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Diffstat (limited to 'ARMeilleure/Instructions/SoftFloat.cs')
| -rw-r--r-- | ARMeilleure/Instructions/SoftFloat.cs | 2757 |
1 files changed, 2757 insertions, 0 deletions
diff --git a/ARMeilleure/Instructions/SoftFloat.cs b/ARMeilleure/Instructions/SoftFloat.cs new file mode 100644 index 00000000..7358e6b2 --- /dev/null +++ b/ARMeilleure/Instructions/SoftFloat.cs @@ -0,0 +1,2757 @@ +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); + } + } + } +} |