RatNum

public struct RatNum : Comparable, CustomStringConvertible

AbstractState: RatNum represents an immutable rational number. It includes all of the elements in the set of rationals, as well as the special NaN (not-a-number) element that results from division by zero.

The NaN element is special in many ways. Any arithmetic operation (such as addition) involving NaN will return NaN. With respect to comparison operations, such as less-than, NaN is considered equal to itself, and larger than all other rationals.

Examples of RatNums include -1/13, 53/7, 4, NaN, and 0.

  • nan

    A constant holding a Not-a-Number (NaN) value of type RatNum

    Declaration

    Swift

    public static let nan: RatNum

  • A constant holding a zero value of type RatNum

    Declaration

    Swift

    public static let zero: RatNum
  • one

    A constant holding a one value of type RatNum

    Declaration

    Swift

    public static let one: RatNum

  • Effect: If d = 0, constructs a new RatNum = NaN. Else constructs a new RatNum = (n / d).

    Declaration

    Swift

    public init(_ n: Int, _ d: Int)

    Parameters

    n

    The numerator of the new RatNum.
    d

    The denominator of the new RatNum.

  • Effect: Constructs a new RatNum = n.

    Declaration

    Swift

    public init(_ n: Int)

    Parameters

    n

    The value of the new RatNum.

  • Makes a RatNum from a string describing it.

    Requires: ‘description’ is an instance of a string, with no spaces, of the form:

    • NaN
    • N/M, where N and M are both integers in decimal notation, and M != 0, or

    • N, where N is an integer in decimal notation.

    • NaN if description = NaN.

    • A RatNum r = ( N / M ), letting M be 1 in the case where only N is passed in.

    Declaration

    Swift

    public init?(_ description: String)

    Parameters

    description

    A string of the format described in the requires clause.

    Return Value

    Either:

  • true iff self is NaN (not-a-number)

    Declaration

    Swift

    public var isNaN: Bool { get }

  • true iff self > 0

    Declaration

    Swift

    public var isPositive: Bool { get }

  • true iff self < 0

    Declaration

    Swift

    public var isNegative: Bool { get }

  • An approximate value of this rational. Note that NaN is mapped to Double.nan, which is treated in a special manner by several arithmetic operations, such as the comparison and equality operators.

    Declaration

    Swift

    public var asDouble: Double { get }

  • A String representing self, in reduced terms. It will either be NaN, or it will take on either of the forms N or N/M, where N and M are both integers in decimal notation and M != 0.

    Declaration

    Swift

    public var description: String { get }

  • Declaration

    Swift

    public static func < (lhs: RatNum, rhs: RatNum) -> Bool

    Return Value

    true iff lhs < rhs

  • Declaration

    Swift

    public static func == (lhs: RatNum, rhs: RatNum) -> Bool

    Return Value

    true iff lhs == rhs

  • Declaration

    Swift

    public static func + (lhs: RatNum, rhs: RatNum) -> RatNum

    Return Value

    lhs + rhs, or NaN if either lhs or rhs is NaN

  • Declaration

    Swift

    public static func - (lhs: RatNum, rhs: RatNum) -> RatNum

    Return Value

    lhs - rhs, or NaN if either lhs or rhs is NaN

  • Declaration

    Swift

    public static func * (lhs: RatNum, rhs: RatNum) -> RatNum

    Return Value

    lhs * rhs, or NaN if either lhs or rhs is NaN

  • Declaration

    Swift

    public static func / (lhs: RatNum, rhs: RatNum) -> RatNum

    Return Value

    lhs / rhs, or NaN if either lhs or rhs is NaN or rhs == 0

  • Declaration

    Swift

    public prefix static func - (n: RatNum) -> RatNum

    Return Value

    the additive inverse of n (ie, 0 - n)