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589 lines
23 KiB
C#
589 lines
23 KiB
C#
#region --- License ---
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/*
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Copyright (c) 2006 - 2008 The Open Toolkit library.
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Permission is hereby granted, free of charge, to any person obtaining a copy of
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this software and associated documentation files (the "Software"), to deal in
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the Software without restriction, including without limitation the rights to
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use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
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of the Software, and to permit persons to whom the Software is furnished to do
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so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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/*
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The conversion functions are derived from OpenEXR's implementation and are
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governed by the following license:
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Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
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Digital Ltd. LLC
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All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are
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met:
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* Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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* Redistributions in binary form must reproduce the above
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copyright notice, this list of conditions and the following disclaimer
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in the documentation and/or other materials provided with the
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distribution.
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* Neither the name of Industrial Light & Magic nor the names of
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its contributors may be used to endorse or promote products derived
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from this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#endregion --- License ---
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using System;
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using System.IO;
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using System.Runtime.InteropServices;
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using System.Runtime.Serialization;
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namespace OpenTK.Math
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{
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/// <summary>
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/// The name Half is derived from half-precision floating-point number.
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/// It occupies only 16 Bits, which are split into 1 Sign bit, 5 Exponent bits and 10 Mantissa bits.
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/// </summary>
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/// <remarks>
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/// Quote from ARB_half_float_pixel specification:
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/// Any representable 16-bit floating-point value is legal as input to a GL command that accepts 16-bit floating-point data. The
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/// result of providing a value that is not a floating-point number (such as infinity or NaN) to such a command is unspecified,
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/// but must not lead to GL interruption or termination. Providing a denormalized number or negative zero to GL must yield
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/// predictable results.
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/// </remarks>
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[Obsolete("OpenTK.Math functions have been moved to the root OpenTK namespace (reason: XNA compatibility")]
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[Serializable, StructLayout(LayoutKind.Sequential)]
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public struct Half : ISerializable, IComparable<Half>, IFormattable, IEquatable<Half>
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{
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#region Internal Field
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UInt16 bits;
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#endregion Internal Field
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#region Properties
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/// <summary>Returns true if the Half is zero.</summary>
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public bool IsZero { get { return (bits == 0) || (bits == 0x8000); } }
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/// <summary>Returns true if the Half represents Not A Number (NaN)</summary>
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public bool IsNaN { get { return (((bits & 0x7C00) == 0x7C00) && (bits & 0x03FF) != 0x0000); } }
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/// <summary>Returns true if the Half represents positive infinity.</summary>
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public bool IsPositiveInfinity { get { return (bits == 31744); } }
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/// <summary>Returns true if the Half represents negative infinity.</summary>
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public bool IsNegativeInfinity { get { return (bits == 64512); } }
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#endregion Properties
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#region Constructors
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/// <summary>
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/// The new Half instance will convert the parameter into 16-Bit Half precision floating point.
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/// </summary>
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/// <param name="f">32-Bit Single precision floating point number.</param>
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public Half(Single f)
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: this()
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{
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unsafe
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{
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bits = SingleToHalf(*(int*)&f);
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}
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}
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/// <summary>
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/// The new Half instance will convert the parameter into 16-Bit Half precision floating point.
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/// </summary>
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/// <param name="f">32-Bit Single precision floating point number.</param>
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/// <param name="throwOnError">Enable checks that will throw if the conversion result is not meaningful.</param>
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public Half(Single f, bool throwOnError)
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: this(f)
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{
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if (throwOnError)
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{
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// handle cases that cause overflow rather than silently ignoring it
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if (f > Half.MaxValue) throw new ArithmeticException("Half: Positive maximum value exceeded.");
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if (f < -Half.MaxValue) throw new ArithmeticException("Half: Negative minimum value exceeded.");
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// handle cases that make no sense
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if (Single.IsNaN(f)) throw new ArithmeticException("Half: input is Not a Number (NaN).");
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if (Single.IsPositiveInfinity(f)) throw new ArithmeticException("Half: input is +infinity.");
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if (Single.IsNegativeInfinity(f)) throw new ArithmeticException("Half: input is -infinity.");
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}
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}
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/// <summary>
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/// The new Half instance will convert the parameter into 16-Bit Half precision floating point.
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/// </summary>
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/// <param name="d">64-Bit Double precision floating point number.</param>
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public Half(Double d) : this((Single)d) { }
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/// <summary>
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/// The new Half instance will convert the parameter into 16-Bit Half precision floating point.
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/// </summary>
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/// <param name="d">64-Bit Double precision floating point number.</param>
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/// <param name="throwOnError">Enable checks that will throw if the conversion result is not meaningful.</param>
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public Half(Double d, bool throwOnError) : this((Single)d, throwOnError) { }
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#endregion Constructors
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#region Single -> Half
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/// <summary>Ported from OpenEXR's IlmBase 1.0.1</summary>
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private UInt16 SingleToHalf(Int32 si32)
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{
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// Our floating point number, F, is represented by the bit pattern in integer i.
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// Disassemble that bit pattern into the sign, S, the exponent, E, and the significand, M.
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// Shift S into the position where it will go in in the resulting half number.
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// Adjust E, accounting for the different exponent bias of float and half (127 versus 15).
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Int32 sign = (si32 >> 16) & 0x00008000;
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Int32 exponent = ((si32 >> 23) & 0x000000ff) - (127 - 15);
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Int32 mantissa = si32 & 0x007fffff;
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// Now reassemble S, E and M into a half:
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if (exponent <= 0)
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{
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if (exponent < -10)
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{
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// E is less than -10. The absolute value of F is less than Half.MinValue
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// (F may be a small normalized float, a denormalized float or a zero).
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//
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// We convert F to a half zero with the same sign as F.
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return (UInt16)sign;
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}
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// E is between -10 and 0. F is a normalized float whose magnitude is less than Half.MinNormalizedValue.
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//
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// We convert F to a denormalized half.
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// Add an explicit leading 1 to the significand.
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mantissa = mantissa | 0x00800000;
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// 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.
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//
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// Rounding may cause the significand to overflow and make our number normalized. Because of the way a half's bits
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// are laid out, we don't have to treat this case separately; the code below will handle it correctly.
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Int32 t = 14 - exponent;
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Int32 a = (1 << (t - 1)) - 1;
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Int32 b = (mantissa >> t) & 1;
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mantissa = (mantissa + a + b) >> t;
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// Assemble the half from S, E (==zero) and M.
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return (UInt16)(sign | mantissa);
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}
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else if (exponent == 0xff - (127 - 15))
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{
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if (mantissa == 0)
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{
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// F is an infinity; convert F to a half infinity with the same sign as F.
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return (UInt16)(sign | 0x7c00);
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}
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else
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{
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// F is a NAN; we produce a half NAN that preserves the sign bit and the 10 leftmost bits of the
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// significand of F, with one exception: If the 10 leftmost bits are all zero, the NAN would turn
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// into an infinity, so we have to set at least one bit in the significand.
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mantissa >>= 13;
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return (UInt16)(sign | 0x7c00 | mantissa | ((mantissa == 0) ? 1 : 0));
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}
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}
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else
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{
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// E is greater than zero. F is a normalized float. We try to convert F to a normalized half.
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// Round to M to the nearest 10-bit value. In case of a tie, round to the nearest even value.
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mantissa = mantissa + 0x00000fff + ((mantissa >> 13) & 1);
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if ((mantissa & 0x00800000) == 1)
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{
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mantissa = 0; // overflow in significand,
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exponent += 1; // adjust exponent
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}
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// exponent overflow
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if (exponent > 30) throw new ArithmeticException("Half: hardware floating point overflow.");
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// Assemble the half from S, E and M.
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return (UInt16)(sign | (exponent << 10) | (mantissa >> 13));
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}
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}
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#endregion Single -> Half
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#region Half -> Single
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/// <summary>Converts the 16-Bit half to 32-Bit floating point.</summary>
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/// <returns>A Single precision floating point Number.</returns>
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public Single ToSingle()
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{
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int i = HalfToFloat(bits);
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unsafe
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{
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return *(float*)&i;
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}
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}
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/// <summary>Ported from OpenEXR's IlmBase 1.0.1</summary>
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private Int32 HalfToFloat(UInt16 ui16)
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{
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Int32 sign = (ui16 >> 15) & 0x00000001;
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Int32 exponent = (ui16 >> 10) & 0x0000001f;
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Int32 mantissa = ui16 & 0x000003ff;
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if (exponent == 0)
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{
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if (mantissa == 0)
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{
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// Plus or minus zero
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return sign << 31;
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}
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else
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{
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// Denormalized number -- renormalize it
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while ((mantissa & 0x00000400) == 0)
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{
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mantissa <<= 1;
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exponent -= 1;
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}
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exponent += 1;
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mantissa &= ~0x00000400;
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}
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}
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else if (exponent == 31)
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{
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if (mantissa == 0)
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{
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// Positive or negative infinity
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return (sign << 31) | 0x7f800000;
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}
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else
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{
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// Nan -- preserve sign and significand bits
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return (sign << 31) | 0x7f800000 | (mantissa << 13);
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}
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}
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// Normalized number
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exponent = exponent + (127 - 15);
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mantissa = mantissa << 13;
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// Assemble S, E and M.
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return (sign << 31) | (exponent << 23) | mantissa;
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}
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#endregion Half -> Single
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#region Conversions
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/// <summary>
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/// Converts a System.Single to a OpenTK.Half.
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/// </summary>
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/// <param name="f">The value to convert.
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/// A <see cref="System.Single"/>
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/// </param>
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/// <returns>The result of the conversion.
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/// A <see cref="Half"/>
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/// </returns>
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public static explicit operator Half(float f)
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{
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return new Half(f);
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}
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/// <summary>
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/// Converts a System.Double to a OpenTK.Half.
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/// </summary>
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/// <param name="d">The value to convert.
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/// A <see cref="System.Double"/>
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/// </param>
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/// <returns>The result of the conversion.
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/// A <see cref="Half"/>
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/// </returns>
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public static explicit operator Half(double d)
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{
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return new Half(d);
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}
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/// <summary>
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/// Converts a OpenTK.Half to a System.Single.
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/// </summary>
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/// <param name="h">The value to convert.
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/// A <see cref="Half"/>
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/// </param>
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/// <returns>The result of the conversion.
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/// A <see cref="System.Single"/>
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/// </returns>
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public static implicit operator float(Half h)
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{
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return h.ToSingle();
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}
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/// <summary>
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/// Converts a OpenTK.Half to a System.Double.
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/// </summary>
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/// <param name="h">The value to convert.
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/// A <see cref="Half"/>
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/// </param>
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/// <returns>The result of the conversion.
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/// A <see cref="System.Double"/>
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/// </returns>
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public static implicit operator double(Half h)
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{
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return (double)h.ToSingle();
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}
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#endregion Conversions
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#region Constants
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/// <summary>The size in bytes for an instance of the Half struct.</summary>
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public static readonly Int32 SizeInBytes = 2;
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/// <summary>Smallest positive half</summary>
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public static readonly Single MinValue = 5.96046448e-08f;
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/// <summary>Smallest positive normalized half</summary>
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public static readonly Single MinNormalizedValue = 6.10351562e-05f;
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/// <summary>Largest positive half</summary>
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public static readonly Single MaxValue = 65504.0f;
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/// <summary>Smallest positive e for which half (1.0 + e) != half (1.0)</summary>
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public static readonly Single Epsilon = 0.00097656f;
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#endregion Constants
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#region ISerializable
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/// <summary>Constructor used by ISerializable to deserialize the object.</summary>
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/// <param name="info"></param>
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/// <param name="context"></param>
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public Half(SerializationInfo info, StreamingContext context)
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{
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this.bits = (ushort)info.GetValue("bits", typeof(ushort));
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}
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/// <summary>Used by ISerialize to serialize the object.</summary>
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/// <param name="info"></param>
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/// <param name="context"></param>
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public void GetObjectData(SerializationInfo info, StreamingContext context)
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{
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info.AddValue("bits", this.bits);
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}
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#endregion ISerializable
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#region Binary dump
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/// <summary>Updates the Half by reading from a Stream.</summary>
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/// <param name="bin">A BinaryReader instance associated with an open Stream.</param>
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public void FromBinaryStream(BinaryReader bin)
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{
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this.bits = bin.ReadUInt16();
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}
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/// <summary>Writes the Half into a Stream.</summary>
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/// <param name="bin">A BinaryWriter instance associated with an open Stream.</param>
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public void ToBinaryStream(BinaryWriter bin)
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{
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bin.Write(this.bits);
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}
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#endregion Binary dump
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#region IEquatable<Half> Members
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const int maxUlps = 1;
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/// <summary>
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/// Returns a value indicating whether this instance is equal to a specified OpenTK.Half value.
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/// </summary>
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/// <param name="other">OpenTK.Half object to compare to this instance..</param>
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/// <returns>True, if other is equal to this instance; false otherwise.</returns>
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public bool Equals(Half other)
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{
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short aInt, bInt;
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unchecked { aInt = (short)other.bits; }
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unchecked { bInt = (short)this.bits; }
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// Make aInt lexicographically ordered as a twos-complement int
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if (aInt < 0)
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aInt = (short)(0x8000 - aInt);
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// Make bInt lexicographically ordered as a twos-complement int
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if (bInt < 0)
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bInt = (short)(0x8000 - bInt);
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short intDiff = System.Math.Abs((short)(aInt - bInt));
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if (intDiff <= maxUlps)
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return true;
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return false;
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}
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#endregion
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#region IComparable<Half> Members
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/// <summary>
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/// Compares this instance to a specified half-precision floating-point number
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/// and returns an integer that indicates whether the value of this instance
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/// is less than, equal to, or greater than the value of the specified half-precision
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/// floating-point number.
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/// </summary>
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/// <param name="other">A half-precision floating-point number to compare.</param>
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/// <returns>
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/// A signed number indicating the relative values of this instance and value. If the number is:
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/// <para>Less than zero, then this instance is less than other, or this instance is not a number
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/// (OpenTK.Half.NaN) and other is a number.</para>
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/// <para>Zero: this instance is equal to value, or both this instance and other
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/// are not a number (OpenTK.Half.NaN), OpenTK.Half.PositiveInfinity, or
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/// OpenTK.Half.NegativeInfinity.</para>
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/// <para>Greater than zero: this instance is greater than othrs, or this instance is a number
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/// and other is not a number (OpenTK.Half.NaN).</para>
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/// </returns>
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public int CompareTo(Half other)
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{
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return ((float)this).CompareTo((float)other);
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}
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#endregion IComparable<Half> Members
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#region IFormattable Members
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/// <summary>Converts this Half into a human-legible string representation.</summary>
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/// <returns>The string representation of this instance.</returns>
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public override string ToString()
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{
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return this.ToSingle().ToString();
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}
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/// <summary>Converts this Half into a human-legible string representation.</summary>
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/// <param name="format">formatting for the output string.</param>
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/// <param name="formatProvider">Culture-specific formatting information.</param>
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/// <returns>The string representation of this instance.</returns>
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public string ToString(string format, IFormatProvider formatProvider)
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{
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return this.ToSingle().ToString(format, formatProvider);
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}
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#endregion IFormattable Members
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#region String -> Half
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/// <summary>Converts the string representation of a number to a Half precision floating point equivalent.</summary>
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/// <param name="s">string representation of the number to convert.</param>
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/// <returns>A new Half instance.</returns>
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public static Half Parse(string s)
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{
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return (Half)Single.Parse(s);
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}
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/// <summary>Converts the string representation of a number to a Half precision floating point equivalent.</summary>
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/// <param name="s">string representation of the number to convert.</param>
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/// <param name="style">specifies the format of s.</param>
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/// <param name="provider">Culture-specific formatting information.</param>
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/// <returns>A new Half instance.</returns>
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public static Half Parse(string s, System.Globalization.NumberStyles style, IFormatProvider provider)
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{
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return (Half)Single.Parse(s, style, provider);
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}
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/// <summary>Converts the string representation of a number to a Half precision floating point equivalent. Returns success.</summary>
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/// <param name="s">string representation of the number to convert.</param>
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/// <param name="result">The Half instance to write to.</param>
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/// <returns>Success.</returns>
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public static bool TryParse(string s, out Half result)
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{
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float f;
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bool b = Single.TryParse(s, out f);
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result = (Half)f;
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return b;
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}
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/// <summary>Converts the string representation of a number to a Half precision floating point equivalent. Returns success.</summary>
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|
/// <param name="s">string representation of the number to convert.</param>
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/// <param name="style">specifies the format of s.</param>
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/// <param name="provider">Culture-specific formatting information.</param>
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/// <param name="result">The Half instance to write to.</param>
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/// <returns>Success.</returns>
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public static bool TryParse(string s, System.Globalization.NumberStyles style, IFormatProvider provider, out Half result)
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|
{
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float f;
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bool b = Single.TryParse(s, style, provider, out f);
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result = (Half)f;
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return b;
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}
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#endregion String -> Half
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#region BitConverter
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/// <summary>Returns the Half as an array of bytes.</summary>
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/// <param name="h">The Half to convert.</param>
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/// <returns>The input as byte array.</returns>
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public static byte[] GetBytes(Half h)
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{
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return BitConverter.GetBytes(h.bits);
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}
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/// <summary>Converts an array of bytes into Half.</summary>
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/// <param name="value">A Half in it's byte[] representation.</param>
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/// <param name="startIndex">The starting position within value.</param>
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/// <returns>A new Half instance.</returns>
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public static Half FromBytes(byte[] value, int startIndex)
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{
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Half h;
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h.bits = BitConverter.ToUInt16(value, startIndex);
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return h;
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}
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#endregion BitConverter
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}
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} |