FlaxEngine/Source/Engine/Core/Math/HalfUtils.cs

// Copyright (c) 2012-2023 Wojciech Figat. All rights reserved.

// -----------------------------------------------------------------------------
// Original code from SharpDX project. https://github.com/sharpdx/SharpDX/
// Greetings to Alexandre Mutel. Original code published with the following license:
// -----------------------------------------------------------------------------
// 
// Copyright (c) 2010-2011 SharpDX - Alexandre Mutel
// 
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
// 
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
// 
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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using System.Runtime.InteropServices;

namespace FlaxEngine
{
    /// <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 half value.
        /// </summary>
        /// <param name="h">The half value.</param>
        /// <returns>The float value</returns>
        public static float Unpack(ushort h)
        {
            var conv = new FloatToUint
            {
                uintValue = HalfToFloatMantissaTable[HalfToFloatOffsetTable[h >> 10] + (((uint)h) & 0x3ff)] + HalfToFloatExponentTable[h >> 10]
            };
            return conv.floatValue;
        }

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

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