src/Bannerlord.LauncherEx/TPac/Half.cs
/// ================ Half.cs ====================
/// The code is free to use for any reason without any restrictions.
/// Ladislav Lang (2009), Joannes Vermorel (2017)
using System;
using System.Diagnostics;
using System.Globalization;
namespace SystemHalf
{
/// <summary>
/// Represents a half-precision floating point number.
/// </summary>
/// <remarks>
/// Note:
/// Half is not fast enought and precision is also very bad,
/// so is should not be used for mathematical computation (use Single instead).
/// The main advantage of Half type is lower memory cost: two bytes per number.
/// Half is typically used in graphical applications.
///
/// Note:
/// All functions, where is used conversion half->float/float->half,
/// are approx. ten times slower than float->double/double->float, i.e. ~3ns on 2GHz CPU.
///
/// References:
/// - Code retrieved from http://sourceforge.net/p/csharp-half/code/HEAD/tree/ on 2015-12-04
/// - Fast Half Float Conversions, Jeroen van der Zijp, link: http://www.fox-toolkit.org/ftp/fasthalffloatconversion.pdf
/// - IEEE 754 revision, link: http://grouper.ieee.org/groups/754/
/// </remarks>
#if !NETSTANDARD1_3
[Serializable]
#endif
internal struct Half : IComparable, IFormattable, IConvertible, IComparable<Half>, IEquatable<Half>
{
/// <summary>
/// Internal representation of the half-precision floating-point number.
/// </summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
internal ushort Value;
#region Constants
/// <summary>
/// Represents the smallest positive System.Half value greater than zero. This field is constant.
/// </summary>
public static readonly Half Epsilon = ToHalf(0x0001);
/// <summary>
/// Represents the largest possible value of System.Half. This field is constant.
/// </summary>
public static readonly Half MaxValue = ToHalf(0x7bff);
/// <summary>
/// Represents the smallest possible value of System.Half. This field is constant.
/// </summary>
public static readonly Half MinValue = ToHalf(0xfbff);
/// <summary>
/// Represents not a number (NaN). This field is constant.
/// </summary>
public static readonly Half NaN = ToHalf(0xfe00);
/// <summary>
/// Represents negative infinity. This field is constant.
/// </summary>
public static readonly Half NegativeInfinity = ToHalf(0xfc00);
/// <summary>
/// Represents positive infinity. This field is constant.
/// </summary>
public static readonly Half PositiveInfinity = ToHalf(0x7c00);
#endregion
#region Constructors
/// <summary>
/// Initializes a new instance of System.Half to the value of the specified single-precision floating-point number.
/// </summary>
/// <param name="value">The value to represent as a System.Half.</param>
public Half(float value) { this = HalfHelper.SingleToHalf(value); }
/// <summary>
/// Initializes a new instance of System.Half to the value of the specified 32-bit signed integer.
/// </summary>
/// <param name="value">The value to represent as a System.Half.</param>
public Half(int value) : this((float) value) { }
/// <summary>
/// Initializes a new instance of System.Half to the value of the specified 64-bit signed integer.
/// </summary>
/// <param name="value">The value to represent as a System.Half.</param>
public Half(long value) : this((float) value) { }
/// <summary>
/// Initializes a new instance of System.Half to the value of the specified double-precision floating-point number.
/// </summary>
/// <param name="value">The value to represent as a System.Half.</param>
public Half(double value) : this((float) value) { }
/// <summary>
/// Initializes a new instance of System.Half to the value of the specified decimal number.
/// </summary>
/// <param name="value">The value to represent as a System.Half.</param>
public Half(decimal value) : this((float) value) { }
/// <summary>
/// Initializes a new instance of System.Half to the value of the specified 32-bit unsigned integer.
/// </summary>
/// <param name="value">The value to represent as a System.Half.</param>
public Half(uint value) : this((float) value) { }
/// <summary>
/// Initializes a new instance of System.Half to the value of the specified 64-bit unsigned integer.
/// </summary>
/// <param name="value">The value to represent as a System.Half.</param>
public Half(ulong value) : this((float) value) { }
#endregion
#region Numeric operators
/// <summary>
/// Returns the result of multiplying the specified System.Half value by negative one.
/// </summary>
/// <param name="half">A System.Half.</param>
/// <returns>A System.Half with the value of half, but the opposite sign. -or- Zero, if half is zero.</returns>
public static Half Negate(Half half) { return -half; }
/// <summary>
/// Adds two specified System.Half values.
/// </summary>
/// <param name="half1">A System.Half.</param>
/// <param name="half2">A System.Half.</param>
/// <returns>A System.Half value that is the sum of half1 and half2.</returns>
public static Half Add(Half half1, Half half2) { return half1 + half2; }
/// <summary>
/// Subtracts one specified System.Half value from another.
/// </summary>
/// <param name="half1">A System.Half (the minuend).</param>
/// <param name="half2">A System.Half (the subtrahend).</param>
/// <returns>The System.Half result of subtracting half2 from half1.</returns>
public static Half Subtract(Half half1, Half half2) { return half1 - half2; }
/// <summary>
/// Multiplies two specified System.Half values.
/// </summary>
/// <param name="half1">A System.Half (the multiplicand).</param>
/// <param name="half2">A System.Half (the multiplier).</param>
/// <returns>A System.Half that is the result of multiplying half1 and half2.</returns>
public static Half Multiply(Half half1, Half half2) { return half1 * half2; }
/// <summary>
/// Divides two specified System.Half values.
/// </summary>
/// <param name="half1">A System.Half (the dividend).</param>
/// <param name="half2">A System.Half (the divisor).</param>
/// <returns>The System.Half that is the result of dividing half1 by half2.</returns>
/// <exception cref="System.DivideByZeroException">half2 is zero.</exception>
public static Half Divide(Half half1, Half half2) { return half1 / half2; }
/// <summary>
/// Returns the value of the System.Half operand (the sign of the operand is unchanged).
/// </summary>
/// <param name="half">The System.Half operand.</param>
/// <returns>The value of the operand, half.</returns>
public static Half operator +(Half half) { return half; }
/// <summary>
/// Negates the value of the specified System.Half operand.
/// </summary>
/// <param name="half">The System.Half operand.</param>
/// <returns>The result of half multiplied by negative one (-1).</returns>
public static Half operator -(Half half) { return HalfHelper.Negate(half); }
/// <summary>
/// Increments the System.Half operand by 1.
/// </summary>
/// <param name="half">The System.Half operand.</param>
/// <returns>The value of half incremented by 1.</returns>
public static Half operator ++(Half half) { return (Half) (half + 1f); }
/// <summary>
/// Decrements the System.Half operand by one.
/// </summary>
/// <param name="half">The System.Half operand.</param>
/// <returns>The value of half decremented by 1.</returns>
public static Half operator --(Half half) { return (Half) (half - 1f); }
/// <summary>
/// Adds two specified System.Half values.
/// </summary>
/// <param name="half1">A System.Half.</param>
/// <param name="half2">A System.Half.</param>
/// <returns>The System.Half result of adding half1 and half2.</returns>
public static Half operator +(Half half1, Half half2) { return (Half) (half1 + (float) half2); }
/// <summary>
/// Subtracts two specified System.Half values.
/// </summary>
/// <param name="half1">A System.Half.</param>
/// <param name="half2">A System.Half.</param>
/// <returns>The System.Half result of subtracting half1 and half2.</returns>
public static Half operator -(Half half1, Half half2) { return (Half) (half1 - (float) half2); }
/// <summary>
/// Multiplies two specified System.Half values.
/// </summary>
/// <param name="half1">A System.Half.</param>
/// <param name="half2">A System.Half.</param>
/// <returns>The System.Half result of multiplying half1 by half2.</returns>
public static Half operator *(Half half1, Half half2) { return (Half) (half1 * (float) half2); }
/// <summary>
/// Divides two specified System.Half values.
/// </summary>
/// <param name="half1">A System.Half (the dividend).</param>
/// <param name="half2">A System.Half (the divisor).</param>
/// <returns>The System.Half result of half1 by half2.</returns>
public static Half operator /(Half half1, Half half2) { return (Half) (half1 / (float) half2); }
/// <summary>
/// Returns a value indicating whether two instances of System.Half are equal.
/// </summary>
/// <param name="half1">A System.Half.</param>
/// <param name="half2">A System.Half.</param>
/// <returns>true if half1 and half2 are equal; otherwise, false.</returns>
public static bool operator ==(Half half1, Half half2) { return (!IsNaN(half1) && (half1.Value == half2.Value)); }
/// <summary>
/// Returns a value indicating whether two instances of System.Half are not equal.
/// </summary>
/// <param name="half1">A System.Half.</param>
/// <param name="half2">A System.Half.</param>
/// <returns>true if half1 and half2 are not equal; otherwise, false.</returns>
public static bool operator !=(Half half1, Half half2) { return half1.Value != half2.Value; }
/// <summary>
/// Returns a value indicating whether a specified System.Half is less than another specified System.Half.
/// </summary>
/// <param name="half1">A System.Half.</param>
/// <param name="half2">A System.Half.</param>
/// <returns>true if half1 is less than half1; otherwise, false.</returns>
public static bool operator <(Half half1, Half half2) { return half1 < (float) half2; }
/// <summary>
/// Returns a value indicating whether a specified System.Half is greater than another specified System.Half.
/// </summary>
/// <param name="half1">A System.Half.</param>
/// <param name="half2">A System.Half.</param>
/// <returns>true if half1 is greater than half2; otherwise, false.</returns>
public static bool operator >(Half half1, Half half2) { return half1 > (float) half2; }
/// <summary>
/// Returns a value indicating whether a specified System.Half is less than or equal to another specified System.Half.
/// </summary>
/// <param name="half1">A System.Half.</param>
/// <param name="half2">A System.Half.</param>
/// <returns>true if half1 is less than or equal to half2; otherwise, false.</returns>
public static bool operator <=(Half half1, Half half2) { return (half1 == half2) || (half1 < half2); }
/// <summary>
/// Returns a value indicating whether a specified System.Half is greater than or equal to another specified System.Half.
/// </summary>
/// <param name="half1">A System.Half.</param>
/// <param name="half2">A System.Half.</param>
/// <returns>true if half1 is greater than or equal to half2; otherwise, false.</returns>
public static bool operator >=(Half half1, Half half2) { return (half1 == half2) || (half1 > half2); }
#endregion
#region Type casting operators
/// <summary>
/// Converts an 8-bit unsigned integer to a System.Half.
/// </summary>
/// <param name="value">An 8-bit unsigned integer.</param>
/// <returns>A System.Half that represents the converted 8-bit unsigned integer.</returns>
public static implicit operator Half(byte value) { return new Half((float) value); }
/// <summary>
/// Converts a 16-bit signed integer to a System.Half.
/// </summary>
/// <param name="value">A 16-bit signed integer.</param>
/// <returns>A System.Half that represents the converted 16-bit signed integer.</returns>
public static implicit operator Half(short value) { return new Half((float) value); }
/// <summary>
/// Converts a Unicode character to a System.Half.
/// </summary>
/// <param name="value">A Unicode character.</param>
/// <returns>A System.Half that represents the converted Unicode character.</returns>
public static implicit operator Half(char value) { return new Half((float) value); }
/// <summary>
/// Converts a 32-bit signed integer to a System.Half.
/// </summary>
/// <param name="value">A 32-bit signed integer.</param>
/// <returns>A System.Half that represents the converted 32-bit signed integer.</returns>
public static implicit operator Half(int value) { return new Half((float) value); }
/// <summary>
/// Converts a 64-bit signed integer to a System.Half.
/// </summary>
/// <param name="value">A 64-bit signed integer.</param>
/// <returns>A System.Half that represents the converted 64-bit signed integer.</returns>
public static implicit operator Half(long value) { return new Half((float) value); }
/// <summary>
/// Converts a single-precision floating-point number to a System.Half.
/// </summary>
/// <param name="value">A single-precision floating-point number.</param>
/// <returns>A System.Half that represents the converted single-precision floating point number.</returns>
public static explicit operator Half(float value) { return new Half(value); }
/// <summary>
/// Converts a double-precision floating-point number to a System.Half.
/// </summary>
/// <param name="value">A double-precision floating-point number.</param>
/// <returns>A System.Half that represents the converted double-precision floating point number.</returns>
public static explicit operator Half(double value) { return new Half((float) value); }
/// <summary>
/// Converts a decimal number to a System.Half.
/// </summary>
/// <param name="value">decimal number</param>
/// <returns>A System.Half that represents the converted decimal number.</returns>
public static explicit operator Half(decimal value) { return new Half((float) value); }
/// <summary>
/// Converts a System.Half to an 8-bit unsigned integer.
/// </summary>
/// <param name="value">A System.Half to convert.</param>
/// <returns>An 8-bit unsigned integer that represents the converted System.Half.</returns>
public static explicit operator byte(Half value) { return (byte) (float) value; }
/// <summary>
/// Converts a System.Half to a Unicode character.
/// </summary>
/// <param name="value">A System.Half to convert.</param>
/// <returns>A Unicode character that represents the converted System.Half.</returns>
public static explicit operator char(Half value) { return (char) (float) value; }
/// <summary>
/// Converts a System.Half to a 16-bit signed integer.
/// </summary>
/// <param name="value">A System.Half to convert.</param>
/// <returns>A 16-bit signed integer that represents the converted System.Half.</returns>
public static explicit operator short(Half value) { return (short) (float) value; }
/// <summary>
/// Converts a System.Half to a 32-bit signed integer.
/// </summary>
/// <param name="value">A System.Half to convert.</param>
/// <returns>A 32-bit signed integer that represents the converted System.Half.</returns>
public static explicit operator int(Half value) { return (int) (float) value; }
/// <summary>
/// Converts a System.Half to a 64-bit signed integer.
/// </summary>
/// <param name="value">A System.Half to convert.</param>
/// <returns>A 64-bit signed integer that represents the converted System.Half.</returns>
public static explicit operator long(Half value) { return (long) (float) value; }
/// <summary>
/// Converts a System.Half to a single-precision floating-point number.
/// </summary>
/// <param name="value">A System.Half to convert.</param>
/// <returns>A single-precision floating-point number that represents the converted System.Half.</returns>
public static implicit operator float(Half value) { return HalfHelper.HalfToSingle(value); }
/// <summary>
/// Converts a System.Half to a double-precision floating-point number.
/// </summary>
/// <param name="value">A System.Half to convert.</param>
/// <returns>A double-precision floating-point number that represents the converted System.Half.</returns>
public static implicit operator double(Half value) { return (float) value; }
/// <summary>
/// Converts a System.Half to a decimal number.
/// </summary>
/// <param name="value">A System.Half to convert.</param>
/// <returns>A decimal number that represents the converted System.Half.</returns>
public static explicit operator decimal(Half value) { return (decimal) (float) value; }
/// <summary>
/// Converts an 8-bit signed integer to a System.Half.
/// </summary>
/// <param name="value">An 8-bit signed integer.</param>
/// <returns>A System.Half that represents the converted 8-bit signed integer.</returns>
public static implicit operator Half(sbyte value) { return new Half((float) value); }
/// <summary>
/// Converts a 16-bit unsigned integer to a System.Half.
/// </summary>
/// <param name="value">A 16-bit unsigned integer.</param>
/// <returns>A System.Half that represents the converted 16-bit unsigned integer.</returns>
public static implicit operator Half(ushort value) { return new Half((float) value); }
/// <summary>
/// Converts a 32-bit unsigned integer to a System.Half.
/// </summary>
/// <param name="value">A 32-bit unsigned integer.</param>
/// <returns>A System.Half that represents the converted 32-bit unsigned integer.</returns>
public static implicit operator Half(uint value) { return new Half((float) value); }
/// <summary>
/// Converts a 64-bit unsigned integer to a System.Half.
/// </summary>
/// <param name="value">A 64-bit unsigned integer.</param>
/// <returns>A System.Half that represents the converted 64-bit unsigned integer.</returns>
public static implicit operator Half(ulong value) { return new Half((float) value); }
/// <summary>
/// Converts a System.Half to an 8-bit signed integer.
/// </summary>
/// <param name="value">A System.Half to convert.</param>
/// <returns>An 8-bit signed integer that represents the converted System.Half.</returns>
public static explicit operator sbyte(Half value) { return (sbyte) (float) value; }
/// <summary>
/// Converts a System.Half to a 16-bit unsigned integer.
/// </summary>
/// <param name="value">A System.Half to convert.</param>
/// <returns>A 16-bit unsigned integer that represents the converted System.Half.</returns>
public static explicit operator ushort(Half value) { return (ushort) (float) value; }
/// <summary>
/// Converts a System.Half to a 32-bit unsigned integer.
/// </summary>
/// <param name="value">A System.Half to convert.</param>
/// <returns>A 32-bit unsigned integer that represents the converted System.Half.</returns>
public static explicit operator uint(Half value) { return (uint) (float) value; }
/// <summary>
/// Converts a System.Half to a 64-bit unsigned integer.
/// </summary>
/// <param name="value">A System.Half to convert.</param>
/// <returns>A 64-bit unsigned integer that represents the converted System.Half.</returns>
public static explicit operator ulong(Half value) { return (ulong) (float) value; }
#endregion
/// <summary>
/// Compares this instance to a specified System.Half object.
/// </summary>
/// <param name="other">A System.Half object.</param>
/// <returns>
/// A signed number indicating the relative values of this instance and value.
/// Return Value Meaning Less than zero This instance is less than value. Zero
/// This instance is equal to value. Greater than zero This instance is greater than value.
/// </returns>
public int CompareTo(Half other)
{
var result = 0;
if (this < other)
{
result = -1;
}
else if (this > other)
{
result = 1;
}
else if (this != other)
{
if (!IsNaN(this))
{
result = 1;
}
else if (!IsNaN(other))
{
result = -1;
}
}
return result;
}
/// <summary>
/// Compares this instance to a specified System.Object.
/// </summary>
/// <param name="obj">An System.Object or null.</param>
/// <returns>
/// A signed number indicating the relative values of this instance and value.
/// Return Value Meaning Less than zero This instance is less than value. Zero
/// This instance is equal to value. Greater than zero This instance is greater
/// than value. -or- value is null.
/// </returns>
/// <exception cref="System.ArgumentException">value is not a System.Half</exception>
public int CompareTo(object? obj)
{
var result = 0;
if (obj == null)
{
result = 1;
}
else
{
if (obj is Half)
{
result = CompareTo((Half) obj);
}
else
{
throw new ArgumentException("Object must be of type Half.");
}
}
return result;
}
/// <summary>
/// Returns a value indicating whether this instance and a specified System.Half object represent the same value.
/// </summary>
/// <param name="other">A System.Half object to compare to this instance.</param>
/// <returns>true if value is equal to this instance; otherwise, false.</returns>
public bool Equals(Half other)
{
return ((other == this) || (IsNaN(other) && IsNaN(this)));
}
/// <summary>
/// Returns a value indicating whether this instance and a specified System.Object
/// represent the same type and value.
/// </summary>
/// <param name="obj">An System.Object.</param>
/// <returns>true if value is a System.Half and equal to this instance; otherwise, false.</returns>
public override bool Equals(object? obj)
{
var result = false;
if (obj is Half half)
{
if ((half == this) || (IsNaN(half) && IsNaN(this)))
{
result = true;
}
}
return result;
}
/// <summary>
/// Returns the hash code for this instance.
/// </summary>
/// <returns>A 32-bit signed integer hash code.</returns>
public override int GetHashCode()
{
return Value.GetHashCode();
}
/// <summary>
/// Returns the System.TypeCode for value type System.Half.
/// </summary>
/// <returns>The enumerated constant (TypeCode)255.</returns>
public TypeCode GetTypeCode()
{
return (TypeCode) 255;
}
#region BitConverter & Math methods for Half
/// <summary>
/// Returns the specified half-precision floating point value as an array of bytes.
/// </summary>
/// <param name="value">The number to convert.</param>
/// <returns>An array of bytes with length 2.</returns>
public static byte[] GetBytes(Half value)
{
return BitConverter.GetBytes(value.Value);
}
/// <summary>
/// Converts the value of a specified instance of System.Half to its equivalent binary representation.
/// </summary>
/// <param name="value">A System.Half value.</param>
/// <returns>A 16-bit unsigned integer that contain the binary representation of value.</returns>
public static ushort GetBits(Half value)
{
return value.Value;
}
/// <summary>
/// Returns a half-precision floating point number converted from two bytes
/// at a specified position in a byte array.
/// </summary>
/// <param name="value">An array of bytes.</param>
/// <param name="startIndex">The starting position within value.</param>
/// <returns>A half-precision floating point number formed by two bytes beginning at startIndex.</returns>
/// <exception cref="System.ArgumentException">
/// startIndex is greater than or equal to the length of value minus 1, and is
/// less than or equal to the length of value minus 1.
/// </exception>
/// <exception cref="System.ArgumentNullException">value is null.</exception>
/// <exception cref="System.ArgumentOutOfRangeException">startIndex is less than zero or greater than the length of value minus 1.</exception>
public static Half ToHalf(byte[] value, int startIndex)
{
return ToHalf((ushort) BitConverter.ToInt16(value, startIndex));
}
/// <summary>
/// Returns a half-precision floating point number converted from its binary representation.
/// </summary>
/// <param name="bits">Binary representation of System.Half value</param>
/// <returns>A half-precision floating point number formed by its binary representation.</returns>
public static Half ToHalf(ushort bits)
{
return new Half { Value = bits };
}
/// <summary>
/// Returns a value indicating the sign of a half-precision floating-point number.
/// </summary>
/// <param name="value">A signed number.</param>
/// <returns>
/// A number indicating the sign of value. Number Description -1 value is less
/// than zero. 0 value is equal to zero. 1 value is greater than zero.
/// </returns>
/// <exception cref="System.ArithmeticException">value is equal to System.Half.NaN.</exception>
public static int Sign(Half value)
{
if (value < 0)
{
return -1;
}
else if (value > 0)
{
return 1;
}
else
{
if (value != 0)
{
throw new ArithmeticException("Function does not accept floating point Not-a-Number values.");
}
}
return 0;
}
/// <summary>
/// Returns the absolute value of a half-precision floating-point number.
/// </summary>
/// <param name="value">A number in the range System.Half.MinValue ≤ value ≤ System.Half.MaxValue.</param>
/// <returns>A half-precision floating-point number, x, such that 0 ≤ x ≤System.Half.MaxValue.</returns>
public static Half Abs(Half value)
{
return HalfHelper.Abs(value);
}
/// <summary>
/// Returns the larger of two half-precision floating-point numbers.
/// </summary>
/// <param name="value1">The first of two half-precision floating-point numbers to compare.</param>
/// <param name="value2">The second of two half-precision floating-point numbers to compare.</param>
/// <returns>
/// Parameter value1 or value2, whichever is larger. If value1, or value2, or both val1
/// and value2 are equal to System.Half.NaN, System.Half.NaN is returned.
/// </returns>
public static Half Max(Half value1, Half value2)
{
return (value1 < value2) ? value2 : value1;
}
/// <summary>
/// Returns the smaller of two half-precision floating-point numbers.
/// </summary>
/// <param name="value1">The first of two half-precision floating-point numbers to compare.</param>
/// <param name="value2">The second of two half-precision floating-point numbers to compare.</param>
/// <returns>
/// Parameter value1 or value2, whichever is smaller. If value1, or value2, or both val1
/// and value2 are equal to System.Half.NaN, System.Half.NaN is returned.
/// </returns>
public static Half Min(Half value1, Half value2)
{
return (value1 < value2) ? value1 : value2;
}
#endregion
/// <summary>
/// Returns a value indicating whether the specified number evaluates to not a number (System.Half.NaN).
/// </summary>
/// <param name="half">A half-precision floating-point number.</param>
/// <returns>true if value evaluates to not a number (System.Half.NaN); otherwise, false.</returns>
public static bool IsNaN(Half half)
{
return HalfHelper.IsNaN(half);
}
/// <summary>
/// Returns a value indicating whether the specified number evaluates to negative or positive infinity.
/// </summary>
/// <param name="half">A half-precision floating-point number.</param>
/// <returns>true if half evaluates to System.Half.PositiveInfinity or System.Half.NegativeInfinity; otherwise, false.</returns>
public static bool IsInfinity(Half half)
{
return HalfHelper.IsInfinity(half);
}
/// <summary>
/// Returns a value indicating whether the specified number evaluates to negative infinity.
/// </summary>
/// <param name="half">A half-precision floating-point number.</param>
/// <returns>true if half evaluates to System.Half.NegativeInfinity; otherwise, false.</returns>
public static bool IsNegativeInfinity(Half half)
{
return HalfHelper.IsNegativeInfinity(half);
}
/// <summary>
/// Returns a value indicating whether the specified number evaluates to positive infinity.
/// </summary>
/// <param name="half">A half-precision floating-point number.</param>
/// <returns>true if half evaluates to System.Half.PositiveInfinity; otherwise, false.</returns>
public static bool IsPositiveInfinity(Half half)
{
return HalfHelper.IsPositiveInfinity(half);
}
#region String operations (Parse and ToString)
/// <summary>
/// Converts the string representation of a number to its System.Half equivalent.
/// </summary>
/// <param name="value">The string representation of the number to convert.</param>
/// <returns>The System.Half number equivalent to the number contained in value.</returns>
/// <exception cref="System.ArgumentNullException">value is null.</exception>
/// <exception cref="System.FormatException">value is not in the correct format.</exception>
/// <exception cref="System.OverflowException">value represents a number less than System.Half.MinValue or greater than System.Half.MaxValue.</exception>
public static Half Parse(string value)
{
return (Half) float.Parse(value, CultureInfo.InvariantCulture);
}
/// <summary>
/// Converts the string representation of a number to its System.Half equivalent
/// using the specified culture-specific format information.
/// </summary>
/// <param name="value">The string representation of the number to convert.</param>
/// <param name="provider">An System.IFormatProvider that supplies culture-specific parsing information about value.</param>
/// <returns>The System.Half number equivalent to the number contained in s as specified by provider.</returns>
/// <exception cref="System.ArgumentNullException">value is null.</exception>
/// <exception cref="System.FormatException">value is not in the correct format.</exception>
/// <exception cref="System.OverflowException">value represents a number less than System.Half.MinValue or greater than System.Half.MaxValue.</exception>
public static Half Parse(string value, IFormatProvider provider)
{
return (Half) float.Parse(value, provider);
}
/// <summary>
/// Converts the string representation of a number in a specified style to its System.Half equivalent.
/// </summary>
/// <param name="value">The string representation of the number to convert.</param>
/// <param name="style">
/// A bitwise combination of System.Globalization.NumberStyles values that indicates
/// the style elements that can be present in value. A typical value to specify is
/// System.Globalization.NumberStyles.Number.
/// </param>
/// <returns>The System.Half number equivalent to the number contained in s as specified by style.</returns>
/// <exception cref="System.ArgumentNullException">value is null.</exception>
/// <exception cref="System.ArgumentException">
/// style is not a System.Globalization.NumberStyles value. -or- style is the
/// System.Globalization.NumberStyles.AllowHexSpecifier value.
/// </exception>
/// <exception cref="System.FormatException">value is not in the correct format.</exception>
/// <exception cref="System.OverflowException">value represents a number less than System.Half.MinValue or greater than System.Half.MaxValue.</exception>
public static Half Parse(string value, NumberStyles style)
{
return (Half) float.Parse(value, style, CultureInfo.InvariantCulture);
}
/// <summary>
/// Converts the string representation of a number to its System.Half equivalent
/// using the specified style and culture-specific format.
/// </summary>
/// <param name="value">The string representation of the number to convert.</param>
/// <param name="style">
/// A bitwise combination of System.Globalization.NumberStyles values that indicates
/// the style elements that can be present in value. A typical value to specify is
/// System.Globalization.NumberStyles.Number.
/// </param>
/// <param name="provider">An System.IFormatProvider object that supplies culture-specific information about the format of value.</param>
/// <returns>The System.Half number equivalent to the number contained in s as specified by style and provider.</returns>
/// <exception cref="System.ArgumentNullException">value is null.</exception>
/// <exception cref="System.ArgumentException">
/// style is not a System.Globalization.NumberStyles value. -or- style is the
/// System.Globalization.NumberStyles.AllowHexSpecifier value.
/// </exception>
/// <exception cref="System.FormatException">value is not in the correct format.</exception>
/// <exception cref="System.OverflowException">value represents a number less than System.Half.MinValue or greater than System.Half.MaxValue.</exception>
public static Half Parse(string value, NumberStyles style, IFormatProvider provider)
{
return (Half) float.Parse(value, style, provider);
}
/// <summary>
/// Converts the string representation of a number to its System.Half equivalent.
/// A return value indicates whether the conversion succeeded or failed.
/// </summary>
/// <param name="value">The string representation of the number to convert.</param>
/// <param name="result">
/// When this method returns, contains the System.Half number that is equivalent
/// to the numeric value contained in value, if the conversion succeeded, or is zero
/// if the conversion failed. The conversion fails if the s parameter is null,
/// is not a number in a valid format, or represents a number less than System.Half.MinValue
/// or greater than System.Half.MaxValue. This parameter is passed uninitialized.
/// </param>
/// <returns>true if s was converted successfully; otherwise, false.</returns>
public static bool TryParse(string value, out Half result)
{
float f;
if (float.TryParse(value, out f))
{
result = (Half) f;
return true;
}
result = new Half();
return false;
}
/// <summary>
/// Converts the string representation of a number to its System.Half equivalent
/// using the specified style and culture-specific format. A return value indicates
/// whether the conversion succeeded or failed.
/// </summary>
/// <param name="value">The string representation of the number to convert.</param>
/// <param name="style">
/// A bitwise combination of System.Globalization.NumberStyles values that indicates
/// the permitted format of value. A typical value to specify is System.Globalization.NumberStyles.Number.
/// </param>
/// <param name="provider">An System.IFormatProvider object that supplies culture-specific parsing information about value.</param>
/// <param name="result">
/// When this method returns, contains the System.Half number that is equivalent
/// to the numeric value contained in value, if the conversion succeeded, or is zero
/// if the conversion failed. The conversion fails if the s parameter is null,
/// is not in a format compliant with style, or represents a number less than
/// System.Half.MinValue or greater than System.Half.MaxValue. This parameter is passed uninitialized.
/// </param>
/// <returns>true if s was converted successfully; otherwise, false.</returns>
/// <exception cref="System.ArgumentException">
/// style is not a System.Globalization.NumberStyles value. -or- style
/// is the System.Globalization.NumberStyles.AllowHexSpecifier value.
/// </exception>
public static bool TryParse(string value, NumberStyles style, IFormatProvider provider, out Half result)
{
var parseResult = false;
float f;
if (float.TryParse(value, style, provider, out f))
{
result = (Half) f;
parseResult = true;
}
else
{
result = new Half();
}
return parseResult;
}
/// <summary>
/// Converts the numeric value of this instance to its equivalent string representation.
/// </summary>
/// <returns>A string that represents the value of this instance.</returns>
public override string ToString()
{
return ((float) this).ToString(CultureInfo.InvariantCulture);
}
/// <summary>
/// Converts the numeric value of this instance to its equivalent string representation
/// using the specified culture-specific format information.
/// </summary>
/// <param name="formatProvider">An System.IFormatProvider that supplies culture-specific formatting information.</param>
/// <returns>The string representation of the value of this instance as specified by provider.</returns>
public string ToString(IFormatProvider formatProvider)
{
return ((float) this).ToString(formatProvider);
}
/// <summary>
/// Converts the numeric value of this instance to its equivalent string representation, using the specified format.
/// </summary>
/// <param name="format">A numeric format string.</param>
/// <returns>The string representation of the value of this instance as specified by format.</returns>
public string ToString(string format)
{
return ((float) this).ToString(format, CultureInfo.InvariantCulture);
}
/// <summary>
/// Converts the numeric value of this instance to its equivalent string representation
/// using the specified format and culture-specific format information.
/// </summary>
/// <param name="format">A numeric format string.</param>
/// <param name="formatProvider">An System.IFormatProvider that supplies culture-specific formatting information.</param>
/// <returns>The string representation of the value of this instance as specified by format and provider.</returns>
/// <exception cref="System.FormatException">format is invalid.</exception>
public string ToString(string? format, IFormatProvider? formatProvider)
{
return ((float) this).ToString(format, formatProvider);
}
#endregion
#region IConvertible Members
float IConvertible.ToSingle(IFormatProvider? provider)
{
return this;
}
TypeCode IConvertible.GetTypeCode()
{
return GetTypeCode();
}
bool IConvertible.ToBoolean(IFormatProvider? provider)
{
return Convert.ToBoolean(this);
}
byte IConvertible.ToByte(IFormatProvider? provider)
{
return Convert.ToByte(this);
}
char IConvertible.ToChar(IFormatProvider? provider)
{
throw new InvalidCastException(string.Format(CultureInfo.CurrentCulture, "Invalid cast from '{0}' to '{1}'.", "Half", "Char"));
}
DateTime IConvertible.ToDateTime(IFormatProvider? provider)
{
throw new InvalidCastException(string.Format(CultureInfo.CurrentCulture, "Invalid cast from '{0}' to '{1}'.", "Half", "DateTime"));
}
decimal IConvertible.ToDecimal(IFormatProvider? provider)
{
return Convert.ToDecimal(this);
}
double IConvertible.ToDouble(IFormatProvider? provider)
{
return Convert.ToDouble(this);
}
short IConvertible.ToInt16(IFormatProvider? provider)
{
return Convert.ToInt16(this);
}
int IConvertible.ToInt32(IFormatProvider? provider)
{
return Convert.ToInt32(this);
}
long IConvertible.ToInt64(IFormatProvider? provider)
{
return Convert.ToInt64(this);
}
sbyte IConvertible.ToSByte(IFormatProvider? provider)
{
return Convert.ToSByte(this);
}
string IConvertible.ToString(IFormatProvider? provider)
{
return Convert.ToString(this, CultureInfo.InvariantCulture);
}
object IConvertible.ToType(Type conversionType, IFormatProvider? provider)
{
return (((float) this) as IConvertible).ToType(conversionType, provider);
}
ushort IConvertible.ToUInt16(IFormatProvider? provider)
{
return Convert.ToUInt16(this);
}
uint IConvertible.ToUInt32(IFormatProvider? provider)
{
return Convert.ToUInt32(this);
}
ulong IConvertible.ToUInt64(IFormatProvider? provider)
{
return Convert.ToUInt64(this);
}
#endregion
}
}
/// ================ HalfHelper.cs ====================
namespace SystemHalf
{
/// <summary>
/// Helper class for Half conversions and some low level operations.
/// This class is internally used in the Half class.
/// </summary>
/// <remarks>
/// References:
/// - Code retrieved from http://sourceforge.net/p/csharp-half/code/HEAD/tree/ on 2015-12-04
/// - Fast Half Float Conversions, Jeroen van der Zijp, link: http://www.fox-toolkit.org/ftp/fasthalffloatconversion.pdf
/// </remarks>
internal static class HalfHelper
{
private static readonly uint[] MantissaTable = GenerateMantissaTable();
private static readonly uint[] ExponentTable = GenerateExponentTable();
private static readonly ushort[] OffsetTable = GenerateOffsetTable();
private static readonly ushort[] BaseTable = GenerateBaseTable();
private static readonly sbyte[] ShiftTable = GenerateShiftTable();
// Transforms the subnormal representation to a normalized one.
private static uint ConvertMantissa(int i)
{
var 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()
{
var mantissaTable = new uint[2048];
mantissaTable[0] = 0;
for (var i = 1; i < 1024; i++)
{
mantissaTable[i] = ConvertMantissa(i);
}
for (var i = 1024; i < 2048; i++)
{
mantissaTable[i] = (uint) (0x38000000 + ((i - 1024) << 13));
}
return mantissaTable;
}
private static uint[] GenerateExponentTable()
{
var exponentTable = new uint[64];
exponentTable[0] = 0;
for (var i = 1; i < 31; i++)
{
exponentTable[i] = (uint) (i << 23);
}
exponentTable[31] = 0x47800000;
exponentTable[32] = 0x80000000;
for (var i = 33; i < 63; i++)
{
exponentTable[i] = (uint) (0x80000000 + ((i - 32) << 23));
}
exponentTable[63] = 0xc7800000;
return exponentTable;
}
private static ushort[] GenerateOffsetTable()
{
var offsetTable = new ushort[64];
offsetTable[0] = 0;
for (var i = 1; i < 32; i++)
{
offsetTable[i] = 1024;
}
offsetTable[32] = 0;
for (var i = 33; i < 64; i++)
{
offsetTable[i] = 1024;
}
return offsetTable;
}
private static ushort[] GenerateBaseTable()
{
var baseTable = new ushort[512];
for (var i = 0; i < 256; ++i)
{
var 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()
{
var shiftTable = new sbyte[512];
for (var i = 0; i < 256; ++i)
{
var 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 float HalfToSingle(Half half)
{
var result = MantissaTable[OffsetTable[half.Value >> 10] + (half.Value & 0x3ff)] + ExponentTable[half.Value >> 10];
return BitConverter.ToSingle(new[] { (byte) (result & 0xFF), (byte) ((result >> 8) & 0xFF), (byte) ((result >> 16) & 0xFF), (byte) ((result >> 24) & 0xFF) }, 0);
}
public static Half SingleToHalf(float single)
{
var bits = BitConverter.GetBytes(single);
var value = (uint) bits[0] | ((uint) bits[1] << 8) | ((uint) bits[2] << 16) | ((uint) bits[3] << 24);
var 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;
}
}
}