`protocol FixedWidthInteger`

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

Inheritance | `BinaryInteger, LosslessStringConvertible` |
---|---|

Conforming Types | `Int, Int16, Int32, Int64, Int8, UInt, UInt16, UInt32, UInt64, UInt8` |

### Initializers

Creates an integer from its big-endian representation, changing the byte order if necessary.

- Parameter value: A value to use as the big-endian representation of the new integer.

#### Declaration

`init(bigEndian value: Self)`

Creates an integer from its little-endian representation, changing the byte order if necessary.

- Parameter value: A value to use as the little-endian representation of the new integer.

#### Declaration

`init(littleEndian value: Self)`

### Instance Variables

The big-endian representation of this integer.

If necessary, the byte order of this value is reversed from the typical
byte order of this integer type. On a big-endian platform, for any
integer `x`

, `x == x.bigEndian`

.

#### Declaration

`var bigEndian: Self`

A representation of this integer with the byte order swapped.

#### Declaration

`var byteSwapped: Self`

The number of leading zeros in this value's binary representation.

For example, in a fixed-width integer type with a `bitWidth`

value of 8,
the number *31* has three leading zeros.

```
let x: Int8 = 0b0001_1111
// x == 31
// x.leadingZeroBitCount == 3
```

If the value is zero, then `leadingZeroBitCount`

is equal to `bitWidth`

.

#### Declaration

`var leadingZeroBitCount: Int`

The little-endian representation of this integer.

If necessary, the byte order of this value is reversed from the typical
byte order of this integer type. On a little-endian platform, for any
integer `x`

, `x == x.littleEndian`

.

#### Declaration

`var littleEndian: Self`

The number of bits equal to 1 in this value's binary representation.

For example, in a fixed-width integer type with a `bitWidth`

value of 8,
the number *31* has five bits equal to *1*.

```
let x: Int8 = 0b0001_1111
// x == 31
// x.nonzeroBitCount == 5
```

#### Declaration

`var nonzeroBitCount: Int`

### Instance Methods

Returns the sum of this value and the given value, along with a Boolean value indicating whether overflow occurred in the operation.

- Parameter rhs: The value to add to this value.

#### Declaration

`func addingReportingOverflow(_ rhs: Self) -> (partialValue: Self, overflow: Bool)`

Returns the quotient obtained by dividing this value by the given value, along with a Boolean value indicating whether overflow occurred in the operation.

Dividing by zero is not an error when using this method. For a value `x`

,
the result of `x.dividedReportingOverflow(by: 0)`

is `(x, true)`

.

- Parameter rhs: The value to divide this value by.

#### Declaration

`func dividedReportingOverflow(by rhs: Self) -> (partialValue: Self, overflow: Bool)`

Returns a tuple containing the quotient and remainder obtained by dividing the given value by this value.

The resulting quotient must be representable within the bounds of the type. If the quotient is too large to represent in the type, a runtime error may occur.

The following example divides a value that is too large to be represented
using a single `Int`

instance by another `Int`

value. Because the quotient
is representable as an `Int`

, the division succeeds.

```
// 'dividend' represents the value 0x506f70652053616e74612049494949
let dividend = (22640526660490081, 7959093232766896457 as UInt)
let divisor = 2241543570477705381
let (quotient, remainder) = divisor.dividingFullWidth(dividend)
// quotient == 186319822866995413
// remainder == 0
```

- Parameter dividend: A tuple containing the high and low parts of a double-width integer.

#### Declaration

`func dividingFullWidth(_ dividend: (high: Self, low: Self.Magnitude)) -> (quotient: Self, remainder: Self)`

Returns a tuple containing the high and low parts of the result of multiplying this value by the given value.

Use this method to calculate the full result of a product that would
otherwise overflow. Unlike traditional truncating multiplication, the
`multipliedFullWidth(by:)`

method returns a tuple containing both the
`high`

and `low`

parts of the product of this value and `other`

. The
following example uses this method to multiply two `Int8`

values that
normally overflow when multiplied:

```
let x: Int8 = 48
let y: Int8 = -40
let result = x.multipliedFullWidth(by: y)
// result.high == -8
// result.low == 128
```

The product of `x`

and `y`

is `-1920`

, which is too large to represent in
an `Int8`

instance. The `high`

and `low`

compnents of the `result`

value
represent `-1920`

when concatenated to form a double-width integer; that
is, using `result.high`

as the high byte and `result.low`

as the low byte
of an `Int16`

instance.

```
let z = Int16(result.high) << 8 | Int16(result.low)
// z == -1920
```

- Parameter other: The value to multiply this value by.

#### Declaration

`func multipliedFullWidth(by other: Self) -> (high: Self, low: Self.Magnitude)`

Returns the product of this value and the given value, along with a Boolean value indicating whether overflow occurred in the operation.

- Parameter rhs: The value to multiply by this value.

#### Declaration

`func multipliedReportingOverflow(by rhs: Self) -> (partialValue: Self, overflow: Bool)`

Returns the remainder after dividing this value by the given value, along with a Boolean value indicating whether overflow occurred during division.

Dividing by zero is not an error when using this method. For a value `x`

,
the result of `x.remainderReportingOverflow(dividingBy: 0)`

is
`(x, true)`

.

- Parameter rhs: The value to divide this value by.

#### Declaration

`func remainderReportingOverflow(dividingBy rhs: Self) -> (partialValue: Self, overflow: Bool)`

Returns the difference obtained by subtracting the given value from this value, along with a Boolean value indicating whether overflow occurred in the operation.

- Parameter rhs: The value to subtract from this value.

#### Declaration

`func subtractingReportingOverflow(_ rhs: Self) -> (partialValue: Self, overflow: Bool)`

### Type Variables

The number of bits used for the underlying binary representation of values of this type.

An unsigned, fixed-width integer type can represent values from 0 through
`(2 ** bitWidth) - 1`

, where `**`

is exponentiation. A signed,
fixed-width integer type can represent values from
`-(2 ** (bitWidth - 1))`

through `(2 ** (bitWidth - 1)) - 1`

. For example,
the `Int8`

type has a `bitWidth`

value of 8 and can store any integer in
the range `-128...127`

.

#### Declaration

`var bitWidth: Int`

The maximum representable integer in this type.

For unsigned integer types, this value is `(2 ** bitWidth) - 1`

, where
`**`

is exponentiation. For signed integer types, this value is
`(2 ** (bitWidth - 1)) - 1`

.

#### Declaration

`var max: Self`

The minimum representable integer in this type.

For unsigned integer types, this value is always `0`

. For signed integer
types, this value is `-(2 ** (bitWidth - 1))`

, where `**`

is
exponentiation.

#### Declaration

`var min: Self`

### Type Methods

Returns the result of shifting a value's binary representation the specified number of digits to the left, masking the shift amount to the type's bit width.

Use the masking left shift operator (`&<<`

) when you need to perform a
shift and are sure that the shift amount is in the range
`0..<lhs.bitWidth`

. Before shifting, the masking left shift operator
masks the shift to this range. The shift is performed using this masked
value.

The following example defines `x`

as an instance of `UInt8`

, an 8-bit,
unsigned integer type. If you use `2`

as the right-hand-side value in an
operation on `x`

, the shift amount requires no masking.

```
let x: UInt8 = 30 // 0b00011110
let y = x &<< 2
// y == 120 // 0b01111000
```

However, if you use `8`

as the shift amount, the method first masks the
shift amount to zero, and then performs the shift, resulting in no change
to the original value.

```
let z = x &<< 8
// z == 30 // 0b00011110
```

If the bit width of the shifted integer type is a power of two, masking is performed using a bitmask; otherwise, masking is performed using a modulo operation.

#### Declaration

`static func &<<(lhs: Self, rhs: Self) -> Self`

Returns the result of shifting a value's binary representation the specified number of digits to the left, masking the shift amount to the type's bit width, and stores the result in the left-hand-side variable.

The `&<<=`

operator performs a *masking shift*, where the value used as
`rhs`

is masked to produce a value in the range `0..<lhs.bitWidth`

. The
shift is performed using this masked value.

The following example defines `x`

as an instance of `UInt8`

, an 8-bit,
unsigned integer type. If you use `2`

as the right-hand-side value in an
operation on `x`

, the shift amount requires no masking.

```
var x: UInt8 = 30 // 0b00011110
x &<<= 2
// x == 120 // 0b01111000
```

However, if you pass `19`

as `rhs`

, the method first bitmasks `rhs`

to
`3`

, and then uses that masked value as the number of bits to shift `lhs`

.

```
var y: UInt8 = 30 // 0b00011110
y &<<= 19
// y == 240 // 0b11110000
```

#### Declaration

`static func &<<=(lhs: inout Self, rhs: Self)`

Returns the result of shifting a value's binary representation the specified number of digits to the right, masking the shift amount to the type's bit width.

Use the masking right shift operator (`&>>`

) when you need to perform a
shift and are sure that the shift amount is in the range
`0..<lhs.bitWidth`

. Before shifting, the masking right shift operator
masks the shift to this range. The shift is performed using this masked
value.

The following example defines `x`

as an instance of `UInt8`

, an 8-bit,
unsigned integer type. If you use `2`

as the right-hand-side value in an
operation on `x`

, the shift amount requires no masking.

```
let x: UInt8 = 30 // 0b00011110
let y = x &>> 2
// y == 7 // 0b00000111
```

However, if you use `8`

as the shift amount, the method first masks the
shift amount to zero, and then performs the shift, resulting in no change
to the original value.

```
let z = x &>> 8
// z == 30 // 0b00011110
```

If the bit width of the shifted integer type is a power of two, masking is performed using a bitmask; otherwise, masking is performed using a modulo operation.

#### Declaration

`static func &>>(lhs: Self, rhs: Self) -> Self`

Calculates the result of shifting a value's binary representation the specified number of digits to the right, masking the shift amount to the type's bit width, and stores the result in the left-hand-side variable.

The `&>>=`

operator performs a *masking shift*, where the value passed as
`rhs`

is masked to produce a value in the range `0..<lhs.bitWidth`

. The
shift is performed using this masked value.

`x`

as an instance of `UInt8`

, an 8-bit,
unsigned integer type. If you use `2`

as the right-hand-side value in an
operation on `x`

, the shift amount requires no masking.

```
var x: UInt8 = 30 // 0b00011110
x &>>= 2
// x == 7 // 0b00000111
```

However, if you use `19`

as `rhs`

, the operation first bitmasks `rhs`

to
`3`

, and then uses that masked value as the number of bits to shift `lhs`

.

```
var y: UInt8 = 30 // 0b00011110
y &>>= 19
// y == 3 // 0b00000011
```

#### Declaration

`static func &>>=(lhs: inout Self, rhs: Self)`

### Default Implementations

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

You can check the inequality of instances of any `BinaryInteger`

types
using the not-equal-to operator (`!=`

). For example, you can test
whether the first `UInt8`

value in a string's UTF-8 encoding is not
equal to the first `UInt32`

value in its Unicode scalar view:

```
let gameName = "Red Light, Green Light"
if let firstUTF8 = gameName.utf8.first,
let firstScalar = gameName.unicodeScalars.first?.value {
print("First code values are different: \(firstUTF8 != firstScalar)")
}
// Prints "First code values are different: false"
```

#### Declaration

`public static func !=<Other>(lhs: Self, rhs: Other) -> Bool where Other: BinaryInteger`

#### Declaration

`public static func !=(lhs: Self, rhs: Self) -> Bool`

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

A bitwise AND operation results in a value that has each bit set to `1`

where *both* of its arguments have that bit set to `1`

. For example:

```
let x: UInt8 = 5 // 0b00000101
let y: UInt8 = 14 // 0b00001110
let z = x & y // 0b00000100
// z == 4
```

#### Declaration

`public static func &(lhs: Self, rhs: Self) -> Self`

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

You can compare instances of any `BinaryInteger`

types using the
less-than operator (`<`

), even if the two instances are of different
types.

#### Declaration

`public static func <<Other>(lhs: Self, rhs: Other) -> Bool where Other: BinaryInteger`

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

The `<<`

operator performs a *smart shift*, which defines a result for a
shift of any value.

The following example defines `x`

as an instance of `UInt8`

, an 8-bit,
unsigned integer type. If you use `2`

as the right-hand-side value in an
operation on `x`

, the value is shifted left by two bits.

```
let x: UInt8 = 30 // 0b00011110
let y = x << 2
// y == 120 // 0b01111000
```

If you use `11`

as `rhs`

, `x`

is overshifted such that all of its bits
are set to zero.

```
let z = x << 11
// z == 0 // 0b00000000
```

Using a negative value as `rhs`

is the same as performing a right shift
with `abs(rhs)`

.

```
let a = x << -3
// a == 3 // 0b00000011
let b = x >> 3
// b == 3 // 0b00000011
```

#### Declaration

`public static func <<<RHS>(lhs: Self, rhs: RHS) -> Self where RHS: BinaryInteger`

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

You can compare instances of any `BinaryInteger`

types using the
less-than-or-equal-to operator (`<=`

), even if the two instances are of
different types.

#### Declaration

`public static func <=<Other>(lhs: Self, rhs: Other) -> Bool where Other: BinaryInteger`

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

#### Declaration

`public static func <=(lhs: Self, rhs: Self) -> Bool`

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

You can check the equality of instances of any `BinaryInteger`

types
using the equal-to operator (`==`

). For example, you can test whether
the first `UInt8`

value in a string's UTF-8 encoding is equal to the
first `UInt32`

value in its Unicode scalar view:

```
let gameName = "Red Light, Green Light"
if let firstUTF8 = gameName.utf8.first,
let firstScalar = gameName.unicodeScalars.first?.value {
print("First code values are equal: \(firstUTF8 == firstScalar)")
}
// Prints "First code values are equal: true"
```

#### Declaration

`public static func ==<Other>(lhs: Self, rhs: Other) -> Bool where Other: BinaryInteger`

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

You can compare instances of any `BinaryInteger`

types using the
greater-than operator (`>`

), even if the two instances are of different
types.

#### Declaration

`public static func ><Other>(lhs: Self, rhs: Other) -> Bool where Other: BinaryInteger`

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

#### Declaration

`public static func >(lhs: Self, rhs: 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.

You can compare instances of any `BinaryInteger`

types using the
greater-than-or-equal-to operator (`>=`

), even if the two instances are
of different types.

#### Declaration

`public static func >=<Other>(lhs: Self, rhs: Other) -> Bool where Other: BinaryInteger`

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

#### Declaration

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

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

The `>>`

operator performs a *smart shift*, which defines a result for a
shift of any value.

The following example defines `x`

as an instance of `UInt8`

, an 8-bit,
unsigned integer type. If you use `2`

as the right-hand-side value in an
operation on `x`

, the value is shifted right by two bits.

```
let x: UInt8 = 30 // 0b00011110
let y = x >> 2
// y == 7 // 0b00000111
```

If you use `11`

as `rhs`

, `x`

is overshifted such that all of its bits
are set to zero.

```
let z = x >> 11
// z == 0 // 0b00000000
```

Using a negative value as `rhs`

is the same as performing a left shift
using `abs(rhs)`

.

```
let a = x >> -3
// a == 240 // 0b11110000
let b = x << 3
// b == 240 // 0b11110000
```

Right shift operations on negative values "fill in" the high bits with ones instead of zeros.

```
let q: Int8 = -30 // 0b11100010
let r = q >> 2
// r == -8 // 0b11111000
let s = q >> 11
// s == -1 // 0b11111111
```

#### Declaration

`public static func >><RHS>(lhs: Self, rhs: RHS) -> Self where RHS: BinaryInteger`

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

A bitwise XOR operation, also known as an exclusive OR operation, results
in a value that has each bit set to `1`

where *one or the other but not
both* of its arguments had that bit set to `1`

. For example:

```
let x: UInt8 = 5 // 0b00000101
let y: UInt8 = 14 // 0b00001110
let z = x ^ y // 0b00001011
// z == 11
```

#### Declaration

`public static func ^(lhs: Self, rhs: Self) -> Self`

Returns a value that is offset the specified distance from this value.

Use the `advanced(by:)`

method in generic code to offset a value by a
specified distance. If you're working directly with numeric values, use
the addition operator (`+`

) instead of this method.

For a value `x`

, a distance `n`

, and a value `y = x.advanced(by: n)`

,
`x.distance(to: y) == n`

.

- Parameter n: The distance to advance this value.

#### Declaration

`@inlinable public func advanced(by n: Int) -> Self`

A textual representation of this value.

#### Declaration

`var description: String`

Returns the distance from this value to the given value, expressed as a stride.

For two values `x`

and `y`

, and a distance `n = x.distance(to: y)`

,
`x.advanced(by: n) == y`

.

- Parameter other: The value to calculate the distance to.

#### Declaration

`@inlinable public func distance(to other: Self) -> Int`

Creates a new value equal to zero.

#### Declaration

`public init()`

Returns `true`

if this value is a multiple of the given value, and `false`

otherwise.

For two integers *a* and *b*, *a* is a multiple of *b* if there exists a
third integer *q* such that *a = q*b*. For example, *6* is a multiple of
*3* because *6 = 2*3*. Zero is a multiple of everything because *0 = 0*x*
for any integer *x*.

Two edge cases are worth particular attention:

- Parameter other: The value to test.

#### Declaration

`@inlinable public func isMultiple(of other: Self) -> Bool`

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

Use this method to calculate the quotient and remainder of a division at the same time.

```
let x = 1_000_000
let (q, r) = x.quotientAndRemainder(dividingBy: 933)
// q == 1071
// r == 757
```

- Parameter rhs: The value to divide this value by.

#### Declaration

`@inlinable public func quotientAndRemainder(dividingBy rhs: Self) -> (quotient: Self, remainder: Self)`

Returns `-1`

if this value is negative and `1`

if it's positive;
otherwise, `0`

.

#### Declaration

`@inlinable public func signum() -> Self`

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

A bitwise OR operation results in a value that has each bit set to `1`

where *one or both* of its arguments have that bit set to `1`

. For
example:

```
let x: UInt8 = 5 // 0b00000101
let y: UInt8 = 14 // 0b00001110
let z = x | y // 0b00001111
// z == 15
```

#### Declaration

`public static func |(lhs: Self, rhs: Self) -> Self`

The

`FixedWidthInteger`

protocol adds binary bitwise operations, bit shifts, and overflow handling to the operations supported by the`BinaryInteger`

protocol.Use the

`FixedWidthInteger`

protocol as a constraint or extension point when writing operations that depend on bit shifting, performing bitwise operations, catching overflows, or having access to the maximum or minimum representable value of a type. For example, the following code provides a`binaryString`

property on every fixed-width integer that represents the number's binary representation, split into 8-bit chunks.The

`binaryString`

implementation uses the static`bitWidth`

property and the right shift operator (`>>`

), both of which are available to any type that conforms to the`FixedWidthInteger`

protocol.The next example declares a generic

`squared`

function, which accepts an instance`x`

of any fixed-width integer type. The function uses the`multipliedReportingOverflow(by:)`

method to multiply`x`

by itself and check whether the result is too large to represent in the same type.## Conforming to the FixedWidthInteger Protocol

To make your own custom type conform to the

`FixedWidthInteger`

protocol, declare the required initializers, properties, and methods. The required methods that are suffixed with`ReportingOverflow`

serve as the customization points for arithmetic operations. When you provide just those methods, the standard library provides default implementations for all other arithmetic methods and operators.