinity(sign) : FPMaxNormal(sign); FPProcessException(FPException.Overflow, context); FPProcessException(FPException.Inexact, context); } else if ((context.Fpcr & FPCR.Fz) != 0 && (MathF.Abs(value) >= MathF.Pow(2f, 126))) { result = FPZero(sign); context.Fpsr |= FPSR.Ufc; } else { ulong fraction = (ulong)(op & 0x007FFFFFu) << 29; uint exp = (op & 0x7F800000u) >> 23; if (exp == 0u) { if ((fraction & 0x0008000000000000ul) == 0ul) { fraction = (fraction & 0x0003FFFFFFFFFFFFul) << 2; exp -= 1u; } else { fraction = (fraction & 0x0007FFFFFFFFFFFFul) << 1; } } uint scaled = (uint)(((fraction & 0x000FF00000000000ul) | 0x0010000000000000ul) >> 44); uint resultExp = 253u - exp; uint estimate = (uint)SoftFloat.RecipEstimateTable[scaled - 256u] + 256u; fraction = (ulong)(estimate & 0xFFu) << 44; if (resultExp == 0u) { fraction = ((fraction & 0x000FFFFFFFFFFFFEul) | 0x0010000000000000ul) >> 1; } else if (resultExp + 1u == 0u) { fraction = ((fraction & 0x000FFFFFFFFFFFFCul) | 0x0010000000000000ul) >> 2; resultExp = 0u; } result = BitConverter.Int32BitsToSingle( (int)((sign ? 1u : 0u) << 31 | (resultExp & 0xFFu) << 23 | (uint)(fraction >> 29) & 0x007FFFFFu)); } return result; } public static float FPRecipStepFused(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPNeg(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out uint op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out uint op2, context); float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if ((inf1 && zero2) || (zero1 && inf2)) { result = FPTwo(false); } else if (inf1 || inf2) { result = FPInfinity(sign1 ^ sign2); } else { // TODO: When available, use: T MathF.FusedMultiplyAdd(T, T, T); // https://github.com/dotnet/corefx/issues/31903 result = 2f + (value1 * value2); if ((context.Fpcr & FPCR.Fz) != 0 && float.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0f); } } } return result; } public static float FPRecpX(float value) { ExecutionContext context = NativeInterface.GetContext(); value.FPUnpack(out FPType type, out bool sign, out uint op, context); float result; if (type == FPType.SNaN || type == FPType.QNaN) { result = FPProcessNaN(type, op, context); } else { uint notExp = (~op >> 23) & 0xFFu; uint maxExp = 0xFEu; result = BitConverter.Int32BitsToSingle( (int)((sign ? 1u : 0u) << 31 | (notExp == 0xFFu ? maxExp : notExp) << 23)); } return result; } public static float FPRSqrtEstimate(float value) { ExecutionContext context = NativeInterface.GetContext(); value.FPUnpack(out FPType type, out bool sign, out uint op, context); float result; if (type == FPType.SNaN || type == FPType.QNaN) { result = FPProcessNaN(type, op, context); } else if (type == FPType.Zero) { result = FPInfinity(sign); FPProcessException(FPException.DivideByZero, context); } else if (sign) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else if (type == FPType.Infinity) { result = FPZero(false); } else { ulong fraction = (ulong)(op & 0x007FFFFFu) << 29; uint exp = (op & 0x7F800000u) >> 23; if (exp == 0u) { while ((fraction & 0x0008000000000000ul) == 0ul) { fraction = (fraction & 0x0007FFFFFFFFFFFFul) << 1; exp -= 1u; } fraction = (fraction & 0x0007FFFFFFFFFFFFul) << 1; } uint scaled; if ((exp & 1u) == 0u) { scaled = (uint)(((fraction & 0x000FF00000000000ul) | 0x0010000000000000ul) >> 44); } else { scaled = (uint)(((fraction & 0x000FE00000000000ul) | 0x0010000000000000ul) >> 45); } uint resultExp = (380u - exp) >> 1; uint estimate = (uint)SoftFloat.RecipSqrtEstimateTable[scaled - 128u] + 256u; result = BitConverter.Int32BitsToSingle((int)((resultExp & 0xFFu) << 23 | (estimate & 0xFFu) << 15)); } return result; } public static float FPRSqrtStepFused(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPNeg(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out uint op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out uint op2, context); float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if ((inf1 && zero2) || (zero1 && inf2)) { result = FPOnePointFive(false); } else if (inf1 || inf2) { result = FPInfinity(sign1 ^ sign2); } else { // TODO: When available, use: T MathF.FusedMultiplyAdd(T, T, T); // https://github.com/dotnet/corefx/issues/31903 result = (3f + (value1 * value2)) / 2f; if ((context.Fpcr & FPCR.Fz) != 0 && float.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0f); } } } return result; } public static float FPSqrt(float value) { ExecutionContext context = NativeInterface.GetContext(); value = value.FPUnpack(out FPType type, out bool sign, out uint op, context); float result; if (type == FPType.SNaN || type == FPType.QNaN) { result = FPProcessNaN(type, op, context); } else if (type == FPType.Zero) { result = FPZero(sign); } else if (type == FPType.Infinity && !sign) { result = FPInfinity(sign); } else if (sign) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else { result = MathF.Sqrt(value); if ((context.Fpcr & FPCR.Fz) != 0 && float.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0f); } } return result; } public static float FPSub(float value1, float value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out uint op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out uint op2, context); float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if (inf1 && inf2 && sign1 == sign2) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else if ((inf1 && !sign1) || (inf2 && sign2)) { result = FPInfinity(false); } else if ((inf1 && sign1) || (inf2 && !sign2)) { result = FPInfinity(true); } else if (zero1 && zero2 && sign1 == !sign2) { result = FPZero(sign1); } else { result = value1 - value2; if ((context.Fpcr & FPCR.Fz) != 0 && float.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0f); } } } return result; } private static float FPDefaultNaN() { return -float.NaN; } private static float FPInfinity(bool sign) { return sign ? float.NegativeInfinity : float.PositiveInfinity; } private static float FPZero(bool sign) { return sign ? -0f : +0f; } private static float FPMaxNormal(bool sign) { return sign ? float.MinValue : float.MaxValue; } private static float FPTwo(bool sign) { return sign ? -2f : +2f; } private static float FPOnePointFive(bool sign) { return sign ? -1.5f : +1.5f; } private static float FPNeg(this float value) { return -value; } private static float ZerosOrOnes(bool ones) { return BitConverter.Int32BitsToSingle(ones ? -1 : 0); } private static float FPUnpack( this float value, out FPType type, out bool sign, out uint valueBits, ExecutionContext context) { valueBits = (uint)BitConverter.SingleToInt32Bits(value); sign = (~valueBits & 0x80000000u) == 0u; if ((valueBits & 0x7F800000u) == 0u) { if ((valueBits & 0x007FFFFFu) == 0u || (context.Fpcr & FPCR.Fz) != 0) { type = FPType.Zero; value = FPZero(sign); if ((valueBits & 0x007FFFFFu) != 0u) { FPProcessException(FPException.InputDenorm, context); } } else { type = FPType.Nonzero; } } else if ((~valueBits & 0x7F800000u) == 0u) { if ((valueBits & 0x007FFFFFu) == 0u) { type = FPType.Infinity; } else { type = (~valueBits & 0x00400000u) == 0u ? FPType.QNaN : FPType.SNaN; value = FPZero(sign); } } else { type = FPType.Nonzero; } return value; } private static float FPProcessNaNs( FPType type1, FPType type2, uint op1, uint op2, out bool done, ExecutionContext context) { done = true; if (type1 == FPType.SNaN) { return FPProcessNaN(type1, op1, context); } else if (type2 == FPType.SNaN) { return FPProcessNaN(type2, op2, context); } else if (type1 == FPType.QNaN) { return FPProcessNaN(type1, op1, context); } else if (type2 == FPType.QNaN) { return FPProcessNaN(type2, op2, context); } done = false; return FPZero(false); } private static float FPProcessNaNs3( FPType type1, FPType type2, FPType type3, uint op1, uint op2, uint op3, out bool done, ExecutionContext context) { done = true; if (type1 == FPType.SNaN) { return FPProcessNaN(type1, op1, context); } else if (type2 == FPType.SNaN) { return FPProcessNaN(type2, op2, context); } else if (type3 == FPType.SNaN) { return FPProcessNaN(type3, op3, context); } else if (type1 == FPType.QNaN) { return FPProcessNaN(type1, op1, context); } else if (type2 == FPType.QNaN) { return FPProcessNaN(type2, op2, context); } else if (type3 == FPType.QNaN) { return FPProcessNaN(type3, op3, context); } done = false; return FPZero(false); } private static float FPProcessNaN(FPType type, uint op, ExecutionContext context) { if (type == FPType.SNaN) { op |= 1u << 22; FPProcessException(FPException.InvalidOp, context); } if ((context.Fpcr & FPCR.Dn) != 0) { return FPDefaultNaN(); } return BitConverter.Int32BitsToSingle((int)op); } private static void FPProcessException(FPException exc, ExecutionContext context) { int enable = (int)exc + 8; if ((context.Fpcr & (FPCR)(1 << enable)) != 0) { throw new NotImplementedException("Floating-point trap handling."); } else { context.Fpsr |= (FPSR)(1 << (int)exc); } } } static class SoftFloat64 { public static double FPAdd(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out ulong op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out ulong op2, context); double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if (inf1 && inf2 && sign1 == !sign2) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else if ((inf1 && !sign1) || (inf2 && !sign2)) { result = FPInfinity(false); } else if ((inf1 && sign1) || (inf2 && sign2)) { result = FPInfinity(true); } else if (zero1 && zero2 && sign1 == sign2) { result = FPZero(sign1); } else { result = value1 + value2; if ((context.Fpcr & FPCR.Fz) != 0 && double.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0d); } } } return result; } public static int FPCompare(double value1, double value2, bool signalNaNs) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out _, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out _, context); int result; if (type1 == FPType.SNaN || type1 == FPType.QNaN || type2 == FPType.SNaN || type2 == FPType.QNaN) { result = 0b0011; if (type1 == FPType.SNaN || type2 == FPType.SNaN || signalNaNs) { FPProcessException(FPException.InvalidOp, context); } } else { if (value1 == value2) { result = 0b0110; } else if (value1 < value2) { result = 0b1000; } else { result = 0b0010; } } return result; } public static double FPCompareEQ(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out _, out _, context); value2 = value2.FPUnpack(out FPType type2, out _, out _, context); double result; if (type1 == FPType.SNaN || type1 == FPType.QNaN || type2 == FPType.SNaN || type2 == FPType.QNaN) { result = ZerosOrOnes(false); if (type1 == FPType.SNaN || type2 == FPType.SNaN) { FPProcessException(FPException.InvalidOp, context); } } else { result = ZerosOrOnes(value1 == value2); } return result; } public static double FPCompareGE(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out _, out _, context); value2 = value2.FPUnpack(out FPType type2, out _, out _, context); double result; if (type1 == FPType.SNaN || type1 == FPType.QNaN || type2 == FPType.SNaN || type2 == FPType.QNaN) { result = ZerosOrOnes(false); FPProcessException(FPException.InvalidOp, context); } else { result = ZerosOrOnes(value1 >= value2); } return result; } public static double FPCompareGT(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out _, out _, context); value2 = value2.FPUnpack(out FPType type2, out _, out _, context); double result; if (type1 == FPType.SNaN || type1 == FPType.QNaN || type2 == FPType.SNaN || type2 == FPType.QNaN) { result = ZerosOrOnes(false); FPProcessException(FPException.InvalidOp, context); } else { result = ZerosOrOnes(value1 > value2); } return result; } public static double FPCompareLE(double value1, double value2) { return FPCompareGE(value2, value1); } public static double FPCompareLT(double value1, double value2) { return FPCompareGT(value2, value1); } public static double FPDiv(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out ulong op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out ulong op2, context); double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if ((inf1 && inf2) || (zero1 && zero2)) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else if (inf1 || zero2) { result = FPInfinity(sign1 ^ sign2); if (!inf1) { FPProcessException(FPException.DivideByZero, context); } } else if (zero1 || inf2) { result = FPZero(sign1 ^ sign2); } else { result = value1 / value2; if ((context.Fpcr & FPCR.Fz) != 0 && double.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0d); } } } return result; } public static double FPMax(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out ulong op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out ulong op2, context); double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { if (value1 > value2) { if (type1 == FPType.Infinity) { result = FPInfinity(sign1); } else if (type1 == FPType.Zero) { result = FPZero(sign1 && sign2); } else { result = value1; } } else { if (type2 == FPType.Infinity) { result = FPInfinity(sign2); } else if (type2 == FPType.Zero) { result = FPZero(sign1 && sign2); } else { result = value2; if ((context.Fpcr & FPCR.Fz) != 0 && double.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0d); } } } } return result; } public static double FPMaxNum(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1.FPUnpack(out FPType type1, out _, out _, context); value2.FPUnpack(out FPType type2, out _, out _, context); if (type1 == FPType.QNaN && type2 != FPType.QNaN) { value1 = FPInfinity(true); } else if (type1 != FPType.QNaN && type2 == FPType.QNaN) { value2 = FPInfinity(true); } return FPMax(value1, value2); } public static double FPMin(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out ulong op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out ulong op2, context); double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { if (value1 < value2) { if (type1 == FPType.Infinity) { result = FPInfinity(sign1); } else if (type1 == FPType.Zero) { result = FPZero(sign1 || sign2); } else { result = value1; } } else { if (type2 == FPType.Infinity) { result = FPInfinity(sign2); } else if (type2 == FPType.Zero) { result = FPZero(sign1 || sign2); } else { result = value2; if ((context.Fpcr & FPCR.Fz) != 0 && double.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0d); } } } } return result; } public static double FPMinNum(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1.FPUnpack(out FPType type1, out _, out _, context); value2.FPUnpack(out FPType type2, out _, out _, context); if (type1 == FPType.QNaN && type2 != FPType.QNaN) { value1 = FPInfinity(false); } else if (type1 != FPType.QNaN && type2 == FPType.QNaN) { value2 = FPInfinity(false); } return FPMin(value1, value2); } public static double FPMul(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out ulong op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out ulong op2, context); double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if ((inf1 && zero2) || (zero1 && inf2)) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else if (inf1 || inf2) { result = FPInfinity(sign1 ^ sign2); } else if (zero1 || zero2) { result = FPZero(sign1 ^ sign2); } else { result = value1 * value2; if ((context.Fpcr & FPCR.Fz) != 0 && double.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0d); } } } return result; } public static double FPMulAdd(double valueA, double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); valueA = valueA.FPUnpack(out FPType typeA, out bool signA, out ulong addend, context); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out ulong op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out ulong op2, context); bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; double result = FPProcessNaNs3(typeA, type1, type2, addend, op1, op2, out bool done, context); if (typeA == FPType.QNaN && ((inf1 && zero2) || (zero1 && inf2))) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } if (!done) { bool infA = typeA == FPType.Infinity; bool zeroA = typeA == FPType.Zero; bool signP = sign1 ^ sign2; bool infP = inf1 || inf2; bool zeroP = zero1 || zero2; if ((inf1 && zero2) || (zero1 && inf2) || (infA && infP && signA != signP)) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else if ((infA && !signA) || (infP && !signP)) { result = FPInfinity(false); } else if ((infA && signA) || (infP && signP)) { result = FPInfinity(true); } else if (zeroA && zeroP && signA == signP) { result = FPZero(signA); } else { // TODO: When available, use: T Math.FusedMultiplyAdd(T, T, T); // https://github.com/dotnet/corefx/issues/31903 result = valueA + (value1 * value2); if ((context.Fpcr & FPCR.Fz) != 0 && double.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0d); } } } return result; } public static double FPMulSub(double valueA, double value1, double value2) { value1 = value1.FPNeg(); return FPMulAdd(valueA, value1, value2); } public static double FPMulX(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out ulong op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out ulong op2, context); double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if ((inf1 && zero2) || (zero1 && inf2)) { result = FPTwo(sign1 ^ sign2); } else if (inf1 || inf2) { result = FPInfinity(sign1 ^ sign2); } else if (zero1 || zero2) { result = FPZero(sign1 ^ sign2); } else { result = value1 * value2; if ((context.Fpcr & FPCR.Fz) != 0 && double.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0d); } } } return result; } public static double FPRecipEstimate(double value) { ExecutionContext context = NativeInterface.GetContext(); value.FPUnpack(out FPType type, out bool sign, out ulong op, context); double result; if (type == FPType.SNaN || type == FPType.QNaN) { result = FPProcessNaN(type, op, context); } else if (type == FPType.Infinity) { result = FPZero(sign); } else if (type == FPType.Zero) { result = FPInfinity(sign); FPProcessException(FPException.DivideByZero, context); } else if (Math.Abs(value) < Math.Pow(2d, -1024)) { bool overflowToInf; switch (context.Fpcr.GetRoundingMode()) { default: case FPRoundingMode.ToNearest: overflowToInf = true; break; case FPRoundingMode.TowardsPlusInfinity: overflowToInf = !sign; break; case FPRoundingMode.TowardsMinusInfinity: overflowToInf = sign; break; case FPRoundingMode.TowardsZero: overflowToInf = false; break; } result = overflowToInf ? FPInfinity(sign) : FPMaxNormal(sign); FPProcessException(FPException.Overflow, context); FPProcessException(FPException.Inexact, context); } else if ((context.Fpcr & FPCR.Fz) != 0 && (Math.Abs(value) >= Math.Pow(2d, 1022))) { result = FPZero(sign); context.Fpsr |= FPSR.Ufc; } else { ulong fraction = op & 0x000FFFFFFFFFFFFFul; uint exp = (uint)((op & 0x7FF0000000000000ul) >> 52); if (exp == 0u) { if ((fraction & 0x0008000000000000ul) == 0ul) { fraction = (fraction & 0x0003FFFFFFFFFFFFul) << 2; exp -= 1u; } else { fraction = (fraction & 0x0007FFFFFFFFFFFFul) << 1; } } uint scaled = (uint)(((fraction & 0x000FF00000000000ul) | 0x0010000000000000ul) >> 44); uint resultExp = 2045u - exp; uint estimate = (uint)SoftFloat.RecipEstimateTable[scaled - 256u] + 256u; fraction = (ulong)(estimate & 0xFFu) << 44; if (resultExp == 0u) { fraction = ((fraction & 0x000FFFFFFFFFFFFEul) | 0x0010000000000000ul) >> 1; } else if (resultExp + 1u == 0u) { fraction = ((fraction & 0x000FFFFFFFFFFFFCul) | 0x0010000000000000ul) >> 2; resultExp = 0u; } result = BitConverter.Int64BitsToDouble( (long)((sign ? 1ul : 0ul) << 63 | (resultExp & 0x7FFul) << 52 | (fraction & 0x000FFFFFFFFFFFFFul))); } return result; } public static double FPRecipStepFused(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPNeg(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out ulong op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out ulong op2, context); double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if ((inf1 && zero2) || (zero1 && inf2)) { result = FPTwo(false); } else if (inf1 || inf2) { result = FPInfinity(sign1 ^ sign2); } else { // TODO: When available, use: T Math.FusedMultiplyAdd(T, T, T); // https://github.com/dotnet/corefx/issues/31903 result = 2d + (value1 * value2); if ((context.Fpcr & FPCR.Fz) != 0 && double.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0d); } } } return result; } public static double FPRecpX(double value) { ExecutionContext context = NativeInterface.GetContext(); value.FPUnpack(out FPType type, out bool sign, out ulong op, context); double result; if (type == FPType.SNaN || type == FPType.QNaN) { result = FPProcessNaN(type, op, context); } else { ulong notExp = (~op >> 52) & 0x7FFul; ulong maxExp = 0x7FEul; result = BitConverter.Int64BitsToDouble( (long)((sign ? 1ul : 0ul) << 63 | (notExp == 0x7FFul ? maxExp : notExp) << 52)); } return result; } public static double FPRSqrtEstimate(double value) { ExecutionContext context = NativeInterface.GetContext(); value.FPUnpack(out FPType type, out bool sign, out ulong op, context); double result; if (type == FPType.SNaN || type == FPType.QNaN) { result = FPProcessNaN(type, op, context); } else if (type == FPType.Zero) { result = FPInfinity(sign); FPProcessException(FPException.DivideByZero, context); } else if (sign) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else if (type == FPType.Infinity) { result = FPZero(false); } else { ulong fraction = op & 0x000FFFFFFFFFFFFFul; uint exp = (uint)((op & 0x7FF0000000000000ul) >> 52); if (exp == 0u) { while ((fraction & 0x0008000000000000ul) == 0ul) { fraction = (fraction & 0x0007FFFFFFFFFFFFul) << 1; exp -= 1u; } fraction = (fraction & 0x0007FFFFFFFFFFFFul) << 1; } uint scaled; if ((exp & 1u) == 0u) { scaled = (uint)(((fraction & 0x000FF00000000000ul) | 0x0010000000000000ul) >> 44); } else { scaled = (uint)(((fraction & 0x000FE00000000000ul) | 0x0010000000000000ul) >> 45); } uint resultExp = (3068u - exp) >> 1; uint estimate = (uint)SoftFloat.RecipSqrtEstimateTable[scaled - 128u] + 256u; result = BitConverter.Int64BitsToDouble((long)((resultExp & 0x7FFul) << 52 | (estimate & 0xFFul) << 44)); } return result; } public static double FPRSqrtStepFused(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPNeg(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out ulong op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out ulong op2, context); double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if ((inf1 && zero2) || (zero1 && inf2)) { result = FPOnePointFive(false); } else if (inf1 || inf2) { result = FPInfinity(sign1 ^ sign2); } else { // TODO: When available, use: T Math.FusedMultiplyAdd(T, T, T); // https://github.com/dotnet/corefx/issues/31903 result = (3d + (value1 * value2)) / 2d; if ((context.Fpcr & FPCR.Fz) != 0 && double.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0d); } } } return result; } public static double FPSqrt(double value) { ExecutionContext context = NativeInterface.GetContext(); value = value.FPUnpack(out FPType type, out bool sign, out ulong op, context); double result; if (type == FPType.SNaN || type == FPType.QNaN) { result = FPProcessNaN(type, op, context); } else if (type == FPType.Zero) { result = FPZero(sign); } else if (type == FPType.Infinity && !sign) { result = FPInfinity(sign); } else if (sign) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else { result = Math.Sqrt(value); if ((context.Fpcr & FPCR.Fz) != 0 && double.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0d); } } return result; } public static double FPSub(double value1, double value2) { ExecutionContext context = NativeInterface.GetContext(); value1 = value1.FPUnpack(out FPType type1, out bool sign1, out ulong op1, context); value2 = value2.FPUnpack(out FPType type2, out bool sign2, out ulong op2, context); double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, context); if (!done) { bool inf1 = type1 == FPType.Infinity; bool zero1 = type1 == FPType.Zero; bool inf2 = type2 == FPType.Infinity; bool zero2 = type2 == FPType.Zero; if (inf1 && inf2 && sign1 == sign2) { result = FPDefaultNaN(); FPProcessException(FPException.InvalidOp, context); } else if ((inf1 && !sign1) || (inf2 && sign2)) { result = FPInfinity(false); } else if ((inf1 && sign1) || (inf2 && !sign2)) { result = FPInfinity(true); } else if (zero1 && zero2 && sign1 == !sign2) { result = FPZero(sign1); } else { result = value1 - value2; if ((context.Fpcr & FPCR.Fz) != 0 && double.IsSubnormal(result)) { context.Fpsr |= FPSR.Ufc; result = FPZero(result < 0d); } } } return result; } private static double FPDefaultNaN() { return -double.NaN; } private static double FPInfinity(bool sign) { return sign ? double.NegativeInfinity : double.PositiveInfinity; } private static double FPZero(bool sign) { return sign ? -0d : +0d; } private static double FPMaxNormal(bool sign) { return sign ? double.MinValue : double.MaxValue; } private static double FPTwo(bool sign) { return sign ? -2d : +2d; } private static double FPOnePointFive(bool sign) { return sign ? -1.5d : +1.5d; } private static double FPNeg(this double value) { return -value; } private static double ZerosOrOnes(bool ones) { return BitConverter.Int64BitsToDouble(ones ? -1L : 0L); } private static double FPUnpack( this double value, out FPType type, out bool sign, out ulong valueBits, ExecutionContext context) { valueBits = (ulong)BitConverter.DoubleToInt64Bits(value); sign = (~valueBits & 0x8000000000000000ul) == 0ul; if ((valueBits & 0x7FF0000000000000ul) == 0ul) { if ((valueBits & 0x000FFFFFFFFFFFFFul) == 0ul || (context.Fpcr & FPCR.Fz) != 0) { type = FPType.Zero; value = FPZero(sign); if ((valueBits & 0x000FFFFFFFFFFFFFul) != 0ul) { FPProcessException(FPException.InputDenorm, context); } } else { type = FPType.Nonzero; } } else if ((~valueBits & 0x7FF0000000000000ul) == 0ul) { if ((valueBits & 0x000FFFFFFFFFFFFFul) == 0ul) { type = FPType.Infinity; } else { type = (~valueBits & 0x0008000000000000ul) == 0ul ? FPType.QNaN : FPType.SNaN; value = FPZero(sign); } } else { type = FPType.Nonzero; } return value; } private static double FPProcessNaNs( FPType type1, FPType type2, ulong op1, ulong op2, out bool done, ExecutionContext context) { done = true; if (type1 == FPType.SNaN) { return FPProcessNaN(type1, op1, context); } else if (type2 == FPType.SNaN) { return FPProcessNaN(type2, op2, context); } else if (type1 == FPType.QNaN) { return FPProcessNaN(type1, op1, context); } else if (type2 == FPType.QNaN) { return FPProcessNaN(type2, op2, context); } done = false; return FPZero(false); } private static double FPProcessNaNs3( FPType type1, FPType type2, FPType type3, ulong op1, ulong op2, ulong op3, out bool done, ExecutionContext context) { done = true; if (type1 == FPType.SNaN) { return FPProcessNaN(type1, op1, context); } else if (type2 == FPType.SNaN) { return FPProcessNaN(type2, op2, context); } else if (type3 == FPType.SNaN) { return FPProcessNaN(type3, op3, context); } else if (type1 == FPType.QNaN) { return FPProcessNaN(type1, op1, context); } else if (type2 == FPType.QNaN) { return FPProcessNaN(type2, op2, context); } else if (type3 == FPType.QNaN) { return FPProcessNaN(type3, op3, context); } done = false; return FPZero(false); } private static double FPProcessNaN(FPType type, ulong op, ExecutionContext context) { if (type == FPType.SNaN) { op |= 1ul << 51; FPProcessException(FPException.InvalidOp, context); } if ((context.Fpcr & FPCR.Dn) != 0) { return FPDefaultNaN(); } return BitConverter.Int64BitsToDouble((long)op); } private static void FPProcessException(FPException exc, ExecutionContext context) { int enable = (int)exc + 8; if ((context.Fpcr & (FPCR)(1 << enable)) != 0) { throw new NotImplementedException("Floating-point trap handling."); } else { context.Fpsr |= (FPSR)(1 << (int)exc); } } } }