ryujinx/ChocolArm64/Instruction/ASoftFloat.cs

using System;

namespace ChocolArm64.Instruction
{
    static class ASoftFloat
    {
        static ASoftFloat()
        {
            InvSqrtEstimateTable = BuildInvSqrtEstimateTable();
            RecipEstimateTable = BuildRecipEstimateTable();
        }

        private static readonly byte[] RecipEstimateTable;
        private static readonly byte[] InvSqrtEstimateTable;

        private static byte[] BuildInvSqrtEstimateTable()
        {
            byte[] Table = new byte[512];
            for (ulong index = 128; index < 512; index++)
            {
                ulong a = index;
                if (a < 256)
                {
                    a = (a << 1) + 1;
                }
                else
                {
                    a = (a | 1) << 1;
                }

                ulong b = 256;
                while (a * (b + 1) * (b + 1) < (1ul << 28))
                {
                    b++;
                }
                b = (b + 1) >> 1;

                Table[index] = (byte)(b & 0xFF);
            }
            return Table;
        }

        private static byte[] BuildRecipEstimateTable()
        {
            byte[] Table = new byte[256];
            for (ulong index = 0; index < 256; index++)
            {
                ulong a = index | 0x100;

                a = (a << 1) + 1;
                ulong b = 0x80000 / a;
                b = (b + 1) >> 1;

                Table[index] = (byte)(b & 0xFF);
            }
            return Table;
        }

        public static float InvSqrtEstimate(float x)
        {
            return (float)InvSqrtEstimate((double)x);
        }

        public static double InvSqrtEstimate(double x)
        {
            ulong x_bits = (ulong)BitConverter.DoubleToInt64Bits(x);
            ulong x_sign = x_bits & 0x8000000000000000;
            long x_exp = (long)((x_bits >> 52) & 0x7FF);
            ulong scaled = x_bits & ((1ul << 52) - 1);

            if (x_exp == 0x7FF && scaled != 0)
            {
                // NaN
                return BitConverter.Int64BitsToDouble((long)(x_bits | 0x0008000000000000));
            }

            if (x_exp == 0)
            {
                if (scaled == 0)
                {
                    // Zero -> Infinity
                    return BitConverter.Int64BitsToDouble((long)(x_sign | 0x7FF0000000000000));
                }

                // Denormal
                while ((scaled & (1 << 51)) == 0)
                {
                    scaled <<= 1;
                    x_exp--;
                }
                scaled <<= 1;
            }

            if (x_sign != 0)
            {
                // Negative -> NaN
                return BitConverter.Int64BitsToDouble((long)0x7FF8000000000000);
            }

            if (x_exp == 0x7ff && scaled == 0)
            {
                // Infinity -> Zero
                return BitConverter.Int64BitsToDouble((long)x_sign);
            }

            if (((ulong)x_exp & 1) == 1)
            {
                scaled >>= 45;
                scaled &= 0xFF;
                scaled |= 0x80;
            }
            else
            {
                scaled >>= 44;
                scaled &= 0xFF;
                scaled |= 0x100;
            }

            ulong result_exp = ((ulong)(3068 - x_exp) / 2) & 0x7FF;
            ulong estimate = (ulong)InvSqrtEstimateTable[scaled];
            ulong fraction = estimate << 44;

            ulong result = x_sign | (result_exp << 52) | fraction;
            return BitConverter.Int64BitsToDouble((long)result);
        }

        public static float RecipEstimate(float x)
        {
            return (float)RecipEstimate((double)x);
        }

        public static double RecipEstimate(double x)
        {
            ulong x_bits = (ulong)BitConverter.DoubleToInt64Bits(x);
            ulong x_sign = x_bits & 0x8000000000000000;
            ulong x_exp = (x_bits >> 52) & 0x7FF;
            ulong scaled = x_bits & ((1ul << 52) - 1);

            if (x_exp >= 2045)
            {
                if (x_exp == 0x7ff && scaled != 0)
                {
                    // NaN
                    return BitConverter.Int64BitsToDouble((long)(x_bits | 0x0008000000000000));
                }

                // Infinity, or Out of range -> Zero
                return BitConverter.Int64BitsToDouble((long)x_sign);
            }

            if (x_exp == 0)
            {
                if (scaled == 0)
                {
                    // Zero -> Infinity
                    return BitConverter.Int64BitsToDouble((long)(x_sign | 0x7FF0000000000000));
                }

                // Denormal
                if ((scaled & (1ul << 51)) == 0)
                {
                    x_exp = ~0ul;
                    scaled <<= 2;
                }
                else
                {
                    scaled <<= 1;
                }
            }

            scaled >>= 44;
            scaled &= 0xFF;

            ulong result_exp = (2045 - x_exp) & 0x7FF;
            ulong estimate = (ulong)RecipEstimateTable[scaled];
            ulong fraction = estimate << 44;

            if (result_exp == 0)
            {
                fraction >>= 1;
                fraction |= 1ul << 51;
            }
            else if (result_exp == 0x7FF)
            {
                result_exp = 0;
                fraction >>= 2;
                fraction |= 1ul << 50;
            }

            ulong result = x_sign | (result_exp << 52) | fraction;
            return BitConverter.Int64BitsToDouble((long)result);
        }

        public static float RecipStep(float op1, float op2)
        {
            return (float)RecipStep((double)op1, (double)op2);
        }

        public static double RecipStep(double op1, double op2)
        {
            op1 = -op1;

            ulong op1_bits = (ulong)BitConverter.DoubleToInt64Bits(op1);
            ulong op2_bits = (ulong)BitConverter.DoubleToInt64Bits(op2);

            ulong op1_sign = op1_bits & 0x8000000000000000;
            ulong op2_sign = op2_bits & 0x8000000000000000;
            ulong op1_other = op1_bits & 0x7FFFFFFFFFFFFFFF;
            ulong op2_other = op2_bits & 0x7FFFFFFFFFFFFFFF;

            bool inf1 = op1_other == 0x7FF0000000000000;
            bool inf2 = op2_other == 0x7FF0000000000000;
            bool zero1 = op1_other == 0;
            bool zero2 = op2_other == 0;

            if ((inf1 && zero2) || (zero1 && inf2))
            {
                return 2.0;
            }
            else if (inf1 || inf2)
            {
                // Infinity
                return BitConverter.Int64BitsToDouble((long)(0x7FF0000000000000 | (op1_sign ^ op2_sign)));
            }

            return 2.0 + op1 * op2;
        }

        public static float ConvertHalfToSingle(ushort x)
        {
            uint x_sign = (uint)(x >> 15) & 0x0001;
            uint x_exp = (uint)(x >> 10) & 0x001F;
            uint x_mantissa = (uint)x & 0x03FF;

            if (x_exp == 0 && x_mantissa == 0)
            {
                // Zero
                return BitConverter.Int32BitsToSingle((int)(x_sign << 31));
            }

            if (x_exp == 0x1F)
            {
                // NaN or Infinity
                return BitConverter.Int32BitsToSingle((int)((x_sign << 31) | 0x7F800000 | (x_mantissa << 13)));
            }

            int exponent = (int)x_exp - 15;

            if (x_exp == 0)
            {
                // Denormal
                x_mantissa <<= 1;
                while ((x_mantissa & 0x0400) == 0)
                {
                    x_mantissa <<= 1;
                    exponent--;
                }
                x_mantissa &= 0x03FF;
            }

            uint new_exp = (uint)((exponent + 127) & 0xFF) << 23;
            return BitConverter.Int32BitsToSingle((int)((x_sign << 31) | new_exp | (x_mantissa << 13)));
        }

        public static float MaxNum(float op1, float op2)
        {
            uint op1_bits = (uint)BitConverter.SingleToInt32Bits(op1);
            uint op2_bits = (uint)BitConverter.SingleToInt32Bits(op2);

            if (IsQNaN(op1_bits) && !IsQNaN(op2_bits))
            {
                op1 = float.NegativeInfinity;
            }
            else if (!IsQNaN(op1_bits) && IsQNaN(op2_bits))
            {
                op2 = float.NegativeInfinity;
            }

            return Max(op1, op2);
        }

        public static double MaxNum(double op1, double op2)
        {
            ulong op1_bits = (ulong)BitConverter.DoubleToInt64Bits(op1);
            ulong op2_bits = (ulong)BitConverter.DoubleToInt64Bits(op2);

            if (IsQNaN(op1_bits) && !IsQNaN(op2_bits))
            {
                op1 = double.NegativeInfinity;
            }
            else if (!IsQNaN(op1_bits) && IsQNaN(op2_bits))
            {
                op2 = double.NegativeInfinity;
            }

            return Max(op1, op2);
        }

        public static float Max(float op1, float op2)
        {
            // Fast path
            if (op1 > op2)
            {
                return op1;
            }

            if (op1 < op2 || (op1 == op2 && op2 != 0))
            {
                return op2;
            }

            uint op1_bits = (uint)BitConverter.SingleToInt32Bits(op1);
            uint op2_bits = (uint)BitConverter.SingleToInt32Bits(op2);

            // Handle NaN cases
            if (ProcessNaNs(op1_bits, op2_bits, out uint op_bits))
            {
                return BitConverter.Int32BitsToSingle((int)op_bits);
            }

            // Return the most positive zero
            if ((op1_bits & op2_bits) == 0x80000000u)
            {
                return BitConverter.Int32BitsToSingle(int.MinValue);
            }

            return 0;
        }

        public static double Max(double op1, double op2)
        {
            // Fast path
            if (op1 > op2)
            {
                return op1;
            }

            if (op1 < op2 || (op1 == op2 && op2 != 0))
            {
                return op2;
            }

            ulong op1_bits = (ulong)BitConverter.DoubleToInt64Bits(op1);
            ulong op2_bits = (ulong)BitConverter.DoubleToInt64Bits(op2);

            // Handle NaN cases
            if (ProcessNaNs(op1_bits, op2_bits, out ulong op_bits))
            {
                return BitConverter.Int64BitsToDouble((long)op_bits);
            }

            // Return the most positive zero
            if ((op1_bits & op2_bits) == 0x8000000000000000ul)
            {
                return BitConverter.Int64BitsToDouble(long.MinValue);
            }

            return 0;
        }

        public static float MinNum(float op1, float op2)
        {
            uint op1_bits = (uint)BitConverter.SingleToInt32Bits(op1);
            uint op2_bits = (uint)BitConverter.SingleToInt32Bits(op2);

            if (IsQNaN(op1_bits) && !IsQNaN(op2_bits))
            {
                op1 = float.PositiveInfinity;
            }
            else if (!IsQNaN(op1_bits) && IsQNaN(op2_bits))
            {
                op2 = float.PositiveInfinity;
            }

            return Min(op1, op2);
        }

        public static double MinNum(double op1, double op2)
        {
            ulong op1_bits = (ulong)BitConverter.DoubleToInt64Bits(op1);
            ulong op2_bits = (ulong)BitConverter.DoubleToInt64Bits(op2);

            if (IsQNaN(op1_bits) && !IsQNaN(op2_bits))
            {
                op1 = double.PositiveInfinity;
            }
            else if (!IsQNaN(op1_bits) && IsQNaN(op2_bits))
            {
                op2 = double.PositiveInfinity;
            }

            return Min(op1, op2);
        }

        public static float Min(float op1, float op2)
        {
            // Fast path
            if (op1 < op2)
            {
                return op1;
            }

            if (op1 > op2 || (op1 == op2 && op2 != 0))
            {
                return op2;
            }

            uint op1_bits = (uint)BitConverter.SingleToInt32Bits(op1);
            uint op2_bits = (uint)BitConverter.SingleToInt32Bits(op2);

            // Handle NaN cases
            if (ProcessNaNs(op1_bits, op2_bits, out uint op_bits))
            {
                return BitConverter.Int32BitsToSingle((int)op_bits);
            }

            // Return the most negative zero
            if ((op1_bits | op2_bits) == 0x80000000u)
            {
                return BitConverter.Int32BitsToSingle(int.MinValue);
            }

            return 0;
        }

        public static double Min(double op1, double op2)
        {
            // Fast path
            if (op1 < op2)
            {
                return op1;
            }

            if (op1 > op2 || (op1 == op2 && op2 != 0))
            {
                return op2;
            }

            ulong op1_bits = (ulong)BitConverter.DoubleToInt64Bits(op1);
            ulong op2_bits = (ulong)BitConverter.DoubleToInt64Bits(op2);

            // Handle NaN cases
            if (ProcessNaNs(op1_bits, op2_bits, out ulong op_bits))
            {
                return BitConverter.Int64BitsToDouble((long)op_bits);
            }

            // Return the most negative zero
            if ((op1_bits | op2_bits) == 0x8000000000000000ul)
            {
                return BitConverter.Int64BitsToDouble(long.MinValue);
            }

            return 0;
        }

        private static bool ProcessNaNs(uint op1_bits, uint op2_bits, out uint op_bits)
        {
            if (IsSNaN(op1_bits))
            {
                op_bits = op1_bits | (1u << 22); // op1 is SNaN, return QNaN op1
            }
            else if (IsSNaN(op2_bits))
            {
                op_bits = op2_bits | (1u << 22); // op2 is SNaN, return QNaN op2
            }
            else if (IsQNaN(op1_bits))
            {
                op_bits = op1_bits; // op1 is QNaN, return QNaN op1
            }
            else if (IsQNaN(op2_bits))
            {
                op_bits = op2_bits; // op2 is QNaN, return QNaN op2
            }
            else
            {
                op_bits = 0;

                return false;
            }

            return true;
        }

        private static bool ProcessNaNs(ulong op1_bits, ulong op2_bits, out ulong op_bits)
        {
            if (IsSNaN(op1_bits))
            {
                op_bits = op1_bits | (1ul << 51); // op1 is SNaN, return QNaN op1
            }
            else if (IsSNaN(op2_bits))
            {
                op_bits = op2_bits | (1ul << 51); // op2 is SNaN, return QNaN op2
            }
            else if (IsQNaN(op1_bits))
            {
                op_bits = op1_bits; // op1 is QNaN, return QNaN op1
            }
            else if (IsQNaN(op2_bits))
            {
                op_bits = op2_bits; // op2 is QNaN, return QNaN op2
            }
            else
            {
                op_bits = 0;

                return false;
            }

            return true;
        }

        private static bool IsQNaN(uint op_bits)
        {
            return (op_bits & 0x007FFFFF) != 0 &&
                   (op_bits & 0x7FC00000) == 0x7FC00000;
        }

        private static bool IsQNaN(ulong op_bits)
        {
            return (op_bits & 0x000FFFFFFFFFFFFF) != 0 &&
                   (op_bits & 0x7FF8000000000000) == 0x7FF8000000000000;
        }

        private static bool IsSNaN(uint op_bits)
        {
            return (op_bits & 0x007FFFFF) != 0 &&
                   (op_bits & 0x7FC00000) == 0x7F800000;
        }

        private static bool IsSNaN(ulong op_bits)
        {
            return (op_bits & 0x000FFFFFFFFFFFFF) != 0 &&
                   (op_bits & 0x7FF8000000000000) == 0x7FF0000000000000;
        }
    }
}