sharplib/math/HalfUtils.cs

// Copyright (c) Xenko contributors (https://xenko.com) and Silicon Studio Corp. (https://www.siliconstudio.co.jp)
// Distributed under the MIT license. See the LICENSE.md file in the project root for more information.
//
// Copyright (c) 2010-2011 SharpDX - Alexandre Mutel
//
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using System.Runtime.InteropServices;
using System.Runtime.Serialization;

namespace math
{
    /// <summary>
    /// Helper class to perform Half/Float conversion.
    /// Code extract from paper : www.fox-toolkit.org/ftp/fasthalffloatconversion.pdf by Jeroen van der Zijp
    /// </summary>
    internal class HalfUtils
    {
        [StructLayout( LayoutKind.Explicit, Pack = 4 )]
        private struct FloatToUint
        {
            [FieldOffset( 0 )]
            public uint UIntValue;
            [FieldOffset( 0 )]
            public float FloatValue;
        }

        /// <summary>
        /// Unpacks the specified h.
        /// </summary>
        /// <param name="h">The packed value.</param>
        /// <returns>The float representation of the packed value.</returns>
        public static float Unpack( ushort h )
        {
            var conv = new FloatToUint();
            conv.UIntValue = HalfToFloatMantissaTable[HalfToFloatOffsetTable[h >> 10] + ( ( (uint)h ) & 0x3ff )] + HalfToFloatExponentTable[h >> 10];
            return conv.FloatValue;
        }

        /// <summary>
        /// Packs the specified f.
        /// </summary>
        /// <param name="f">The float value.</param>
        /// <returns>The packed representation of the float value.</returns>
        public static ushort Pack( float f )
        {
            FloatToUint conv = new FloatToUint();
            conv.FloatValue = f;
            return (ushort)( FloatToHalfBaseTable[( conv.UIntValue >> 23 ) & 0x1ff] + ( ( conv.UIntValue & 0x007fffff ) >> FloatToHalfShiftTable[( conv.UIntValue >> 23 ) & 0x1ff] ) );
        }

        private static readonly uint[] HalfToFloatMantissaTable = new uint[2048];
        private static readonly uint[] HalfToFloatExponentTable = new uint[64];
        private static readonly uint[] HalfToFloatOffsetTable = new uint[64];
        private static readonly ushort[] FloatToHalfBaseTable = new ushort[512];
        private static readonly byte[] FloatToHalfShiftTable = new byte[512];

        static HalfUtils()
        {
            int i;

            // -------------------------------------------------------------------
            // Half to Float tables
            // -------------------------------------------------------------------

            // Mantissa table

            // 0 => 0
            HalfToFloatMantissaTable[0] = 0;

            // Transform subnormal to normalized
            for( i = 1; i < 1024; i++ )
            {
                uint m = ( (uint)i ) << 13;
                uint e = 0;

                while( ( m & 0x00800000 ) == 0 )
                {
                    e -= 0x00800000;
                    m <<= 1;
                }
                m &= ~0x00800000U;
                e += 0x38800000;
                HalfToFloatMantissaTable[i] = m | e;
            }

            // Normal case
            for( i = 1024; i < 2048; i++ )
                HalfToFloatMantissaTable[i] = 0x38000000 + ( ( (uint)( i - 1024 ) ) << 13 );

            // Exponent table

            // 0 => 0
            HalfToFloatExponentTable[0] = 0;

            for( i = 1; i < 63; i++ )
            {
                if( i < 31 ) // Positive Numbers
                    HalfToFloatExponentTable[i] = ( (uint)i ) << 23;
                else // Negative Numbers
                    HalfToFloatExponentTable[i] = 0x80000000 + ( ( (uint)( i - 32 ) ) << 23 );
            }
            HalfToFloatExponentTable[31] = 0x47800000;
            HalfToFloatExponentTable[32] = 0x80000000;
            HalfToFloatExponentTable[63] = 0xC7800000;

            // Offset table
            HalfToFloatOffsetTable[0] = 0;
            for( i = 1; i < 64; i++ )
                HalfToFloatOffsetTable[i] = 1024;
            HalfToFloatOffsetTable[32] = 0;

            // -------------------------------------------------------------------
            // Float to Half tables
            // -------------------------------------------------------------------

            for( i = 0; i < 256; i++ )
            {
                int e = i - 127;
                if( e < -24 )
                { // Very small numbers map to zero
                    FloatToHalfBaseTable[i | 0x000] = 0x0000;
                    FloatToHalfBaseTable[i | 0x100] = 0x8000;
                    FloatToHalfShiftTable[i | 0x000] = 24;
                    FloatToHalfShiftTable[i | 0x100] = 24;
                }
                else if( e < -14 )
                { // Small numbers map to denorms
                    FloatToHalfBaseTable[i | 0x000] = (ushort)( ( 0x0400 >> ( -e - 14 ) ) );
                    FloatToHalfBaseTable[i | 0x100] = (ushort)( ( 0x0400 >> ( -e - 14 ) ) | 0x8000 );
                    FloatToHalfShiftTable[i | 0x000] = (byte)( -e - 1 );
                    FloatToHalfShiftTable[i | 0x100] = (byte)( -e - 1 );
                }
                else if( e <= 15 )
                { // Normal numbers just lose precision
                    FloatToHalfBaseTable[i | 0x000] = (ushort)( ( ( e + 15 ) << 10 ) );
                    FloatToHalfBaseTable[i | 0x100] = (ushort)( ( ( e + 15 ) << 10 ) | 0x8000 );
                    FloatToHalfShiftTable[i | 0x000] = 13;
                    FloatToHalfShiftTable[i | 0x100] = 13;
                }
                else if( e < 128 )
                { // Large numbers map to Infinity
                    FloatToHalfBaseTable[i | 0x000] = 0x7C00;
                    FloatToHalfBaseTable[i | 0x100] = 0xFC00;
                    FloatToHalfShiftTable[i | 0x000] = 24;
                    FloatToHalfShiftTable[i | 0x100] = 24;
                }
                else
                { // Infinity and NaN's stay Infinity and NaN's
                    FloatToHalfBaseTable[i | 0x000] = 0x7C00;
                    FloatToHalfBaseTable[i | 0x100] = 0xFC00;
                    FloatToHalfShiftTable[i | 0x000] = 13;
                    FloatToHalfShiftTable[i | 0x100] = 13;
                }
            }
        }
    }
}