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Fraction.cs
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Fraction.cs
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using Qowaiv.Conversion.Mathematics;
using System.Runtime.InteropServices;
namespace Qowaiv.Mathematics;
/// <summary>Represents a fraction.</summary>
[DebuggerDisplay("{DebuggerDisplay}")]
[Serializable]
[SingleValueObject(SingleValueStaticOptions.Continuous, typeof(Tuple<long, long>))]
[OpenApiDataType(description: "Faction", type: "string", format: "faction", pattern: "-?[0-9]+(/[0-9]+)?", example: "13/42")]
[TypeConverter(typeof(FractionTypeConverter))]
#if NET6_0_OR_GREATER
[System.Text.Json.Serialization.JsonConverter(typeof(Json.Mathematics.FractionJsonConverter))]
#endif
[StructLayout(LayoutKind.Sequential)]
public readonly partial struct Fraction : IXmlSerializable, IFormattable, IEquatable<Fraction>, IComparable, IComparable<Fraction>
#if NET8_0_OR_GREATER
#else
, ISerializable
#endif
{
/// <summary>Represents the zero (0) <see cref="Fraction"/> value.</summary>
/// <remarks>
/// Is the default value of <see cref="Fraction"/>.
/// </remarks>
public static Fraction Zero => default;
/// <summary>Represents the one (1) <see cref="Fraction"/> value.</summary>
public static Fraction One => New(1, 1);
/// <summary>Represents the smallest positive <see cref="Fraction"/> value that is greater than zero.</summary>
public static readonly Fraction Epsilon = New(1, long.MaxValue);
/// <summary>Represents the largest possible value of a <see cref="Fraction"/>.</summary>
public static Fraction MaxValue => New(+long.MaxValue, 1);
/// <summary>Represents the smallest possible value of a <see cref="Fraction"/>.</summary>
public static Fraction MinValue => New(-long.MaxValue, 1);
internal static partial class Formatting
{
public const string SuperScript = "⁰¹²³⁴⁵⁶⁷⁸⁹";
public const string SubScript = "₀₁₂₃₄₅₆₇₈₉";
public const char Slash = '/';
public const char Colon = ':';
public const char DivisionSign = '÷';
public const char FractionSlash = (char)0x2044;
public const char DivisionSlash = (char)0x2215;
public const char ShortSlash = (char)0x337;
public const char LongSlash = (char)0x338;
/// <summary>The different supported fraction bar characters.</summary>
/// <remarks>
/// name | c | code
/// ---------------|---|------
/// slash | / | 5C
/// colon | : | 3A
/// division sign | ÷ | F7
/// fraction slash | ⁄ | 2044
/// division slash | ∕ | 2215
/// short slash | ̷ | 337
/// long slash | ̸ | 338.
/// </remarks>
public static readonly string FractionBars = new(
[
Slash,
Colon,
DivisionSign,
FractionSlash,
DivisionSlash,
ShortSlash,
LongSlash,
]);
public static readonly Regex Pattern = GetPattern();
#if NET8_0_OR_GREATER
[GeneratedRegex(@"^(\[(?<Whole>.+)\] ?)?(?<Numerator>.+?)(?<FractionBars>[/:÷⁄∕̷̸])(?<Denominator>.+)$", RegOptions.Default, RegOptions.TimeoutMilliseconds)]
private static partial Regex GetPattern();
#else
[Pure]
private static Regex GetPattern() => new(
@"^(\[(?<Whole>.+)\] ?)?(?<Numerator>.+?)(?<FractionBars>[/:÷⁄∕̷̸])(?<Denominator>.+)$",
RegOptions.Default,
RegOptions.Timeout);
#endif
/// <summary>Returns true if the <see cref="char"/> is a supported fraction bar.</summary>
[Pure]
public static bool IsFractionBar(char ch) => FractionBars.Contains(ch);
}
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private readonly long numerator;
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private readonly long denominator;
/// <summary>Initializes a new instance of the <see cref="Fraction"/> struct.</summary>
/// <param name="numerator">
/// The numerator part of the fraction.
/// </param>
/// <param name="denominator">
/// The denominator part of the fraction.
/// </param>
/// <exception cref="DivideByZeroException">
/// if the <paramref name="denominator"/> is zero.
/// </exception>
/// <remarks>
/// If the fraction is negative, the numerator 'carries' the sign.
/// Furthermore, the numerator and denominator are reduced (so 2/4
/// becomes 1/2).
/// </remarks>
public Fraction(long numerator, long denominator)
: this(new Data(numerator, denominator).Guard().Simplify()) { }
/// <summary>Initializes a new instance of the <see cref="Fraction"/> struct.</summary>
private Fraction(Data data)
{
numerator = data.numerator;
denominator = data.denominator;
}
/// <summary>Gets the numerator of the fraction.</summary>
public long Numerator => numerator;
/// <summary>Gets the denominator of the fraction.</summary>
public long Denominator => IsZero() ? 1 : denominator;
/// <summary>Get whole of the fraction.</summary>
public long Whole => IsZero() ? 0 : numerator / denominator;
/// <summary>Gets the remainder of the fraction.</summary>
/// <remarks>
/// The remainder is expressed as an absolute value.
/// </remarks>
public long Remainder => IsZero() ? 0 : (numerator % denominator).Abs();
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private string DebuggerDisplay => this.DebuggerDisplay("{0:super⁄sub} = {0:0.########}");
/// <summary>Returns true if the faction is zero.</summary>
[Pure]
public bool IsZero() => numerator == 0;
/// <summary>Gets the sign of the fraction.</summary>
[Pure]
public int Sign() => Math.Sign(numerator);
/// <summary>Returns the absolute value of the fraction.</summary>
[Pure]
public Fraction Abs() => New(numerator.Abs(), denominator);
/// <summary>Gets the inverse of a faction.</summary>
/// <exception cref="DivideByZeroException">
/// When the fraction is <see cref="Zero"/>.
/// </exception>
[Pure]
public Fraction Inverse()
=> IsZero()
? throw new DivideByZeroException()
: New(Sign() * denominator, numerator.Abs());
/// <summary>Returns a formatted <see cref = "string "/> that represents the fraction.</summary>
/// <param name = "format">
/// The format that this describes the formatting.
/// </param>
/// <param name = "formatProvider">
/// The format provider.
/// </param>
[Pure]
public string ToString(string? format, IFormatProvider? formatProvider)
{
if (StringFormatter.TryApplyCustomFormatter(format, this, formatProvider, out string formatted))
{
return formatted;
}
else if (Formatting.Pattern.Match(format.WithDefault("0/0")) is { Success: true } match)
{
return ToString(formatProvider, match);
}
// if no fraction bar character has been provided, format as a decimal.
else if (!format.WithDefault().Any(Formatting.IsFractionBar))
{
return ToDecimal().ToString(format, formatProvider);
}
else throw new FormatException(QowaivMessages.FormatException_InvalidFormat);
}
[Pure]
private string ToString(IFormatProvider? formatProvider, Match match)
{
var sb = new StringBuilder();
var remainder = AppendWhole(sb, match.Groups[nameof(Whole)].Value, formatProvider);
AppendNumerator(sb, remainder, match.Groups[nameof(Numerator)].Value, formatProvider);
sb.Append(match.Groups[nameof(Formatting.FractionBars)].Value);
AppendDenominator(sb, match.Groups[nameof(Denominator)].Value, formatProvider);
return sb.ToString();
}
[Impure]
private long AppendWhole(StringBuilder sb, string format, IFormatProvider? formatProvider)
{
if (!string.IsNullOrEmpty(format))
{
sb.Append(Whole.ToString(format, formatProvider));
// For -0 n/d
if (Whole == 0 && Sign() == -1 && sb.Length != 0 && !sb.ToString().Contains(formatProvider.NegativeSign()))
{
sb.Insert(0, formatProvider.NegativeSign());
}
return Remainder;
}
else return numerator;
}
private void AppendNumerator(StringBuilder sb, long remainder, string format, IFormatProvider? formatProvider)
{
if (format == "super")
{
if (sb.Length == 0 && Sign() == -1)
{
sb.Append(formatProvider.NegativeSign());
}
// use invariant as we want to convert to superscript.
var super = remainder.Abs().ToString(CultureInfo.InvariantCulture).Select(ch => Formatting.SuperScript[ASCII.Number(ch)]).ToArray();
sb.Append(super);
}
else
{
if (sb.Length != 0 && sb[^1] != ' ')
{
sb.Append(' ');
}
sb.Append(remainder.ToString(format, formatProvider));
}
}
private void AppendDenominator(StringBuilder sb, string format, IFormatProvider? formatProvider)
{
if (format == "sub")
{
// use invariant as we want to convert to superscript.
var super = Denominator.ToString(CultureInfo.InvariantCulture).Select(ch => Formatting.SubScript[ASCII.Number(ch)]).ToArray();
sb.Append(super);
}
else
{
sb.Append(Denominator.ToString(format, formatProvider));
}
}
/// <inheritdoc/>
[Pure]
public bool Equals(Fraction other)
{
// to deal with zero (default should be zero).
if (IsZero() && other.IsZero())
{
return true;
}
return denominator == other.denominator
&& numerator == other.numerator;
}
/// <inheritdoc/>
[Pure]
public override int GetHashCode() => Hash.Code(denominator).And(numerator);
/// <inheritdoc/>
[Pure]
public int CompareTo(Fraction other)
{
if (denominator == other.denominator || IsZero() || other.IsZero())
{
return numerator.CompareTo(other.numerator);
}
// To prevent overflows, normalize the numerators as double only.
var self = (double)numerator * other.denominator;
var othr = (double)other.numerator * denominator;
return self.CompareTo(othr);
}
#if NET8_0_OR_GREATER
#else
/// <summary>Initializes a new instance of the <see cref="Fraction"/> struct.</summary>
/// <param name="info">The serialization info.</param>
/// <param name="context">The streaming context.</param>
private Fraction(SerializationInfo info, StreamingContext context)
{
Guard.NotNull(info);
var n = info.GetInt64(nameof(numerator));
var d = info.GetInt64(nameof(denominator));
if (n != default || d != default)
{
var data = new Data(n, d).Guard().Simplify();
numerator = data.numerator;
denominator = data.denominator;
}
}
/// <summary>Adds the underlying property of the fraction to the serialization info.</summary>
/// <param name="info">The serialization info.</param>
/// <param name="context">The streaming context.</param>
void ISerializable.GetObjectData(SerializationInfo info, StreamingContext context)
{
Guard.NotNull(info);
info.AddValue(nameof(numerator), numerator);
info.AddValue(nameof(denominator), denominator);
}
#endif
/// <summary>Gets an XML string representation of the fraction.</summary>
[Pure]
private string ToXmlString() => ToString(CultureInfo.InvariantCulture);
/// <summary>Gets an JSON representation of the fraction.</summary>
[Pure]
public string ToJson() => ToString(CultureInfo.InvariantCulture);
/// <summary>Deserializes the fraction from a JSON number.</summary>
/// <param name = "json">
/// The JSON number to deserialize.
/// </param>
/// <returns>
/// The deserialized fraction.
/// </returns>
[Pure]
public static Fraction FromJson(decimal json) => Cast(json);
/// <summary>Deserializes the fraction from a JSON number.</summary>
/// <param name = "json">
/// The JSON number to deserialize.
/// </param>
/// <returns>
/// The deserialized fraction.
/// </returns>
[Pure]
public static Fraction FromJson(double json) => Cast(json);
/// <summary>Deserializes the fraction from a JSON number.</summary>
/// <param name = "json">
/// The JSON number to deserialize.
/// </param>
/// <returns>
/// The deserialized fraction.
/// </returns>
[Pure]
public static Fraction FromJson(long json) => New(json, 1);
/// <summary>Casts the fraction to a <see cref="decimal"/>.</summary>
[Pure]
private decimal ToDecimal() => IsZero() ? decimal.Zero : numerator / (decimal)denominator;
/// <summary>Casts the fraction to a <see cref="double"/>.</summary>
[Pure]
private double ToDouble() => IsZero() ? 0d : numerator / (double)denominator;
/// <summary>Casts a <see cref="decimal"/> to a fraction.</summary>
[Pure]
private static Fraction Cast(decimal number)
=> number < MinValue.numerator || number > MaxValue.numerator
? throw new OverflowException(QowaivMessages.OverflowException_Fraction)
: Create(number, MinimumError);
/// <summary>Casts a <see cref="double"/> to a fraction.</summary>
[Pure]
private static Fraction Cast(double number)
=> number < MinValue.numerator || number > MaxValue.numerator
? throw new OverflowException(QowaivMessages.OverflowException_Fraction)
: Create((decimal)number, MinimumError);
/// <summary>Casts a <see cref="decimal"/> to a <see cref="Fraction"/>.</summary>
public static explicit operator Fraction(decimal number) => Cast(number);
/// <summary>Casts a <see cref="decimal"/> to a <see cref="Fraction"/>.</summary>
public static explicit operator decimal(Fraction fraction) => fraction.ToDecimal();
/// <summary>Casts a <see cref="Percentage"/> to a <see cref="Fraction"/>.</summary>
public static explicit operator Fraction(Percentage number) => Cast((decimal)number);
/// <summary>Casts a <see cref="Percentage"/> to a <see cref="Fraction"/>.</summary>
public static explicit operator Percentage(Fraction fraction) => Percentage.Create(fraction.ToDecimal());
/// <summary>Casts a <see cref="double"/> to a <see cref="Fraction"/>.</summary>
public static explicit operator Fraction(double number) => Cast(number);
/// <summary>Casts a <see cref="double"/> to a <see cref="Fraction"/>.</summary>
public static explicit operator double(Fraction fraction) => fraction.ToDouble();
/// <summary>Casts a <see cref="long"/> to a <see cref="Fraction"/>.</summary>
public static explicit operator Fraction(long number) => Create(number);
/// <summary>Casts a <see cref="long"/> to a <see cref="Fraction"/>.</summary>
public static explicit operator long(Fraction fraction) => fraction.Whole;
/// <summary>Converts the <see cref = "string "/> to <see cref = "Fraction"/>.
/// A return value indicates whether the conversion succeeded.
/// </summary>
/// <param name = "s">
/// A string containing the fraction to convert.
/// </param>
/// <param name = "provider">
/// The specified format provider.
/// </param>
/// <param name = "result">
/// The result of the parsing.
/// </param>
/// <returns>
/// True if the string was converted successfully, otherwise false.
/// </returns>
public static bool TryParse(string? s, IFormatProvider? provider, out Fraction result)
{
if (s is { Length: > 0 } && FractionParser.Parse(s, provider) is { } fraction)
{
result = fraction;
return true;
}
else
{
result = Zero;
return false;
}
}
/// <summary>Creates a fraction based on a <see cref="decimal"/>.</summary>
/// <param name="number">
/// The decimal value to represent as a fraction.
/// </param>
[Pure]
public static Fraction Create(decimal number) => Create(number, MinimumError);
/// <summary>Creates a fraction based on a <see cref="double"/>.</summary>
/// <param name="number">
/// The double value to represent as a fraction.
/// </param>
[Pure]
public static Fraction Create(double number)
=> number < (double)decimal.MinValue || number > (double)decimal.MaxValue
? throw new ArgumentOutOfRangeException(nameof(number), QowaivMessages.OverflowException_Fraction)
: Create((decimal)number, MinimumError);
/// <summary>Creates a fraction based on a <see cref="long"/>.</summary>
/// <param name="number">
/// The long value to represent as a fraction.
/// </param>
[Pure]
public static Fraction Create(long number) => number == 0 ? Zero : New(number, 1);
/// <summary>Initializes a new instance of the <see cref="Fraction"/> class.</summary>
/// <exception cref="OverflowException">
/// If the numerator is <see cref="long.MinValue"/>.
/// </exception>
/// <remarks>
/// This pseudo constructor differs from the public constructor that it
/// does not reduce any value, nor checks the denominator.
/// </remarks>
[Pure]
private static Fraction New(long n, long d)
=> n == long.MinValue
? throw new OverflowException(QowaivMessages.OverflowException_Fraction)
: new(new Data(numerator: n, denominator: d));
/// <summary>Reduce the numbers based on the greatest common divisor.</summary>
private static void Reduce(ref long a, ref long b)
{
var gcd = Gcd(a, b);
a /= gcd;
b /= gcd;
}
/// <summary>Gets the Greatest Common Divisor.</summary>
/// <remarks>
/// See: https://en.wikipedia.org/wiki/Greatest_common_divisor.
/// </remarks>
[Pure]
private static long Gcd(long a, long b)
{
long even = 1;
// while both are even.
while ((a & 1) == 0 && (b & 1) == 0)
{
a >>= 1;
b >>= 1;
even <<= 1;
}
while (b != 0)
{
(a, b) = (b, a % b);
}
return a * even;
}
/// <remarks>
/// to pass the two components around during creation.
/// </remarks>
private ref struct Data(long numerator, long denominator)
{
public long numerator = numerator;
public long denominator = denominator;
[FluentSyntax]
public readonly Data Guard()
{
#pragma warning disable S3928 // Parameter names used into ArgumentException constructors should match an existing one
if (numerator == long.MinValue)
{
throw new ArgumentOutOfRangeException(nameof(numerator), QowaivMessages.OverflowException_Fraction);
}
if (denominator == 0 || denominator == long.MinValue)
{
throw new ArgumentOutOfRangeException(nameof(denominator), QowaivMessages.OverflowException_Fraction);
}
#pragma warning restore S3928 // Parameter names used into ArgumentException constructors should match an existing one
return this;
}
/// <summary>Reduce the numbers based on the greatest common divisor.</summary>
[FluentSyntax]
public Data Simplify()
{
var negative = numerator < 0 ^ denominator < 0;
numerator = Math.Abs(numerator);
denominator = Math.Abs(denominator);
Reduce(ref numerator, ref denominator);
if (negative)
{
numerator = -numerator;
}
return this;
}
}
}