Protocol

BinaryInteger

An integer type with a binary representation.

Declaration

protocol BinaryInteger where Self.Magnitude : BinaryInteger, Self.Magnitude == Self.Magnitude.Magnitude

Overview

The BinaryInteger protocol is the basis for all the integer types provided by the standard library. All of the standard library’s integer types, such as Int and UInt32, conform to BinaryInteger.

Converting Between Numeric Types

You can create new instances of a type that conforms to the BinaryInteger protocol from a floating-point number or another binary integer of any type. The BinaryInteger protocol provides initializers for four different kinds of conversion.

Range-Checked Conversion

You use the default init(_:) initializer to create a new instance when you’re sure that the value passed is representable in the new type. For example, an instance of Int16 can represent the value 500, so the first conversion in the code sample below succeeds. That same value is too large to represent as an Int8 instance, so the second conversion fails, triggering a runtime error.

let x: Int = 500
let y = Int16(x)
// y == 500

let z = Int8(x)
// Error: Not enough bits to represent...

When you create a binary integer from a floating-point value using the default initializer, the value is rounded toward zero before the range is checked. In the following example, the value 127.75 is rounded to 127, which is representable by the Int8 type. 128.25 is rounded to 128, which is not representable as an Int8 instance, triggering a runtime error.

let e = Int8(127.75)
// e == 127

let f = Int8(128.25)
// Error: Double value cannot be converted...

Exact Conversion

Use the init?(exactly:) initializer to create a new instance after checking whether the passed value is representable. Instead of trapping on out-of-range values, using the failable exact initializer results in nil.

let x = Int16(exactly: 500)
// x == Optional(500)

let y = Int8(exactly: 500)
// y == nil

When converting floating-point values, the init?(exact:) initializer checks both that the passed value has no fractional part and that the value is representable in the resulting type.

let e = Int8(exactly: 23.0)       // integral value, representable
// e == Optional(23)

let f = Int8(exactly: 23.75)      // fractional value, representable
// f == nil

let g = Int8(exactly: 500.0)      // integral value, nonrepresentable
// g == nil

Clamping Conversion

Use the init(clamping:) initializer to create a new instance of a binary integer type where out-of-range values are clamped to the representable range of the type. For a type T, the resulting value is in the range T.min...T.max.

let x = Int16(clamping: 500)
// x == 500

let y = Int8(clamping: 500)
// y == 127

let z = UInt8(clamping: -500)
// z == 0

Bit Pattern Conversion

Use the init(truncatingIfNeeded:) initializer to create a new instance with the same bit pattern as the passed value, extending or truncating the value’s representation as necessary. Note that the value may not be preserved, particularly when converting between signed to unsigned integer types or when the destination type has a smaller bit width than the source type. The following example shows how extending and truncating work for nonnegative integers:

let q: Int16 = 850
// q == 0b00000011_01010010

let r = Int8(truncatingIfNeeded: q)      // truncate 'q' to fit in 8 bits
// r == 82
//   == 0b01010010

let s = Int16(truncatingIfNeeded: r)     // extend 'r' to fill 16 bits
// s == 82
//   == 0b00000000_01010010

Any padding is performed by sign-extending the passed value. When nonnegative integers are extended, the result is padded with zeroes. When negative integers are extended, the result is padded with ones. This example shows several extending conversions of a negative value—note that negative values are sign-extended even when converting to an unsigned type.

let t: Int8 = -100
// t == -100
// t's binary representation == 0b10011100

let u = UInt8(truncatingIfNeeded: t)
// u == 156
// u's binary representation == 0b10011100

let v = Int16(truncatingIfNeeded: t)
// v == -100
// v's binary representation == 0b11111111_10011100

let w = UInt16(truncatingIfNeeded: t)
// w == 65436
// w's binary representation == 0b11111111_10011100

Comparing Across Integer Types

You can use relational operators, such as the less-than and equal-to operators (< and ==), to compare instances of different binary integer types. The following example compares instances of the Int, UInt, and UInt8 types:

let x: Int = -23
let y: UInt = 1_000
let z: UInt8 = 23

if x < y {
    print("\(x) is less than \(y).")
}
// Prints "-23 is less than 1000."

if z > x {
    print("\(z) is greater than \(x).")
}
// Prints "23 is greater than -23."

Topics

Associated Types

associatedtype Words

A type that represents the words of a binary integer.

Required.

Initializers

init()

Creates a new value equal to zero.

init<T>(T)

Creates an integer from the given floating-point value, rounding toward zero.

Required. Default implementations provided.

init<T>(T)

Creates a new instance from the given integer.

Required.

init<T>(clamping: T)

Creates a new instance with the representable value that’s closest to the given integer.

Required. Default implementation provided.

init?<T>(exactly: T)

Creates an integer from the given floating-point value, if it can be represented exactly.

Required. Default implementations provided.

init<T>(truncatingIfNeeded: T)

Creates a new instance from the bit pattern of the given instance by sign-extending or truncating to fit this type.

Required. Default implementation provided.

Instance Properties

var bitWidth: Int

The number of bits in the current binary representation of this value.

Required.

var trailingZeroBitCount: Int

The number of trailing zeros in this value’s binary representation.

Required.

var words: Self.Words

A collection containing the words of this value’s binary representation, in order from the least significant to most significant.

Required.

Type Properties

static var isSigned: Bool

A Boolean value indicating whether this type is a signed integer type.

Required. Default implementations provided.

Instance Methods

func quotientAndRemainder(dividingBy: Self) -> (quotient: Self, remainder: Self)

Returns the quotient and remainder of this value divided by the given value.

Required. Default implementation provided.

func signum() -> Self

Returns -1 if this value is negative and 1 if it’s positive; otherwise, 0.

Required. Default implementation provided.

Operator Functions

static func != <Other>(Self, Other) -> Bool

Returns a Boolean value indicating whether the two given values are not equal.

static func % (Self, Self) -> Self

Returns the remainder of dividing the first value by the second.

Required.

static func %= (inout Self, Self)

Divides the first value by the second and stores the remainder in the left-hand-side variable.

Required.

static func & (Self, Self) -> Self

Returns the result of performing a bitwise AND operation on the two given values.

Required. Default implementation provided.

static func &= (inout Self, Self)

Stores the result of performing a bitwise AND operation on the two given values in the left-hand-side variable.

Required.

static func * (Self, Self) -> Self

Multiplies two values and produces their product.

Required.

static func *= (inout Self, Self)

Multiplies two values and stores the result in the left-hand-side variable.

Required.

static func + (Self, Self) -> Self

Adds two values and produces their sum.

Required.

static func += (inout Self, Self)

Adds two values and stores the result in the left-hand-side variable.

Required.

static func - (Self, Self) -> Self

Subtracts one value from another and produces their difference.

Required.

static func -= (inout Self, Self)

Subtracts the second value from the first and stores the difference in the left-hand-side variable.

Required.

static func / (Self, Self) -> Self

Returns the quotient of dividing the first value by the second.

Required.

static func /= (inout Self, Self)

Divides the first value by the second and stores the quotient in the left-hand-side variable.

Required.

static func < <Other>(Self, Other) -> Bool

Returns a Boolean value indicating whether the value of the first argument is less than that of the second argument.

static func << <RHS>(Self, RHS) -> Self

Returns the result of shifting a value’s binary representation the specified number of digits to the left.

Required. Default implementations provided.

static func <<= <RHS>(inout Self, RHS)

Stores the result of shifting a value’s binary representation the specified number of digits to the left in the left-hand-side variable.

Required. Default implementation provided.

static func <= (Self, Self) -> Bool

Returns a Boolean value indicating whether the value of the first argument is less than or equal to that of the second argument.

static func <= <Other>(Self, Other) -> Bool

Returns a Boolean value indicating whether the value of the first argument is less than or equal to that of the second argument.

static func == <Other>(Self, Other) -> Bool

Returns a Boolean value indicating whether the two given values are equal.

static func > <Other>(Self, Other) -> Bool

Returns a Boolean value indicating whether the value of the first argument is greater than that of the second argument.

static func > (Self, Self) -> Bool

Returns a Boolean value indicating whether the value of the first argument is greater than that of the second argument.

static func >= (Self, Self) -> Bool

Returns a Boolean value indicating whether the value of the first argument is greater than or equal to that of the second argument.

static func >= <Other>(Self, Other) -> Bool

Returns a Boolean value indicating whether the value of the first argument is greater than or equal to that of the second argument.

static func >> <RHS>(Self, RHS) -> Self

Returns the result of shifting a value’s binary representation the specified number of digits to the right.

Required. Default implementations provided.

static func >>= <RHS>(inout Self, RHS)

Stores the result of shifting a value’s binary representation the specified number of digits to the right in the left-hand-side variable.

Required. Default implementation provided.

static func ^ (Self, Self) -> Self

Returns the result of performing a bitwise XOR operation on the two given values.

Required. Default implementation provided.

static func ^= (inout Self, Self)

Stores the result of performing a bitwise XOR operation on the two given values in the left-hand-side variable.

Required.

static func | (Self, Self) -> Self

Returns the result of performing a bitwise OR operation on the two given values.

Required. Default implementation provided.

static func |= (inout Self, Self)

Stores the result of performing a bitwise OR operation on the two given values in the left-hand-side variable.

Required.

static func ~ (Self) -> Self

Returns the inverse of the bits set in the argument.

Required. Default implementation provided.

See Also

Integer

protocol FixedWidthInteger

An integer type that uses a fixed size for every instance.

protocol SignedInteger

An integer type that can represent both positive and negative values.

protocol UnsignedInteger

An integer type that can represent only nonnegative values.