FloatingPoint

protocol FloatingPoint

A floating-point numeric type.

Floating-point types are used to represent fractional numbers, like 5.5, 100.0, or 3.14159274. Each floating-point type has its own possible range and precision. The floating-point types in the standard library are Float, Double, and Float80 where available.

Create new instances of floating-point types using integer or floating-point literals. For example:

let temperature = 33.2
let recordHigh = 37.5

The FloatingPoint protocol declares common arithmetic operations, so you can write functions and algorithms that work on any floating-point type. The following example declares a function that calculates the length of the hypotenuse of a right triangle given its two perpendicular sides. Because the hypotenuse(_:_:) function uses a generic parameter constrained to the FloatingPoint protocol, you can call it using any floating-point type.

func hypotenuse<T: FloatingPoint>(_ a: T, _ b: T) -> T {
    return (a * a + b * b).squareRoot()
}

let (dx, dy) = (3.0, 4.0)
let distance = hypotenuse(dx, dy)
// distance == 5.0

Floating-point values are represented as a sign and a magnitude, where the magnitude is calculated using the type's radix and the instance's significand and exponent. This magnitude calculation takes the following form for a floating-point value x of type F, where ** is exponentiation:

x.significand * F.radix ** x.exponent

Here's an example of the number -8.5 represented as an instance of the Double type, which defines a radix of 2.

let y = -8.5
// y.sign == .minus
// y.significand == 1.0625
// y.exponent == 3

let magnitude = 1.0625 * Double(2 ** 3)
// magnitude == 8.5

Types that conform to the FloatingPoint protocol provide most basic (clause 5) operations of the IEEE 754 specification. The base, precision, and exponent range are not fixed in any way by this protocol, but it enforces the basic requirements of any IEEE 754 floating-point type.

Additional Considerations

In addition to representing specific numbers, floating-point types also have special values for working with overflow and nonnumeric results of calculation.

Infinity

Any value whose magnitude is so great that it would round to a value outside the range of representable numbers is rounded to infinity. For a type F, positive and negative infinity are represented as F.infinity and -F.infinity, respectively. Positive infinity compares greater than every finite value and negative infinity, while negative infinity compares less than every finite value and positive infinity. Infinite values with the same sign are equal to each other.

let values: [Double] = [10.0, 25.0, -10.0, .infinity, -.infinity]
print(values.sorted())
// Prints "[-inf, -10.0, 10.0, 25.0, inf]"

Operations with infinite values follow real arithmetic as much as possible: Adding or subtracting a finite value, or multiplying or dividing infinity by a nonzero finite value, results in infinity.

NaN ("not a number")

Floating-point types represent values that are neither finite numbers nor infinity as NaN, an abbreviation for "not a number." Comparing a NaN with any value, including another NaN, results in false.

let myNaN = Double.nan
print(myNaN > 0)
// Prints "false"
print(myNaN < 0)
// Prints "false"
print(myNaN == .nan)
// Prints "false"

Because testing whether one NaN is equal to another NaN results in false, use the isNaN property to test whether a value is NaN.

print(myNaN.isNaN)
// Prints "true"

NaN propagates through many arithmetic operations. When you are operating on many values, this behavior is valuable because operations on NaN simply forward the value and don't cause runtime errors. The following example shows how NaN values operate in different contexts.

Imagine you have a set of temperature data for which you need to report some general statistics: the total number of observations, the number of valid observations, and the average temperature. First, a set of observations in Celsius is parsed from strings to Double values:

let temperatureData = ["21.5", "19.25", "27", "no data", "28.25", "no data", "23"]
let tempsCelsius = temperatureData.map { Double($0) ?? .nan }
// tempsCelsius == [21.5, 19.25, 27, nan, 28.25, nan, 23.0]

Note that some elements in the temperatureData array are not valid numbers. When these invalid strings are parsed by the Double failable initializer, the example uses the nil-coalescing operator (??) to provide NaN as a fallback value.

Next, the observations in Celsius are converted to Fahrenheit:

let tempsFahrenheit = tempsCelsius.map { $0 * 1.8 + 32 }
// tempsFahrenheit == [70.7, 66.65, 80.6, nan, 82.85, nan, 73.4]

The NaN values in the tempsCelsius array are propagated through the conversion and remain NaN in tempsFahrenheit.

Because calculating the average of the observations involves combining every value of the tempsFahrenheit array, any NaN values cause the result to also be NaN, as seen in this example:

let badAverage = tempsFahrenheit.reduce(0.0, combine: +) / Double(tempsFahrenheit.count)
// badAverage.isNaN == true

Instead, when you need an operation to have a specific numeric result, filter out any NaN values using the isNaN property.

let validTemps = tempsFahrenheit.filter { !$0.isNaN }
let average = validTemps.reduce(0.0, combine: +) / Double(validTemps.count)

Finally, report the average temperature and observation counts:

print("Average: \(average)°F in \(validTemps.count) " +
      "out of \(tempsFahrenheit.count) observations.")
// Prints "Average: 74.84°F in 5 out of 7 observations."
Inheritance Arithmetic, Comparable, Equatable, ExpressibleByIntegerLiteral, SignedNumber, Strideable View Protocol Hierarchy →
Associated Types
Exponent : SignedInteger

A type that represents any written exponent.

Magnitude : Equatable, ExpressibleByIntegerLiteral
IntegerLiteralType

A type that represents an integer literal.

The standard library integer and floating-point types are all valid types for IntegerLiteralType.

Stride : SignedNumber

A type that represents the distance between two values of Self.

Import import Swift

Initializers

init(_: Int) Required

Creates a new value, rounded to the closest possible representation.

If two representable values are equally close, the result is the value with more trailing zeros in its significand bit pattern.

value: The integer to convert to a floating-point value.

Declaration

init(_ value: Int)
init(_: Int8) Required

Creates a new value, rounded to the closest possible representation.

If two representable values are equally close, the result is the value with more trailing zeros in its significand bit pattern.

value: The integer to convert to a floating-point value.

Declaration

init(_ value: Int8)
init(_: Int16) Required

Creates a new value, rounded to the closest possible representation.

If two representable values are equally close, the result is the value with more trailing zeros in its significand bit pattern.

value: The integer to convert to a floating-point value.

Declaration

init(_ value: Int16)
init(_: Int32) Required

Creates a new value, rounded to the closest possible representation.

If two representable values are equally close, the result is the value with more trailing zeros in its significand bit pattern.

value: The integer to convert to a floating-point value.

Declaration

init(_ value: Int32)
init(_: Int64) Required

Creates a new value, rounded to the closest possible representation.

If two representable values are equally close, the result is the value with more trailing zeros in its significand bit pattern.

value: The integer to convert to a floating-point value.

Declaration

init(_ value: Int64)
init(_: UInt) Required

Creates a new value, rounded to the closest possible representation.

If two representable values are equally close, the result is the value with more trailing zeros in its significand bit pattern.

value: The integer to convert to a floating-point value.

Declaration

init(_ value: UInt)
init(_: UInt8) Required

Creates a new value, rounded to the closest possible representation.

If two representable values are equally close, the result is the value with more trailing zeros in its significand bit pattern.

value: The integer to convert to a floating-point value.

Declaration

init(_ value: UInt8)
init(_: UInt16) Required

Creates a new value, rounded to the closest possible representation.

If two representable values are equally close, the result is the value with more trailing zeros in its significand bit pattern.

value: The integer to convert to a floating-point value.

Declaration

init(_ value: UInt16)
init(_: UInt32) Required

Creates a new value, rounded to the closest possible representation.

If two representable values are equally close, the result is the value with more trailing zeros in its significand bit pattern.

value: The integer to convert to a floating-point value.

Declaration

init(_ value: UInt32)
init(_: UInt64) Required

Creates a new value, rounded to the closest possible representation.

If two representable values are equally close, the result is the value with more trailing zeros in its significand bit pattern.

value: The integer to convert to a floating-point value.

Declaration

init(_ value: UInt64)
init(sign:exponent:significand:) Required

Creates a new value from the given sign, exponent, and significand.

The following example uses this initializer to create a new Double instance. Double is a binary floating-point type that has a radix of 2.

let x = Double(sign: .plus, exponent: -2, significand: 1.5)
// x == 0.375

This initializer is equivalent to the following calculation, where ** is exponentiation, computed as if by a single, correctly rounded, floating-point operation:

let sign: FloatingPointSign = .plus
let exponent = -2
let significand = 1.5
let y = (sign == .minus ? -1 : 1) * significand * Double.radix ** exponent
// y == 0.375

As with any basic operation, if this value is outside the representable range of the type, overflow or underflow occurs, and zero, a subnormal value, or infinity may result. In addition, there are two other edge cases:

  • If the value you pass to significand is zero or infinite, the result is zero or infinite, regardless of the value of exponent.
  • If the value you pass to significand is NaN, the result is NaN.

For any floating-point value x of type F, the result of the following is equal to x, with the distinction that the result is canonicalized if x is in a noncanonical encoding:

let x0 = F(sign: x.sign, exponent: x.exponent, significand: x.significand)

This initializer implements the scaleB operation defined by the IEEE 754 specification.

Parameters: sign: The sign to use for the new value. exponent: The new value's exponent. significand: The new value's significand.

Declaration

init(sign: FloatingPointSign, exponent: Self.Exponent, significand: Self)
init(signOf:magnitudeOf:) Required

Creates a new floating-point value using the sign of one value and the magnitude of another.

The following example uses this initializer to create a new Double instance with the sign of a and the magnitude of b:

let a = -21.5
let b = 305.15
let c = Double(signOf: a, magnitudeOf: b)
print(c)
// Prints "-305.15"

This initializer implements the IEEE 754 copysign operation.

Parameters: signOf: A value from which to use the sign. The result of the initializer has the same sign as signOf. magnitudeOf: A value from which to use the magnitude. The result of the initializer has the same magnitude as magnitudeOf.

Declaration

init(signOf: Self, magnitudeOf: Self)
init(integerLiteral:) Required

Creates an instance initialized to the specified integer value.

Do not call this initializer directly. Instead, initialize a variable or constant using an integer literal. For example:

let x = 23

In this example, the assignment to the x constant calls this integer literal initializer behind the scenes.

value: The value to create.

Declaration

init(integerLiteral value: Self.IntegerLiteralType)

Declared In

ExpressibleByIntegerLiteral

Static Variables

static var greatestFiniteMagnitude: Self Required

The greatest finite number representable by this type.

This value compares greater than or equal to all finite numbers, but less than infinity.

This value corresponds to type-specific C macros such as FLT_MAX and DBL_MAX. The naming of those macros is slightly misleading, because infinity is greater than this value.

Declaration

static var greatestFiniteMagnitude: Self { get }
static var infinity: Self Required

Positive infinity.

Infinity compares greater than all finite numbers and equal to other infinite values.

let x = Double.greatestFiniteMagnitude
let y = x * 2
// y == Double.infinity
// y > x

Declaration

static var infinity: Self { get }
static var leastNonzeroMagnitude: Self Required

The least positive number.

This value compares less than or equal to all positive numbers, but greater than zero. If the type supports subnormal values, leastNonzeroMagnitude is smaller than leastNormalMagnitude; otherwise they are equal.

Declaration

static var leastNonzeroMagnitude: Self { get }
static var leastNormalMagnitude: Self Required

The least positive normal number.

This value compares less than or equal to all positive normal numbers. There may be smaller positive numbers, but they are subnormal, meaning that they are represented with less precision than normal numbers.

This value corresponds to type-specific C macros such as FLT_MIN and DBL_MIN. The naming of those macros is slightly misleading, because subnormals, zeros, and negative numbers are smaller than this value.

Declaration

static var leastNormalMagnitude: Self { get }
static var nan: Self Required

A quiet NaN ("not a number").

A NaN compares not equal, not greater than, and not less than every value, including itself. Passing a NaN to an operation generally results in NaN.

let x = 1.21
// x > Double.nan == false
// x < Double.nan == false
// x == Double.nan == false

Because a NaN always compares not equal to itself, to test whether a floating-point value is NaN, use its isNaN property instead of the equal-to operator (==). In the following example, y is NaN.

let y = x + Double.nan
print(y == Double.nan)
// Prints "false"
print(y.isNaN)
// Prints "true"

See Also: isNaN, signalingNaN

Declaration

static var nan: Self { get }
static var pi: Self Required

The mathematical constant pi.

This value should be rounded toward zero to keep user computations with angles from inadvertently ending up in the wrong quadrant. A type that conforms to the FloatingPoint protocol provides the value for pi at its best possible precision.

print(Double.pi)
// Prints "3.14159265358979"

Declaration

static var pi: Self { get }
static var radix: Int Required

The radix, or base of exponentiation, for a floating-point type.

The magnitude of a floating-point value x of type F can be calculated by using the following formula, where ** is exponentiation:

let magnitude = x.significand * F.radix ** x.exponent

A conforming type may use any integer radix, but values other than 2 (for binary floating-point types) or 10 (for decimal floating-point types) are extraordinarily rare in practice.

Declaration

static var radix: Int { get }
static var signalingNaN: Self Required

A signaling NaN ("not a number").

The default IEEE 754 behavior of operations involving a signaling NaN is to raise the Invalid flag in the floating-point environment and return a quiet NaN.

Operations on types conforming to the FloatingPoint protocol should support this behavior, but they might also support other options. For example, it would be reasonable to implement alternative operations in which operating on a signaling NaN triggers a runtime error or results in a diagnostic for debugging purposes. Types that implement alternative behaviors for a signaling NaN must document the departure.

Other than these signaling operations, a signaling NaN behaves in the same manner as a quiet NaN.

See Also: nan

Declaration

static var signalingNaN: Self { get }
static var ulpOfOne: Self

The unit in the last place of 1.0.

The positive difference between 1.0 and the next greater representable number. The ulpOfOne constant corresponds to the C macros FLT_EPSILON, DBL_EPSILON, and others with a similar purpose.

Declaration

static var ulpOfOne: Self { get }

Instance Variables

var exponent: Self.Exponent Required

The exponent of the floating-point value.

The exponent of a floating-point value is the integer part of the logarithm of the value's magnitude. For a value x of a floating-point type F, the magnitude can be calculated as the following, where ** is exponentiation:

let magnitude = x.significand * F.radix ** x.exponent

In the next example, y has a value of 21.5, which is encoded as 1.34375 * 2 ** 4. The significand of y is therefore 1.34375.

let y: Double = 21.5
// y.significand == 1.34375
// y.exponent == 4
// Double.radix == 2

The exponent property has the following edge cases:

  • If x is zero, then x.exponent is Int.min.
  • If x is +/-infinity or NaN, then x.exponent is Int.max

This property implements the logB operation defined by the IEEE 754 specification.

Declaration

var exponent: Self.Exponent { get }
var floatingPointClass: FloatingPointClassification

The classification of this value.

A value's floatingPointClass property describes its "class" as described by the IEEE 754 specification.

Declaration

var floatingPointClass: FloatingPointClassification { get }
var isCanonical: Bool Required

A Boolean value indicating whether the instance's representation is in the canonical form.

The IEEE 754 specification defines a canonical, or preferred, encoding of a floating-point value's representation. Every Float or Double value is canonical, but noncanonical values of the Float80 type exist, and noncanonical values may exist for other types that conform to the FloatingPoint protocol.

Declaration

var isCanonical: Bool { get }
var isFinite: Bool Required

A Boolean value indicating whether this instance is finite.

All values other than NaN and infinity are considered finite, whether normal or subnormal.

Declaration

var isFinite: Bool { get }
var isInfinite: Bool Required

A Boolean value indicating whether the instance is infinite.

Note that isFinite and isInfinite do not form a dichotomy, because they are not total: If x is NaN, then both properties are false.

Declaration

var isInfinite: Bool { get }
var isNaN: Bool Required

A Boolean value indicating whether the instance is NaN ("not a number").

Because NaN is not equal to any value, including NaN, use this property instead of the equal-to operator (==) or not-equal-to operator (!=) to test whether a value is or is not NaN. For example:

let x = 0.0
let y = x * .infinity
// y is a NaN

// Comparing with the equal-to operator never returns 'true'
print(x == Double.nan)
// Prints "false"
print(y == Double.nan)
// Prints "false"

// Test with the 'isNaN' property instead
print(x.isNaN)
// Prints "false"
print(y.isNaN)
// Prints "true"

This property is true for both quiet and signaling NaNs.

Declaration

var isNaN: Bool { get }
var isNormal: Bool Required

A Boolean value indicating whether this instance is normal.

A normal value is a finite number that uses the full precision available to values of a type. Zero is neither a normal nor a subnormal number.

Declaration

var isNormal: Bool { get }
var isSignalingNaN: Bool Required

A Boolean value indicating whether the instance is a signaling NaN.

Signaling NaNs typically raise the Invalid flag when used in general computing operations.

Declaration

var isSignalingNaN: Bool { get }
var isSubnormal: Bool Required

A Boolean value indicating whether the instance is subnormal.

A subnormal value is a nonzero number that has a lesser magnitude than the smallest normal number. Subnormal values do not use the full precision available to values of a type.

Zero is neither a normal nor a subnormal number. Subnormal numbers are often called denormal or denormalized---these are different names for the same concept.

Declaration

var isSubnormal: Bool { get }
var isZero: Bool Required

A Boolean value indicating whether the instance is equal to zero.

The isZero property of a value x is true when x represents either -0.0 or +0.0. x.isZero is equivalent to the following comparison: x == 0.0.

let x = -0.0
x.isZero        // true
x == 0.0        // true

Declaration

var isZero: Bool { get }
var nextDown: Self

The greatest representable value that compares less than this value.

For any finite value x, x.nextDown is greater than x. For nan or -infinity, x.nextDown is x itself. The following special cases also apply:

  • If x is infinity, then x.nextDown is greatestFiniteMagnitude.
  • If x is leastNonzeroMagnitude, then x.nextDown is 0.0.
  • If x is zero, then x.nextDown is -leastNonzeroMagnitude.
  • If x is -greatestFiniteMagnitude, then x.nextDown is -infinity.

Declaration

var nextDown: Self { get }
var nextUp: Self Required

The least representable value that compares greater than this value.

For any finite value x, x.nextUp is greater than x. For nan or infinity, x.nextUp is x itself. The following special cases also apply:

  • If x is -infinity, then x.nextUp is -greatestFiniteMagnitude.
  • If x is -leastNonzeroMagnitude, then x.nextUp is -0.0.
  • If x is zero, then x.nextUp is leastNonzeroMagnitude.
  • If x is greatestFiniteMagnitude, then x.nextUp is infinity.

Declaration

var nextUp: Self { get }
var sign: FloatingPointSign Required

The sign of the floating-point value.

The sign property is .minus if the value's signbit is set, and .plus otherwise. For example:

let x = -33.375
// x.sign == .minus

Do not use this property to check whether a floating point value is negative. For a value x, the comparison x.sign == .minus is not necessarily the same as x < 0. In particular, x.sign == .minus if x is -0, and while x < 0 is always false if x is NaN, x.sign could be either .plus or .minus.

Declaration

var sign: FloatingPointSign { get }
var significand: Self Required

The significand of the floating-point value.

The magnitude of a floating-point value x of type F can be calculated by using the following formula, where ** is exponentiation:

let magnitude = x.significand * F.radix ** x.exponent

In the next example, y has a value of 21.5, which is encoded as 1.34375 * 2 ** 4. The significand of y is therefore 1.34375.

let y: Double = 21.5
// y.significand == 1.34375
// y.exponent == 4
// Double.radix == 2

If a type's radix is 2, then for finite nonzero numbers, the significand is in the range 1.0 ..< 2.0. For other values of x, x.significand is defined as follows:

  • If x is zero, then x.significand is 0.0.
  • If x is infinity, then x.significand is 1.0.
  • If x is NaN, then x.significand is NaN. Note: The significand is frequently also called the mantissa, but significand is the preferred terminology in the IEEE 754 specification, to allay confusion with the use of mantissa for the fractional part of a logarithm.

Declaration

var significand: Self { get }
var ulp: Self Required

The unit in the last place of this value.

This is the unit of the least significant digit in this value's significand. For most numbers x, this is the difference between x and the next greater (in magnitude) representable number. There are some edge cases to be aware of:

  • If x is not a finite number, then x.ulp is NaN.
  • If x is very small in magnitude, then x.ulp may be a subnormal number. If a type does not support subnormals, x.ulp may be rounded to zero.
  • greatestFiniteMagnitude.ulp is a finite number, even though the next greater representable value is infinity.

This quantity, or a related quantity, is sometimes called epsilon or machine epsilon. Avoid that name because it has different meanings in different languages, which can lead to confusion, and because it suggests that it is a good tolerance to use for comparisons, which it almost never is.

Declaration

var ulp: Self { get }
var magnitude: Self.Magnitude Required

Declaration

var magnitude: Self.Magnitude { get }

Declared In

Arithmetic

Static Methods

static func maximum(_:_:)

Returns the greater of the two given values.

This method returns the maximum of two values, preserving order and eliminating NaN when possible. For two values x and y, the result of maximum(x, y) is x if x > y, y if x <= y, or whichever of x or y is a number if the other is a quiet NaN. If both x and y are NaN, or either x or y is a signaling NaN, the result is NaN.

Double.maximum(10.0, -25.0)
// 10.0
Double.maximum(10.0, .nan)
// 10.0
Double.maximum(.nan, -25.0)
// -25.0
Double.maximum(.nan, .nan)
// nan

The maximum method implements the maxNum operation defined by the IEEE 754 specification.

Parameters: x: A floating-point value. y: Another floating-point value. Returns: The greater of x and y, or whichever is a number if the other is NaN.

Declaration

static func maximum(_ x: Self, _ y: Self) -> Self
static func maximumMagnitude(_:_:)

Returns the value with greater magnitude.

This method returns the value with greater magnitude of the two given values, preserving order and eliminating NaN when possible. For two values x and y, the result of maximumMagnitude(x, y) is x if x.magnitude > y.magnitude, y if x.magnitude <= y.magnitude, or whichever of x or y is a number if the other is a quiet NaN. If both x and y are NaN, or either x or y is a signaling NaN, the result is NaN.

Double.maximumMagnitude(10.0, -25.0)
// -25.0
Double.maximumMagnitude(10.0, .nan)
// 10.0
Double.maximumMagnitude(.nan, -25.0)
// -25.0
Double.maximumMagnitude(.nan, .nan)
// nan

The maximumMagnitude method implements the maxNumMag operation defined by the IEEE 754 specification.

Parameters: x: A floating-point value. y: Another floating-point value. Returns: Whichever of x or y has greater magnitude, or whichever is a number if the other is NaN.

Declaration

static func maximumMagnitude(_ x: Self, _ y: Self) -> Self
static func minimum(_:_:)

Returns the lesser of the two given values.

This method returns the minimum of two values, preserving order and eliminating NaN when possible. For two values x and y, the result of minimum(x, y) is x if x <= y, y if y < x, or whichever of x or y is a number if the other is a quiet NaN. If both x and y are NaN, or either x or y is a signaling NaN, the result is NaN.

Double.minimum(10.0, -25.0)
// -25.0
Double.minimum(10.0, .nan)
// 10.0
Double.minimum(.nan, -25.0)
// -25.0
Double.minimum(.nan, .nan)
// nan

The minimum method implements the minNum operation defined by the IEEE 754 specification.

Parameters: x: A floating-point value. y: Another floating-point value. Returns: The minimum of x and y, or whichever is a number if the other is NaN.

Declaration

static func minimum(_ x: Self, _ y: Self) -> Self
static func minimumMagnitude(_:_:)

Returns the value with lesser magnitude.

This method returns the value with lesser magnitude of the two given values, preserving order and eliminating NaN when possible. For two values x and y, the result of minimumMagnitude(x, y) is x if x.magnitude <= y.magnitude, y if y.magnitude < x.magnitude, or whichever of x or y is a number if the other is a quiet NaN. If both x and y are NaN, or either x or y is a signaling NaN, the result is NaN.

Double.minimumMagnitude(10.0, -25.0)
// 10.0
Double.minimumMagnitude(10.0, .nan)
// 10.0
Double.minimumMagnitude(.nan, -25.0)
// -25.0
Double.minimumMagnitude(.nan, .nan)
// nan

The minimumMagnitude method implements the minNumMag operation defined by the IEEE 754 specification.

Parameters: x: A floating-point value. y: Another floating-point value. Returns: Whichever of x or y has lesser magnitude, or whichever is a number if the other is NaN.

Declaration

static func minimumMagnitude(_ x: Self, _ y: Self) -> Self

Instance Methods

func <(_:rhs:) Required

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

This function is the only requirement of the Comparable protocol. The remainder of the relational operator functions are implemented by the standard library for any type that conforms to Comparable.

Parameters: lhs: A value to compare. rhs: Another value to compare.

Declaration

func <(lhs: Self, rhs: Self) -> Bool

Declared In

Comparable
func <=(_:rhs:)

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

Parameters: lhs: A value to compare. rhs: Another value to compare.

Declaration

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

Declared In

Comparable
func ==(_:rhs:) Required

Returns a Boolean value indicating whether two values are equal.

Equality is the inverse of inequality. For any values a and b, a == b implies that a != b is false.

Parameters: lhs: A value to compare. rhs: Another value to compare.

Declaration

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

Declared In

Equatable
func >(_:rhs:)

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

Parameters: lhs: A value to compare. rhs: Another value to compare.

Declaration

func >(lhs: Self, rhs: Self) -> Bool

Declared In

Comparable
func >=(_:rhs:)

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

Parameters: lhs: A value to compare. rhs: Another value to compare.

Declaration

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

Declared In

Comparable
prefix func -(_:) Required

Returns the result of negating x.

Declaration

prefix func -(x: Self) -> Self

Declared In

SignedNumber
func -(_:rhs:) Required

Returns the difference between lhs and rhs.

Declaration

func -(lhs: Self, rhs: Self) -> Self

Declared In

SignedNumber
mutating func add(_:) Required

Adds the given value to this value in place, rounded to a representable value.

This method serves as the basis for the in-place addition operator (+=). For example:

var (x, y) = (2.25, 2.25)
x.add(7.0)
// x == 9.25
y += 7.0
// y == 9.25

other: The value to add.

See Also: adding(_:)

Declaration

mutating func add(_ other: Self)

Declared In

FloatingPoint, Arithmetic
mutating func addProduct(_:_:) Required

Adds the product of the two given values to this value in place, computed without intermediate rounding.

Parameters: lhs: One of the values to multiply before adding to this value. rhs: The other value to multiply.

Declaration

mutating func addProduct(_ lhs: Self, _ rhs: Self)
func adding(_:)

Returns the sum of this value and the given value, rounded to a representable value.

This method serves as the basis for the addition operator (+). For example:

let x = 1.5
print(x.adding(2.25))
// Prints "3.75"
print(x + 2.25)
// Prints "3.75"

The adding(_:) method implements the addition operation defined by the IEEE 754 specification.

other: The value to add. Returns: The sum of this value and other, rounded to a representable value.

See Also: add(_:)

Declaration

func adding(_ other: Self) -> Self

Declared In

FloatingPoint, Arithmetic
func addingProduct(_:_:)

Returns the result of adding the product of the two given values to this value, computed without intermediate rounding.

This method is equivalent to the C fma function and implements the fusedMultiplyAdd operation defined by the IEEE 754 specification.

Parameters: lhs: One of the values to multiply before adding to this value. rhs: The other value to multiply. Returns: The product of lhs and rhs, added to this value.

Declaration

func addingProduct(_ lhs: Self, _ rhs: Self) -> Self
func advanced(by:) Required

Returns a Self x such that self.distance(to: x) approximates n.

If Stride conforms to Integer, then self.distance(to: x) == n.

Complexity: O(1).

Declaration

func advanced(by n: Self.Stride) -> Self

Declared In

Strideable
func distance(to:) Required

Returns a stride x such that self.advanced(by: x) approximates other.

If Stride conforms to Integer, then self.advanced(by: x) == other.

Complexity: O(1).

Declaration

func distance(to other: Self) -> Self.Stride

Declared In

Strideable
mutating func divide(by:) Required

Divides this value by the given value in place, rounding to a representable value.

This method serves as the basis for the in-place division operator (/=). For example:

var (x, y) = (16.875, 16.875)
x.divide(by: 2.25)
// x == 7.5
y /= 2.25
// y == 7.5

other: The value to use when dividing this value.

See Also: divided(by:)

Declaration

mutating func divide(by other: Self)

Declared In

FloatingPoint, Arithmetic
func divided(by:)

Returns the quotient of this value and the given value, rounded to a representable value.

This method serves as the basis for the division operator (/). For example:

let x = 7.5
let y = x.divided(by: 2.25)
// y == 16.875
let z = x * 2.25
// z == 16.875

The divided(by:) method implements the division operation defined by the IEEE 754 specification.

other: The value to use when dividing this value. Returns: The quotient of this value and other, rounded to a representable value.

See Also: divide(by:)

Declaration

func divided(by other: Self) -> Self

Declared In

FloatingPoint, Arithmetic
mutating func formRemainder(dividingBy:) Required

Replaces this value with the remainder of itself divided by the given value.

For two finite values x and y, the remainder r of dividing x by y satisfies x == y * q + r, where q is the integer nearest to x / y. If x / y is exactly halfway between two integers, q is chosen to be even. Note that q is not x / y computed in floating-point arithmetic, and that q may not be representable in any available integer type.

The following example calculates the remainder of dividing 8.625 by 0.75:

var x = 8.625
print(x / 0.75)
// Prints "11.5"

let q = (x / 0.75).rounded(.toNearestOrEven)
// q == 12.0
x.formRemainder(dividingBy: 0.75)
// x == -0.375

let x1 = 0.75 * q + x
// x1 == 8.625

If this value and other are finite numbers, the remainder is in the closed range -abs(other / 2)...abs(other / 2). The remainder(dividingBy:) method is always exact.

other: The value to use when dividing this value.

See Also: remainder(dividingBy:), formTruncatingRemainder(dividingBy:)

Declaration

mutating func formRemainder(dividingBy other: Self)
mutating func formSquareRoot() Required

Replaces this value with its square root, rounded to a representable value.

See Also: sqrt(_:), squareRoot()

Declaration

mutating func formSquareRoot()
mutating func formTruncatingRemainder(dividingBy:) Required

Replaces this value with the remainder of itself divided by the given value using truncating division.

Performing truncating division with floating-point values results in a truncated integer quotient and a remainder. For values x and y and their truncated integer quotient q, the remainder r satisfies x == y * q + r.

The following example calculates the truncating remainder of dividing 8.625 by 0.75:

var x = 8.625
print(x / 0.75)
// Prints "11.5"

let q = (x / 0.75).rounded(.towardZero)
// q == 11.0
x.formTruncatingRemainder(dividingBy: 0.75)
// x == 0.375

let x1 = 0.75 * q + x
// x1 == 8.625

If this value and other are both finite numbers, the truncating remainder has the same sign as this value and is strictly smaller in magnitude than other. The formTruncatingRemainder(dividingBy:) method is always exact.

other: The value to use when dividing this value.

See Also: truncatingRemainder(dividingBy:), formRemainder(dividingBy:)

Declaration

mutating func formTruncatingRemainder(dividingBy other: Self)
func isEqual(to:) Required

Returns a Boolean value indicating whether this instance is equal to the given value.

This method serves as the basis for the equal-to operator (==) for floating-point values. When comparing two values with this method, -0 is equal to +0. NaN is not equal to any value, including itself. For example:

let x = 15.0
x.isEqual(to: 15.0)
// true
x.isEqual(to: .nan)
// false
Double.nan.isEqual(to: .nan)
// false

The isEqual(to:) method implements the equality predicate defined by the IEEE 754 specification.

other: The value to compare with this value. Returns: true if other has the same value as this instance; otherwise, false.

Declaration

func isEqual(to other: Self) -> Bool
func isLess(than:) Required

Returns a Boolean value indicating whether this instance is less than the given value.

This method serves as the basis for the less-than operator (<) for floating-point values. Some special cases apply:

  • Because NaN compares not less than nor greater than any value, this method returns false when called on NaN or when NaN is passed as other.
  • -infinity compares less than all values except for itself and NaN.
  • Every value except for NaN and +infinity compares less than +infinity.

    let x = 15.0 x.isLess(than: 20.0) // true x.isLess(than: .nan) // false Double.nan.isLess(than: x) // false

The isLess(than:) method implements the less-than predicate defined by the IEEE 754 specification.

other: The value to compare with this value. Returns: true if other is less than this value; otherwise, false.

Declaration

func isLess(than other: Self) -> Bool
func isLessThanOrEqualTo(_:) Required

Returns a Boolean value indicating whether this instance is less than or equal to the given value.

This method serves as the basis for the less-than-or-equal-to operator (<=) for floating-point values. Some special cases apply:

  • Because NaN is incomparable with any value, this method returns false when called on NaN or when NaN is passed as other.
  • -infinity compares less than or equal to all values except NaN.
  • Every value except NaN compares less than or equal to +infinity.

    let x = 15.0 x.isLessThanOrEqualTo(20.0) // true x.isLessThanOrEqualTo(.nan) // false Double.nan.isLessThanOrEqualTo(x) // false

The isLessThanOrEqualTo(_:) method implements the less-than-or-equal predicate defined by the IEEE 754 specification.

other: The value to compare with this value. Returns: true if other is less than this value; otherwise, false.

Declaration

func isLessThanOrEqualTo(_ other: Self) -> Bool
func isTotallyOrdered(belowOrEqualTo:) Required

Returns a Boolean value indicating whether this instance should precede the given value in an ascending sort.

This relation is a refinement of the less-than-or-equal-to operator (<=) that provides a total order on all values of the type, including noncanonical encodings, signed zeros, and NaNs. Because it is used much less frequently than the usual comparisons, there is no operator form of this relation.

The following example uses isTotallyOrdered(below:) to sort an array of floating-point values, including some that are NaN:

var numbers = [2.5, 21.25, 3.0, .nan, -9.5]
numbers.sort { $0.isTotallyOrdered(below: $1) }
// numbers == [-9.5, 2.5, 3.0, 21.25, nan]

The isTotallyOrdered(belowOrEqualTo:) method implements the total order relation as defined by the IEEE 754 specification.

other: A floating-point value to compare to this value. Returns: true if this value is ordered below other in a total ordering of the floating-point type; otherwise, false.

Declaration

func isTotallyOrdered(belowOrEqualTo other: Self) -> Bool
func multiplied(by:)

Returns the product of this value and the given value, rounded to a representable value.

This method serves as the basis for the multiplication operator (*). For example:

let x = 7.5
print(x.multiplied(by: 2.25))
// Prints "16.875"
print(x * 2.25)
// Prints "16.875"

The multiplied(by:) method implements the multiplication operation defined by the IEEE 754 specification.

other: The value to multiply by this value. Returns: The product of this value and other, rounded to a representable value.

See Also: multiply(by:)

Declaration

func multiplied(by other: Self) -> Self

Declared In

FloatingPoint, Arithmetic
mutating func multiply(by:) Required

Multiplies this value by the given value in place, rounding to a representable value.

This method serves as the basis for the in-place multiplication operator (*=). For example:

var (x, y) = (7.5, 7.5)
x.multiply(by: 2.25)
// x == 16.875
y *= 2.25
// y == 16.875

other: The value to multiply by this value.

See Also: multiplied(by:)

Declaration

mutating func multiply(by other: Self)

Declared In

FloatingPoint, Arithmetic
mutating func negate() Required

Replaces this value with its additive inverse.

The result is always exact. This example uses the negate() method to negate the value of the variable x:

var x = 21.5
x.negate()
// x == -21.5

See Also: negated()

Declaration

mutating func negate()
func negated()

Returns the additive inverse of this value.

The result is always exact. This method serves as the basis for the negation operator (prefixed -). For example:

let x = 21.5
let y = x.negated()
// y == -21.5

Returns: The additive inverse of this value.

See Also: negate()

Declaration

func negated() -> Self
func remainder(dividingBy:)

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

For two finite values x and y, the remainder r of dividing x by y satisfies x == y * q + r, where q is the integer nearest to x / y. If x / y is exactly halfway between two integers, q is chosen to be even. Note that q is not x / y computed in floating-point arithmetic, and that q may not be representable in any available integer type.

The following example calculates the remainder of dividing 8.625 by 0.75:

let x = 8.625
print(x / 0.75)
// Prints "11.5"

let q = (x / 0.75).rounded(.toNearestOrEven)
// q == 12.0
let r = x.remainder(dividingBy: 0.75)
// r == -0.375

let x1 = 0.75 * q + r
// x1 == 8.625

If this value and other are finite numbers, the remainder is in the closed range -abs(other / 2)...abs(other / 2). The remainder(dividingBy:) method is always exact. This method implements the remainder operation defined by the IEEE 754 specification.

other: The value to use when dividing this value. Returns: The remainder of this value divided by other.

See Also: formRemainder(dividingBy:), truncatingRemainder(dividingBy:)

Declaration

func remainder(dividingBy other: Self) -> Self
mutating func round(_:) Required

Rounds the value to an integral value using the specified rounding rule.

The following example rounds a value using four different rounding rules:

// Equivalent to the C 'round' function:
var w = 6.5
w.round(.toNearestOrAwayFromZero)
// w == 7.0

// Equivalent to the C 'trunc' function:
var x = 6.5
x.round(.towardZero)
// x == 6.0

// Equivalent to the C 'ceil' function:
var y = 6.5
y.round(.up)
// y == 7.0

// Equivalent to the C 'floor' function:
var z = 6.5
z.round(.down)
// z == 6.0

For more information about the available rounding rules, see the FloatingPointRoundingRule enumeration. To round a value using the default "schoolbook rounding", you can use the shorter round() method instead.

var w1 = 6.5
w1.round()
// w1 == 7.0

rule: The rounding rule to use.

See Also: round(), rounded(_:), FloatingPointRoundingRule

Declaration

mutating func round(_ rule: FloatingPointRoundingRule)
func rounded(_:)

Returns this value rounded to an integral value using the specified rounding rule.

The following example rounds a value using four different rounding rules:

let x = 6.5

// Equivalent to the C 'round' function:
print(x.rounded(.toNearestOrAwayFromZero))
// Prints "7.0"

// Equivalent to the C 'trunc' function:
print(x.rounded(.towardZero))
// Prints "6.0"

// Equivalent to the C 'ceil' function:
print(x.rounded(.up))
// Prints "7.0"

// Equivalent to the C 'floor' function:
print(x.rounded(.down))
// Prints "6.0"

For more information about the available rounding rules, see the FloatingPointRoundingRule enumeration. To round a value using the default "schoolbook rounding", you can use the shorter rounded() method instead.

print(x.rounded())
// Prints "7.0"

rule: The rounding rule to use. Returns: The integral value found by rounding using rule.

See Also: rounded(), round(_:), FloatingPointRoundingRule

Declaration

func rounded(_ rule: FloatingPointRoundingRule) -> Self
func squareRoot()

Returns the square root of the value, rounded to a representable value.

The following example declares a function that calculates the length of the hypotenuse of a right triangle given its two perpendicular sides.

func hypotenuse(_ a: Double, _ b: Double) -> Double {
    return (a * a + b * b).squareRoot()
}

let (dx, dy) = (3.0, 4.0)
let distance = hypotenuse(dx, dy)
// distance == 5.0

Returns: The square root of the value.

See Also: sqrt(_:), formSquareRoot()

Declaration

func squareRoot() -> Self
mutating func subtract(_:) Required

Subtracts the given value from this value in place, rounding to a representable value.

This method serves as the basis for the in-place subtraction operator (-=). For example:

var (x, y) = (7.5, 7.5)
x.subtract(2.25)
// x == 5.25
y -= 2.25
// y == 5.25

other: The value to subtract.

See Also: subtracting(_:)

Declaration

mutating func subtract(_ other: Self)

Declared In

FloatingPoint, Arithmetic
func subtracting(_:)

Returns the difference of this value and the given value, rounded to a representable value.

This method serves as the basis for the subtraction operator (-). For example:

let x = 7.5
print(x.subtracting(2.25))
// Prints "5.25"
print(x - 2.25)
// Prints "5.25"

The subtracting(_:) method implements the subtraction operation defined by the IEEE 754 specification.

other: The value to subtract from this value. Returns: The difference of this value and other, rounded to a representable value.

See Also: subtract(_:)

Declaration

func subtracting(_ other: Self) -> Self

Declared In

FloatingPoint, Arithmetic
func truncatingRemainder(dividingBy:)

Returns the remainder of this value divided by the given value using truncating division.

Performing truncating division with floating-point values results in a truncated integer quotient and a remainder. For values x and y and their truncated integer quotient q, the remainder r satisfies x == y * q + r.

The following example calculates the truncating remainder of dividing 8.625 by 0.75:

let x = 8.625
print(x / 0.75)
// Prints "11.5"

let q = (x / 0.75).rounded(.towardZero)
// q == 11.0
let r = x.truncatingRemainder(dividingBy: 0.75)
// r == 0.375

let x1 = 0.75 * q + r
// x1 == 8.625

If this value and other are both finite numbers, the truncating remainder has the same sign as this value and is strictly smaller in magnitude than other. The truncatingRemainder(dividingBy:) method is always exact.

other: The value to use when dividing this value. Returns: The remainder of this value divided by other using truncating division.

See Also: formTruncatingRemainder(dividingBy:), remainder(dividingBy:)

Declaration

func truncatingRemainder(dividingBy other: Self) -> Self

Default Implementations

init()

Declaration

init()

Declared In

Arithmetic
static var ulpOfOne: Self

Declaration

static var ulpOfOne: Self { get }
var floatingPointClass: FloatingPointClassification

Declaration

var floatingPointClass: FloatingPointClassification { get }
var nextDown: Self

Declaration

var nextDown: Self { get }
func adding(_:)

Declaration

func adding(_ other: Self) -> Self

Declared In

FloatingPoint, Arithmetic
func addingProduct(_:_:)

Declaration

func addingProduct(_ lhs: Self, _ rhs: Self) -> Self
func divided(by:)

Declaration

func divided(by other: Self) -> Self

Declared In

FloatingPoint, Arithmetic
static func maximum(_:_:)

Declaration

static func maximum(_ x: Self, _ y: Self) -> Self
static func maximumMagnitude(_:_:)

Declaration

static func maximumMagnitude(_ x: Self, _ y: Self) -> Self
static func minimum(_:_:)

Declaration

static func minimum(_ x: Self, _ y: Self) -> Self
static func minimumMagnitude(_:_:)

Declaration

static func minimumMagnitude(_ x: Self, _ y: Self) -> Self
func multiplied(by:)

Declaration

func multiplied(by other: Self) -> Self

Declared In

FloatingPoint, Arithmetic
func negated()

Declaration

func negated() -> Self
func remainder(dividingBy:)

Declaration

func remainder(dividingBy rhs: Self) -> Self
mutating func round()

Rounds this value to an integral value using "schoolbook rounding."

The round() method uses the .toNearestOrAwayFromZero rounding rule, where a value halfway between two integral values is rounded to the one with greater magnitude. The following example rounds several values using this default rule:

var x = 5.2
x.round()
// x == 5.0
var y = 5.5
y.round()
// y == 6.0
var z = -5.5
z.round()
// z == -6.0

To specify an alternative rule for rounding, use the round(_:) method instead.

See Also: round(_:), rounded(), FloatingPointRoundingRule

Declaration

mutating func round()
func rounded()

Returns this value rounded to an integral value using "schoolbook rounding."

The rounded() method uses the .toNearestOrAwayFromZero rounding rule, where a value halfway between two integral values is rounded to the one with greater magnitude. The following example rounds several values using this default rule:

(5.2).rounded()
// 5.0
(5.5).rounded()
// 6.0
(-5.2).rounded()
// -5.0
(-5.5).rounded()
// -6.0

To specify an alternative rule for rounding, use the rounded(_:) method instead.

Returns: The nearest integral value, or, if two integral values are equally close, the integral value with greater magnitude.

See Also: rounded(_:), round(), FloatingPointRoundingRule

Declaration

func rounded() -> Self
func rounded(_:)

Declaration

func rounded(_ rule: FloatingPointRoundingRule) -> Self
func squareRoot()

Declaration

func squareRoot() -> Self
func subtracting(_:)

Declaration

func subtracting(_ other: Self) -> Self

Declared In

FloatingPoint, Arithmetic
func truncatingRemainder(dividingBy:)

Declaration

func truncatingRemainder(dividingBy other: Self) -> Self