protocol FloatingPoint
Inheritance 
AbsoluteValuable, Comparable, Equatable, ExpressibleByIntegerLiteral, SignedNumber, Strideable
View Protocol Hierarchy →


Associated Types 
Exponent : SignedInteger
A type that can represent any written exponent. IntegerLiteralType
Stride : SignedNumber
A type that can represent the distance between two values of 
Import  import Swift 
Initializers
Creates a new value, rounded to the closest possible representatation.
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 floatingpoint value.
Declaration
init(_ value: Int)
Creates a new value, rounded to the closest possible representatation.
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 floatingpoint value.
Declaration
init(_ value: Int8)
Creates a new value, rounded to the closest possible representatation.
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 floatingpoint value.
Declaration
init(_ value: Int16)
Creates a new value, rounded to the closest possible representatation.
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 floatingpoint value.
Declaration
init(_ value: Int32)
Creates a new value, rounded to the closest possible representatation.
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 floatingpoint value.
Declaration
init(_ value: Int64)
Creates a new value, rounded to the closest possible representatation.
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 floatingpoint value.
Declaration
init(_ value: UInt)
Creates a new value, rounded to the closest possible representatation.
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 floatingpoint value.
Declaration
init(_ value: UInt8)
Creates a new value, rounded to the closest possible representatation.
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 floatingpoint value.
Declaration
init(_ value: UInt16)
Creates a new value, rounded to the closest possible representatation.
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 floatingpoint value.
Declaration
init(_ value: UInt32)
Creates a new value, rounded to the closest possible representatation.
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 floatingpoint value.
Declaration
init(_ value: UInt64)
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 floatingpoint 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 exponentation, computed as if by a single, correctly rounded,
floatingpoint 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 ofexponent
.  If the value you pass to
significand
is NaN, the result is NaN.
For any floatingpoint 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)
Creates a new floatingpoint 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)
Create an instance initialized to value
.
Declaration
init(integerLiteral value: Self.IntegerLiteralType)
Declared In
ExpressibleByIntegerLiteral
Static Variables
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 typespecific 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 }
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 }
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 }
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 typespecific 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 }
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
floatingpoint value is NaN, use its isNaN
property instead of the
equalto 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 }
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 }
The radix, or base of exponentiation, for a floatingpoint type.
The magnitude of a floatingpoint 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 floatingpoint types) or 10 (for decimal floatingpoint types) are extraordinarily rare in practice.
Declaration
static var radix: Int { get }
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 floatingpoint 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 }
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
The exponent of the floatingpoint value.
The exponent of a floatingpoint value is the integer part of the
logarithm of the value's magnitude. For a value x
of a floatingpoint
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, thenx.exponent
isInt.min
.  If
x
is +/infinity or NaN, thenx.exponent
isInt.max
This property implements the logB
operation defined by the IEEE 754
specification.
Declaration
var exponent: Self.Exponent { get }
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 }
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 floatingpoint 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 }
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 }
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 }
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 equalto operator (==
) or notequalto 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 equalto 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 }
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 }
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 }
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 denormalizedthese are different names for the same concept.
Declaration
var isSubnormal: Bool { get }
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 }
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
isinfinity
, thenx.nextDown
isgreatestFiniteMagnitude
.  If
x
isleastNonzeroMagnitude
, thenx.nextDown
is0.0
.  If
x
is zero, thenx.nextDown
isleastNonzeroMagnitude
.  If
x
isgreatestFiniteMagnitude
, thenx.nextDown
isinfinity
.
Declaration
var nextDown: Self { get }
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
isinfinity
, thenx.nextUp
isgreatestFiniteMagnitude
.  If
x
isleastNonzeroMagnitude
, thenx.nextUp
is0.0
.  If
x
is zero, thenx.nextUp
isleastNonzeroMagnitude
.  If
x
isgreatestFiniteMagnitude
, thenx.nextUp
isinfinity
.
Declaration
var nextUp: Self { get }
The sign of the floatingpoint 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
Don't 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 }
The significand of the floatingpoint value.
The magnitude of a floatingpoint 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, thenx.significand
is 0.0.  If
x
is infinity, thenx.significand
is 1.0.  If
x
is NaN, thenx.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 }
The unit in the last place of self
.
This is the unit of the least significant digit in the significand of
self
. 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:
greatestFiniteMagnitude.ulp
is a finite number, even though the next greater representable value isinfinity
.x.ulp
isNaN
ifx
is not a finite number. If
x
is very small in magnitude, thenx.ulp
may be a subnormal number. On targets that do not support subnormals,x.ulp
may be rounded to zero.
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 }
Static Methods
Returns the absolute value of x
.
Declaration
static func abs(_ x: Self) > Self
Declared In
AbsoluteValuable
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 floatingpoint value.
y: Another floatingpoint 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
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 floatingpoint value.
y: Another floatingpoint 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
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 floatingpoint value.
y: Another floatingpoint 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
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 floatingpoint value.
y: Another floatingpoint 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
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
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
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
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
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
Returns the result of negating x
.
Declaration
prefix func (x: Self) > Self
Declared In
SignedNumber
Returns the difference between lhs
and rhs
.
Declaration
func (lhs: Self, rhs: Self) > Self
Declared In
SignedNumber
Adds the given value to this value in place, rounded to a representable value.
This method serves as the basis for the inplace 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)
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)
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
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
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
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
Divides this value by the given value in place, rounding to a representable value.
This method serves as the basis for the inplace 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)
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
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
floatingpoint 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)
Replaces this value with its square root, rounded to a representable value.
See Also: sqrt(_:)
, squareRoot()
Declaration
mutating func formSquareRoot()
Replaces this value with the remainder of itself divided by the given value using truncating division.
Performing truncating division with floatingpoint 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 other
and is strictly smaller in
magnitude. 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)
Returns a Boolean value indicating whether this instance is equal to the given value.
This method serves as the basis for the equalto operator (==
) for
floatingpoint 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
Returns a Boolean value indicating whether this instance is less than the given value.
This method serves as the basis for the lessthan operator (<
) for
floatingpoint 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 asother
. 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 lessthan 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
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 lessthanorequalto operator
(<=
) for floatingpoint 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 asother
. 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 lessthanorequal
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
Returns a Boolean value indicating whether this instance should precede the given value in an ascending sort.
This relation is a refinement of the lessthanorequalto 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
floatingpoint 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 floatingpoint value to compare to this value.
Returns: true
if this value is ordered below other
in a total
ordering of the floatingpoint type; otherwise, false
.
Declaration
func isTotallyOrdered(belowOrEqualTo other: Self) > Bool
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
Multiplies this value by the given value in place, rounding to a representable value.
This method serves as the basis for the inplace 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)
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()
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
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
floatingpoint 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
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)
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
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
Subtracts the given value from this value in place, rounding to a representable value.
This method serves as the basis for the inplace 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)
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 addition 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
Returns the remainder of this value divided by the given value using truncating division.
Performing truncating division with floatingpoint 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 other
and is strictly smaller in
magnitude. 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
Declaration
var floatingPointClass: FloatingPointClassification { get }
Declaration
var nextDown: Self { get }
Declaration
static var ulpOfOne: Self { get }
Declaration
func adding(_ other: Self) > Self
Declaration
func addingProduct(_ lhs: Self, _ rhs: Self) > Self
Declaration
func divided(by other: Self) > Self
Declaration
static func maximum(_ x: Self, _ y: Self) > Self
Declaration
static func maximumMagnitude(_ x: Self, _ y: Self) > Self
Declaration
static func minimum(_ x: Self, _ y: Self) > Self
Declaration
static func minimumMagnitude(_ x: Self, _ y: Self) > Self
Declaration
func multiplied(by other: Self) > Self
Declaration
func negated() > Self
Declaration
func remainder(dividingBy rhs: Self) > Self
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()
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
Declaration
func rounded(_ rule: FloatingPointRoundingRule) > Self
Declaration
func squareRoot() > Self
Declaration
func subtracting(_ other: Self) > Self
Declaration
func truncatingRemainder(dividingBy other: Self) > Self
A floatingpoint numeric type.
Floatingpoint types are used to represent fractional numbers, like 5.5, 100.0, or 3.14159274. Each floatingpoint type has its own possible range and precision. The floatingpoint types in the standard library are
Float
,Double
, andFloat80
where available.Create new instances of floatingpoint types using integer or floatingpoint literals. For example:
The
FloatingPoint
protocol declares common arithmetic operations, so you can write functions and algorithms that work on any floatingpoint type. The following example declares a function that calculates the length of the hypotenuse of a right triangle given its two perpendicular sides. Because thehypotenuse(_:_:)
function uses a generic parameter constrained to theFloatingPoint
protocol, you can call it using any floatingpoint type.Floatingpoint 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 floatingpoint value
x
of typeF
, where**
is exponentiation:Here's an example of the number 8.5 represented as an instance of the
Double
type, which defines a radix of 2.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 floatingpoint type.Additional Considerations
In addition to representing specific numbers, floatingpoint 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 asF.infinity
andF.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.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")
Floatingpoint 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
.Because testing whether one NaN is equal to another NaN results in
false
, use theisNaN
property to test whether a value is NaN.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:Note that some elements in the
temperatureData
array are not valid numbers. When these invalid strings are parsed by theDouble
failable initializer, the example uses the nilcoalescing operator (??
) to provide NaN as a fallback value.Next, the observations in Celsius are converted to Fahrenheit:
The NaN values in the
tempsCelsius
array are propagated through the conversion and remain NaN intempsFahrenheit
.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:Instead, when you need an operation to have a specific numeric result, filter out any NaN values using the
isNaN
property.Finally, report the average temperature and observation counts: