HalfHelper.cs

using System.Runtime.InteropServices;

namespace System
{
    /// <summary>
    /// Helper class for Half conversions and some low level operations.
    /// This class is internally used in the Half class.
    /// </summary>
    /// <remarks>
    /// References:
    ///     - Fast Half Float Conversions, Jeroen van der Zijp, link: http://www.fox-toolkit.org/ftp/fasthalffloatconversion.pdf
    /// </remarks>
    [ComVisible(false)]
    internal static class HalfHelper
    {
        private static uint[] mantissaTable = GenerateMantissaTable();
        private static uint[] exponentTable = GenerateExponentTable();
        private static ushort[] offsetTable = GenerateOffsetTable();
        private static ushort[] baseTable = GenerateBaseTable();
        private static sbyte[] shiftTable = GenerateShiftTable();

        // Transforms the subnormal representation to a normalized one. 
        private static uint ConvertMantissa(int i)
        {
            uint m = (uint)(i << 13); // Zero pad mantissa bits
            uint e = 0; // Zero exponent

            // While not normalized
            while ((m & 0x00800000) == 0)
            {
                e -= 0x00800000; // Decrement exponent (1<<23)
                m <<= 1; // Shift mantissa                
            }
            m &= unchecked((uint)~0x00800000); // Clear leading 1 bit
            e += 0x38800000; // Adjust bias ((127-14)<<23)
            return m | e; // Return combined number
        }

        private static uint[] GenerateMantissaTable()
        {
            uint[] mantissaTable = new uint[2048];
            mantissaTable[0] = 0;
            for (int i = 1; i < 1024; i++)
            {
                mantissaTable[i] = ConvertMantissa(i);
            }
            for (int i = 1024; i < 2048; i++)
            {
                mantissaTable[i] = (uint)(0x38000000 + ((i - 1024) << 13));
            }

            return mantissaTable;
        }
        private static uint[] GenerateExponentTable()
        {
            uint[] exponentTable = new uint[64];
            exponentTable[0] = 0;
            for (int i = 1; i < 31; i++)
            {
                exponentTable[i] = (uint)(i << 23);
            }
            exponentTable[31] = 0x47800000;
            exponentTable[32] = 0x80000000;
            for (int i = 33; i < 63; i++)
            {
                exponentTable[i] = (uint)(0x80000000 + ((i - 32) << 23));
            }
            exponentTable[63] = 0xc7800000;

            return exponentTable;
        }
        private static ushort[] GenerateOffsetTable()
        {
            ushort[] offsetTable = new ushort[64];
            offsetTable[0] = 0;
            for (int i = 1; i < 32; i++)
            {
                offsetTable[i] = 1024;
            }
            offsetTable[32] = 0;
            for (int i = 33; i < 64; i++)
            {
                offsetTable[i] = 1024;
            }

            return offsetTable;
        }
        private static ushort[] GenerateBaseTable()
        {
            ushort[] baseTable = new ushort[512];
            for (int i = 0; i < 256; ++i)
            {
                sbyte e = (sbyte)(127 - i);
                if (e > 24)
                { // Very small numbers map to zero
                    baseTable[i | 0x000] = 0x0000;
                    baseTable[i | 0x100] = 0x8000;
                }
                else if (e > 14)
                { // Small numbers map to denorms
                    baseTable[i | 0x000] = (ushort)(0x0400 >> (18 + e));
                    baseTable[i | 0x100] = (ushort)((0x0400 >> (18 + e)) | 0x8000);
                }
                else if (e >= -15)
                { // Normal numbers just lose precision
                    baseTable[i | 0x000] = (ushort)((15 - e) << 10);
                    baseTable[i | 0x100] = (ushort)(((15 - e) << 10) | 0x8000);
                }
                else if (e > -128)
                { // Large numbers map to Infinity
                    baseTable[i | 0x000] = 0x7c00;
                    baseTable[i | 0x100] = 0xfc00;
                }
                else
                { // Infinity and NaN's stay Infinity and NaN's
                    baseTable[i | 0x000] = 0x7c00;
                    baseTable[i | 0x100] = 0xfc00;
                }
            }

            return baseTable;
        }
        private static sbyte[] GenerateShiftTable()
        {
            sbyte[] shiftTable = new sbyte[512];
            for (int i = 0; i < 256; ++i)
            {
                sbyte e = (sbyte)(127 - i);
                if (e > 24)
                { // Very small numbers map to zero
                    shiftTable[i | 0x000] = 24;
                    shiftTable[i | 0x100] = 24;
                }
                else if (e > 14)
                { // Small numbers map to denorms
                    shiftTable[i | 0x000] = (sbyte)(e - 1);
                    shiftTable[i | 0x100] = (sbyte)(e - 1);
                }
                else if (e >= -15)
                { // Normal numbers just lose precision
                    shiftTable[i | 0x000] = 13;
                    shiftTable[i | 0x100] = 13;
                }
                else if (e > -128)
                { // Large numbers map to Infinity
                    shiftTable[i | 0x000] = 24;
                    shiftTable[i | 0x100] = 24;
                }
                else
                { // Infinity and NaN's stay Infinity and NaN's
                    shiftTable[i | 0x000] = 13;
                    shiftTable[i | 0x100] = 13;
                }
            }

            return shiftTable;
        }

        public static unsafe float HalfToSingle(Half half)
        {
            uint result = mantissaTable[offsetTable[half.value >> 10] + (half.value & 0x3ff)] + exponentTable[half.value >> 10];
            return *((float*)&result);
        }
        public static unsafe Half SingleToHalf(float single)
        {
            uint value = *((uint*)&single);

            ushort result = (ushort)(baseTable[(value >> 23) & 0x1ff] + ((value & 0x007fffff) >> shiftTable[value >> 23]));
            return Half.ToHalf(result);
        }
        
        public static Half Negate(Half half)
        {
            return Half.ToHalf((ushort)(half.value ^ 0x8000));
        }
        public static Half Abs(Half half)
        {
            return Half.ToHalf((ushort)(half.value & 0x7fff));
        }

        public static bool IsNaN(Half half)
        {
            return ((half.value & 0x7fff) > 0x7c00);
        }
        public static bool IsInfinity(Half half)
        {
            return ((half.value & 0x7fff) == 0x7c00);
        }        
        public static bool IsPositiveInfinity(Half half)
        {
            return (half.value == 0x7c00);
        }
        public static bool IsNegativeInfinity(Half half)
        {
            return (half.value == 0xfc00);
        }
    }
}