Source/OpenTK/Math/Half.cs

#region --- License ---
/*
Copyright (c) 2006 - 2008 The Open Toolkit library.

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,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
 */
/*
The conversion functions are derived from OpenEXR's implementation and are
governed by the following license:

Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
Digital Ltd. LLC

All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
*       Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
*       Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following disclaimer
in the documentation and/or other materials provided with the
distribution.
*       Neither the name of Industrial Light & Magic nor the names of
its contributors may be used to endorse or promote products derived
from this software without specific prior written permission. 

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
#endregion --- License ---

using System;
using System.IO;
using System.Runtime.InteropServices;
using System.Runtime.Serialization;

namespace OpenTK
{

    [Serializable, StructLayout(LayoutKind.Sequential)]
    public struct Half : ISerializable, IComparable<Half>, IFormattable, IEquatable<Half>
    {
        #region Internal Field

        UInt16 bits;

        #endregion Internal Field

        #region Properties

        public bool IsZero { get { return (bits == 0) || (bits == 0x8000); } }

        public bool IsNaN { get { return (((bits & 0x7C00) == 0x7C00) && (bits & 0x03FF) != 0x0000); } }

        public bool IsPositiveInfinity { get { return (bits == 31744); } }

        public bool IsNegativeInfinity { get { return (bits == 64512); } }

        #endregion Properties

        #region Constructors

        public Half(Single f)
            : this()
        {
            unsafe
            {
                bits = SingleToHalf(*(int*)&f);
            }
        }

        public Half(Single f, bool throwOnError)
            : this(f)
        {
            if (throwOnError)
            {
                // handle cases that cause overflow rather than silently ignoring it
                if (f > Half.MaxValue) throw new ArithmeticException("Half: Positive maximum value exceeded.");
                if (f < -Half.MaxValue) throw new ArithmeticException("Half: Negative minimum value exceeded.");

                // handle cases that make no sense
                if (Single.IsNaN(f)) throw new ArithmeticException("Half: Input is not a number (NaN).");
                if (Single.IsPositiveInfinity(f)) throw new ArithmeticException("Half: Input is positive infinity.");
                if (Single.IsNegativeInfinity(f)) throw new ArithmeticException("Half: Input is negative infinity.");
            }
        }

        public Half(Double d) : this((Single)d) { }

        public Half(Double d, bool throwOnError) : this((Single)d, throwOnError) { }

        #endregion Constructors

        #region Single -> Half

        private UInt16 SingleToHalf(Int32 si32)
        {
            // Our floating point number, F, is represented by the bit pattern in integer i.
            // Disassemble that bit pattern into the sign, S, the exponent, E, and the significand, M.
            // Shift S into the position where it will go in in the resulting half number.
            // Adjust E, accounting for the different exponent bias of float and half (127 versus 15).

            Int32 sign = (si32 >> 16) & 0x00008000;
            Int32 exponent = ((si32 >> 23) & 0x000000ff) - (127 - 15);
            Int32 mantissa = si32 & 0x007fffff;

            // Now reassemble S, E and M into a half:

            if (exponent <= 0)
            {
                if (exponent < -10)
                {
                    // E is less than -10. The absolute value of F is less than Half.MinValue
                    // (F may be a small normalized float, a denormalized float or a zero).
                    //
                    // We convert F to a half zero with the same sign as F.

                    return (UInt16)sign;
                }

                // E is between -10 and 0. F is a normalized float whose magnitude is less than Half.MinNormalizedValue.
                //
                // We convert F to a denormalized half.

                // Add an explicit leading 1 to the significand.

                mantissa = mantissa | 0x00800000;

                // Round to M to the nearest (10+E)-bit value (with E between -10 and 0); in case of a tie, round to the nearest even value.
                //
                // Rounding may cause the significand to overflow and make our number normalized. Because of the way a half's bits
                // are laid out, we don't have to treat this case separately; the code below will handle it correctly.

                Int32 t = 14 - exponent;
                Int32 a = (1 << (t - 1)) - 1;
                Int32 b = (mantissa >> t) & 1;

                mantissa = (mantissa + a + b) >> t;

                // Assemble the half from S, E (==zero) and M.

                return (UInt16)(sign | mantissa);
            }
            else if (exponent == 0xff - (127 - 15))
            {
                if (mantissa == 0)
                {
                    // F is an infinity; convert F to a half infinity with the same sign as F.

                    return (UInt16)(sign | 0x7c00);
                }
                else
                {
                    // F is a NAN; we produce a half NAN that preserves the sign bit and the 10 leftmost bits of the
                    // significand of F, with one exception: If the 10 leftmost bits are all zero, the NAN would turn 
                    // into an infinity, so we have to set at least one bit in the significand.

                    mantissa >>= 13;
                    return (UInt16)(sign | 0x7c00 | mantissa | ((mantissa == 0) ? 1 : 0));
                }
            }
            else
            {
                // E is greater than zero.  F is a normalized float. We try to convert F to a normalized half.

                // Round to M to the nearest 10-bit value. In case of a tie, round to the nearest even value.

                mantissa = mantissa + 0x00000fff + ((mantissa >> 13) & 1);

                if ((mantissa & 0x00800000) == 1)
                {
                    mantissa = 0;        // overflow in significand,
                    exponent += 1;        // adjust exponent
                }

                // exponent overflow
                if (exponent > 30) throw new ArithmeticException("Half: Hardware floating-point overflow.");

                // Assemble the half from S, E and M.

                return (UInt16)(sign | (exponent << 10) | (mantissa >> 13));
            }
        }

        #endregion Single -> Half

        #region Half -> Single

        public Single ToSingle()
        {
            int i = HalfToFloat(bits);

            unsafe
            {
                return *(float*)&i;
            }
        }

        private Int32 HalfToFloat(UInt16 ui16)
        {

            Int32 sign = (ui16 >> 15) & 0x00000001;
            Int32 exponent = (ui16 >> 10) & 0x0000001f;
            Int32 mantissa = ui16 & 0x000003ff;

            if (exponent == 0)
            {
                if (mantissa == 0)
                {
                    // Plus or minus zero

                    return sign << 31;
                }
                else
                {
                    // Denormalized number -- renormalize it

                    while ((mantissa & 0x00000400) == 0)
                    {
                        mantissa <<= 1;
                        exponent -= 1;
                    }

                    exponent += 1;
                    mantissa &= ~0x00000400;
                }
            }
            else if (exponent == 31)
            {
                if (mantissa == 0)
                {
                    // Positive or negative infinity

                    return (sign << 31) | 0x7f800000;
                }
                else
                {
                    // Nan -- preserve sign and significand bits

                    return (sign << 31) | 0x7f800000 | (mantissa << 13);
                }
            }

            // Normalized number

            exponent = exponent + (127 - 15);
            mantissa = mantissa << 13;

            // Assemble S, E and M.

            return (sign << 31) | (exponent << 23) | mantissa;
        }

        #endregion Half -> Single

        #region Conversions

        public static explicit operator Half(float f)
        {
            return new Half(f);
        }

        public static explicit operator Half(double d)
        {
            return new Half(d);
        }

        public static implicit operator float(Half h)
        {
            return h.ToSingle();
        }

        public static implicit operator double(Half h)
        {
            return (double)h.ToSingle();
        }

        #endregion Conversions

        #region Constants

        public static readonly Int32 SizeInBytes = 2;

        public static readonly Single MinValue = 5.96046448e-08f;

        public static readonly Single MinNormalizedValue = 6.10351562e-05f;

        public static readonly Single MaxValue = 65504.0f;

        public static readonly Single Epsilon = 0.00097656f;

        #endregion Constants

        #region ISerializable

        public Half(SerializationInfo info, StreamingContext context)
        {
            this.bits = (ushort)info.GetValue("bits", typeof(ushort));
        }

        public void GetObjectData(SerializationInfo info, StreamingContext context)
        {
            info.AddValue("bits", this.bits);
        }

        #endregion ISerializable

        #region Binary dump

        public void FromBinaryStream(BinaryReader bin)
        {
            this.bits = bin.ReadUInt16();

        }

        public void ToBinaryStream(BinaryWriter bin)
        {
            bin.Write(this.bits);
        }

        #endregion Binary dump

        #region IEquatable<Half> Members

        const int maxUlps = 1;

        public bool Equals(Half other)
        {
            short aInt, bInt;
            unchecked { aInt = (short)other.bits; }
            unchecked { bInt = (short)this.bits; }

            // Make aInt lexicographically ordered as a twos-complement int
            if (aInt < 0)
                aInt = (short)(0x8000 - aInt);

            // Make bInt lexicographically ordered as a twos-complement int
            if (bInt < 0)
                bInt = (short)(0x8000 - bInt);

            short intDiff = System.Math.Abs((short)(aInt - bInt));

            if (intDiff <= maxUlps)
                return true;

            return false;
        }

        #endregion

        #region IComparable<Half> Members

        public int CompareTo(Half other)
        {
            return ((float)this).CompareTo((float)other);
        }

        #endregion IComparable<Half> Members

        #region IFormattable Members

        public override string ToString()
        {
            return this.ToSingle().ToString();
        }

        public string ToString(string format, IFormatProvider formatProvider)
        {
            return this.ToSingle().ToString(format, formatProvider);
        }

        #endregion IFormattable Members

        #region String -> Half

        public static Half Parse(string s)
        {
            return (Half)Single.Parse(s);
        }

        public static Half Parse(string s, System.Globalization.NumberStyles style, IFormatProvider provider)
        {
            return (Half)Single.Parse(s, style, provider);
        }

        public static bool TryParse(string s, out Half result)
        {
            float f;
            bool b = Single.TryParse(s, out f);
            result = (Half)f;
            return b;
        }

        public static bool TryParse(string s, System.Globalization.NumberStyles style, IFormatProvider provider, out Half result)
        {
            float f;
            bool b = Single.TryParse(s, style, provider, out f);
            result = (Half)f;
            return b;
        }

        #endregion String -> Half

        #region BitConverter

        public static byte[] GetBytes(Half h)
        {
            return BitConverter.GetBytes(h.bits);
        }

        public static Half FromBytes(byte[] value, int startIndex)
        {
            Half h;
            h.bits = BitConverter.ToUInt16(value, startIndex);
            return h;
        }

        #endregion BitConverter
    }
}

---