struct Double
A doubleprecision, floatingpoint value type.
Inheritance  BinaryFloatingPoint, Codable, CustomDebugStringConvertible, CustomReflectable, CustomStringConvertible, ExpressibleByIntegerLiteral, Hashable, LosslessStringConvertible, SIMDScalar, Strideable, TextOutputStreamable 

Associated Types 
public typealias SIMDMaskScalar = Int64
public typealias Magnitude = Double
public typealias Exponent = Int
public typealias RawSignificand = UInt64

Nested Types  Double.SIMD2Storage, Double.SIMD4Storage, Double.SIMD8Storage, Double.SIMD16Storage, Double.SIMD32Storage, Double.SIMD64Storage 
Initializers
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.
 Parameter value: The integer to convert to a floatingpoint value.
Declaration
public init(_ v: Int)
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.
 Parameter value: The integer to convert to a floatingpoint value.
Declaration
@inlinable public init<Source>(_ value: Source) where Source: BinaryInteger
Creates a new instance that approximates the given value.
The value of other
is rounded to a representable value, if necessary.
A NaN passed as other
results in another NaN, with a signaling NaN
value converted to quiet NaN.
let x: Float = 21.25
let y = Double(x)
// y == 21.25
let z = Double(Float.nan)
// z.isNaN == true
 Parameter other: The value to use for the new instance.
Declaration
@inlinable public init(_ other: Float)
Creates a new instance initialized to the given value.
The value of other
is represented exactly by the new instance. A NaN
passed as other
results in another NaN, with a signaling NaN value
converted to quiet NaN.
let x: Double = 21.25
let y = Double(x)
// y == 21.25
let z = Double(Double.nan)
// z.isNaN == true
 Parameter other: The value to use for the new instance.
Declaration
@inlinable public init(_ other: Double)
Creates a new instance that approximates the given value.
The value of other
is rounded to a representable value, if necessary.
A NaN passed as other
results in another NaN, with a signaling NaN
value converted to quiet NaN.
let x: Float80 = 21.25
let y = Double(x)
// y == 21.25
let z = Double(Float80.nan)
// z.isNaN == true
 Parameter other: The value to use for the new instance.
Declaration
@inlinable public init(_ other: Float80)
Creates a new instance from the given 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.
 Parameter value: A floatingpoint value to be converted.
Declaration
@inlinable public init<Source>(_ value: Source) where Source: BinaryFloatingPoint
Creates a new value with the given bit pattern.
The value passed as bitPattern
is interpreted in the binary interchange
format defined by the IEEE 754 specification.
 Parameter bitPattern: The integer encoding of a
Double
instance.
Declaration
@inlinable public init(bitPattern: UInt64)
Creates an instance initialized to the specified floatingpoint value.
Do not call this initializer directly. Instead, initialize a variable or constant using a floatingpoint literal. For example:
let x = 21.5
In this example, the assignment to the x
constant calls this
floatingpoint literal initializer behind the scenes.
 Parameter value: The value to create.
Declaration
@inlinable public init(floatLiteral value: Double)
Creates a new instance by decoding from the given decoder.
This initializer throws an error if reading from the decoder fails, or if the data read is corrupted or otherwise invalid.
 Parameter decoder: The decoder to read data from.
Declaration
public init(from decoder: Decoder) throws
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.
 Parameter value: The value to create.
Declaration
public init(integerLiteral value: Int64)
Creates a NaN ("not a number") value with the specified payload.
NaN values compare not equal to every value, including themselves. Most
operations with a NaN operand produce a NaN result. Don't use the
equalto operator (==
) to test whether a value is NaN. Instead, use
the value's isNaN
property.
let x = Double(nan: 0, signaling: false)
print(x == .nan)
// Prints "false"
print(x.isNaN)
// Prints "true"
Declaration
@inlinable public init(nan payload: Double.RawSignificand, signaling: Bool)
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 exponentiation, 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:
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.
Declaration
@inlinable public init(sign: FloatingPointSign, exponent: Int, significand: Double)
Creates a new instance from the specified sign and bit patterns.
The values passed as exponentBitPattern
and significandBitPattern
are
interpreted in the binary interchange format defined by the IEEE 754
specification.
Declaration
@inlinable public init(sign: FloatingPointSign, exponentBitPattern: UInt, significandBitPattern: UInt64)
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.
Declaration
public init(signOf sign: Double, magnitudeOf mag: Double)
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.
Declaration
@inlinable public init(signOf: Self, magnitudeOf: Self)
Creates a new instance from the given string.
The string passed as text
can represent a real number in decimal or
hexadecimal format or special floatingpoint values for infinity and NaN
("not a number").
The given string may begin with a plus or minus sign character (+
or

). The allowed formats for each of these representations is then as
follows:
Passing any other format or any additional characters as text
results
in nil
. For example, the following conversions result in nil
:
Double(" 5.0") // Includes whitespace
Double("±2.0") // Invalid character
Double("0x1.25e4") // Incorrect exponent format
 Parameter text: The input string to convert to a
Double
instance. Iftext
has invalid characters or is in an invalid format, the result isnil
.
Declaration
@inlinable public init?<S>(_ text: S) where S: StringProtocol
Creates a new instance initialized to the given value, if it can be represented without rounding.
If other
can't be represented as an instance of Double
without
rounding, the result of this initializer is nil
. In particular,
passing NaN as other
always results in nil
.
let x: Float = 21.25
let y = Double(exactly: x)
// y == Optional.some(21.25)
let z = Double(exactly: Float.nan)
// z == nil
 Parameter other: The value to use for the new instance.
Declaration
@inlinable public init?(exactly other: Float)
Creates a new instance initialized to the given value, if it can be represented without rounding.
If other
can't be represented as an instance of Double
without
rounding, the result of this initializer is nil
. In particular,
passing NaN as other
always results in nil
.
let x: Double = 21.25
let y = Double(exactly: x)
// y == Optional.some(21.25)
let z = Double(exactly: Double.nan)
// z == nil
 Parameter other: The value to use for the new instance.
Declaration
@inlinable public init?(exactly other: Double)
Creates a new instance initialized to the given value, if it can be represented without rounding.
If other
can't be represented as an instance of Double
without
rounding, the result of this initializer is nil
. In particular,
passing NaN as other
always results in nil
.
let x: Float80 = 21.25
let y = Double(exactly: x)
// y == Optional.some(21.25)
let z = Double(exactly: Float80.nan)
// z == nil
 Parameter other: The value to use for the new instance.
Declaration
@inlinable public init?(exactly other: Float80)
Creates a new instance from the given value, if it can be represented exactly.
If the given floatingpoint value cannot be represented exactly, the
result is nil
.
 Parameter value: A floatingpoint value to be converted.
Declaration
@inlinable public init?<Source>(exactly value: Source) where Source: BinaryFloatingPoint
Instance Variables
The floatingpoint value with the same sign and exponent as this value, but with a significand of 1.0.
A binade is a set of binary floatingpoint values that all have the
same sign and exponent. The binade
property is a member of the same
binade as this value, but with a unit significand.
In this example, x
has a value of 21.5
, which is stored as
1.34375 * 2**4
, where **
is exponentiation. Therefore, x.binade
is
equal to 1.0 * 2**4
, or 16.0
.
let x = 21.5
// x.significand == 1.34375
// x.exponent == 4
let y = x.binade
// y == 16.0
// y.significand == 1.0
// y.exponent == 4
Declaration
var binade: Double
The bit pattern of the value's encoding.
The bit pattern matches the binary interchange format defined by the IEEE 754 specification.
Declaration
var bitPattern: UInt64
A mirror that reflects the Double
instance.
Declaration
var customMirror: Mirror
A custom playground Quick Look for the Double
instance.
Declaration
var customPlaygroundQuickLook: _PlaygroundQuickLook
A textual representation of the value, suitable for debugging.
Declaration
var debugDescription: String
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:
This property implements the logB
operation defined by the IEEE 754
specification.
Declaration
var exponent: Int
The raw encoding of the value's exponent field.
This value is unadjusted by the type's exponent bias.
Declaration
var exponentBitPattern: UInt
A Boolean value indicating whether the instance's representation is in its canonical form.
The IEEE 754 specification defines a canonical, or preferred,
encoding of a floatingpoint value. On platforms that fully support
IEEE 754, every Float
or Double
value is canonical, but
noncanonical values can exist on other platforms or for other types.
Some examples:
Declaration
var isCanonical: Bool
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
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
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
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
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
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
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
The magnitude of this value.
For any numeric value x
, x.magnitude
is the absolute value of x
.
You can use the magnitude
property in operations that are simpler to
implement in terms of unsigned values, such as printing the value of an
integer, which is just printing a '' character in front of an absolute
value.
let x = 200
// x.magnitude == 200
The global abs(_:)
function provides more familiar syntax when you need
to find an absolute value. In addition, because abs(_:)
always returns
a value of the same type, even in a generic context, using the function
instead of the magnitude
property is encouraged.
Declaration
var magnitude: Double
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:
Declaration
var nextUp: Double
The number of scalars, or elements, in the vector.
Declaration
var scalarCount: Int
The number of scalars, or elements, in the vector.
Declaration
var scalarCount: Int
The number of scalars, or elements, in the vector.
Declaration
var scalarCount: Int
The number of scalars, or elements, in the vector.
Declaration
var scalarCount: Int
The number of scalars, or elements, in the vector.
Declaration
var scalarCount: Int
The number of scalars, or elements, in the vector.
Declaration
var scalarCount: Int
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
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
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:
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: Double
The raw encoding of the value's significand field.
The significandBitPattern
property does not include the leading
integral bit of the significand, even for types like Float80
that
store it explicitly.
Declaration
var significandBitPattern: UInt64
The number of bits required to represent the value's significand.
If this value is a finite nonzero number, significandWidth
is the
number of fractional bits required to represent the value of
significand
; otherwise, significandWidth
is 1. The value of
significandWidth
is always 1 or between zero and
significandBitCount
. For example:
Declaration
var significandWidth: Int
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:
See also the ulpOfOne
static property.
Declaration
var ulp: Double
Subscripts
Accesses the element at the specified index.
 Parameter index: The index of the element to access.
index
must be in the range0..<scalarCount
.
Declaration
public subscript(index: Int) > Double
Accesses the element at the specified index.
 Parameter index: The index of the element to access.
index
must be in the range0..<scalarCount
.
Declaration
public subscript(index: Int) > Double
Accesses the element at the specified index.
 Parameter index: The index of the element to access.
index
must be in the range0..<scalarCount
.
Declaration
public subscript(index: Int) > Double
Accesses the element at the specified index.
 Parameter index: The index of the element to access.
index
must be in the range0..<scalarCount
.
Declaration
public subscript(index: Int) > Double
Accesses the element at the specified index.
 Parameter index: The index of the element to access.
index
must be in the range0..<scalarCount
.
Declaration
public subscript(index: Int) > Double
Accesses the element at the specified index.
 Parameter index: The index of the element to access.
index
must be in the range0..<scalarCount
.
Declaration
public subscript(index: Int) > Double
Instance Methods
Adds the product of the two given values to this value in place, computed without intermediate rounding.
Declaration
public mutating func addProduct(_ lhs: Double, _ rhs: Double)
Returns a value that is offset the specified distance from this value.
Use the advanced(by:)
method in generic code to offset a value by a
specified distance. If you're working directly with numeric values, use
the addition operator (+
) instead of this method.
func addOne<T: Strideable>(to x: T) > T
where T.Stride: ExpressibleByIntegerLiteral
{
return x.advanced(by: 1)
}
let x = addOne(to: 5)
// x == 6
let y = addOne(to: 3.5)
// y = 4.5
If this type's Stride
type conforms to BinaryInteger
, then for a
value x
, a distance n
, and a value y = x.advanced(by: n)
,
x.distance(to: y) == n
. Using this method with types that have a
noninteger Stride
may result in an approximation.
 Parameter n: The distance to advance this value.
Complexity: O(1)
Declaration
public func advanced(by amount: Double) > Double
Returns the distance from this value to the given value, expressed as a stride.
If this type's Stride
type conforms to BinaryInteger
, then for two
values x
and y
, and a distance n = x.distance(to: y)
,
x.advanced(by: n) == y
. Using this method with types that have a
noninteger Stride
may result in an approximation.
 Parameter other: The value to calculate the distance to.
Complexity: O(1)
Declaration
public func distance(to other: Double) > Double
Encodes this value into the given encoder.
This function throws an error if any values are invalid for the given encoder's format.
 Parameter encoder: The encoder to write data to.
Declaration
public func encode(to encoder: Encoder) throws
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
formRemainder(dividingBy:)
method is always exact.
 Parameter other: The value to use when dividing this value.
Declaration
@inlinable public mutating func formRemainder(dividingBy other: Double)
Replaces this value with its square root, rounded to a representable value.
Declaration
public 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 this value and is strictly smaller in
magnitude than other
. The formTruncatingRemainder(dividingBy:)
method is always exact.
 Parameter other: The value to use when dividing this value.
Declaration
@inlinable public mutating func formTruncatingRemainder(dividingBy other: Double)
Hashes the essential components of this value by feeding them into the given hasher.
Implement this method to conform to the Hashable
protocol. The
components used for hashing must be the same as the components compared
in your type's ==
operator implementation. Call hasher.combine(_:)
with each of these components.
Important: Never call
finalize()
onhasher
. Doing so may become a compiletime error in the future.
 Parameter hasher: The hasher to use when combining the components of this instance.
Declaration
@inlinable public func hash(into hasher: inout Hasher)
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.
 Parameter other: The value to compare with this value.
Declaration
public func isEqual(to other: Double) > 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:
The isLess(than:)
method implements the lessthan predicate defined by
the IEEE 754 specification.
 Parameter other: The value to compare with this value.
Declaration
public func isLess(than other: Double) > 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:
The isLessThanOrEqualTo(_:)
method implements the lessthanorequal
predicate defined by the IEEE 754 specification.
 Parameter other: The value to compare with this value.
Declaration
public func isLessThanOrEqualTo(_ other: Double) > Bool
Returns a Boolean value indicating whether this instance should precede or tie positions with 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
signed zeros and NaNs.
The following example uses isTotallyOrdered(belowOrEqualTo:)
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 { !$1.isTotallyOrdered(belowOrEqualTo: $0) }
// 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.
 Parameter other: A floatingpoint value to compare to this value.
Declaration
@inlinable public func isTotallyOrdered(belowOrEqualTo other: Self) > Bool
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
Declaration
public mutating func negate()
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
 Parameter rule: The rounding rule to use.
Declaration
public mutating func round(_ rule: FloatingPointRoundingRule)
Writes a textual representation of this instance into the given output stream.
Declaration
public func write<Target>(to target: inout Target) where Target: TextOutputStream
Type Variables
The number of bits used to represent the type's exponent.
A binary floatingpoint type's exponentBitCount
imposes a limit on the
range of the exponent for normal, finite values. The exponent bias of
a type F
can be calculated as the following, where **
is
exponentiation:
let bias = 2 ** (F.exponentBitCount  1)  1
The least normal exponent for values of the type F
is 1  bias
, and
the largest finite exponent is bias
. An allzeros exponent is reserved
for subnormals and zeros, and an allones exponent is reserved for
infinity and NaN.
For example, the Float
type has an exponentBitCount
of 8, which gives
an exponent bias of 127
by the calculation above.
let bias = 2 ** (Float.exponentBitCount  1)  1
// bias == 127
print(Float.greatestFiniteMagnitude.exponent)
// Prints "127"
print(Float.leastNormalMagnitude.exponent)
// Prints "126"
Declaration
var exponentBitCount: Int
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
var greatestFiniteMagnitude: Double
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
var infinity: Double
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
var leastNonzeroMagnitude: Double
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
var leastNormalMagnitude: Double
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"
Declaration
var nan: Double
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
var pi: Double
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
var radix: Int
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.
Declaration
var signalingNaN: Double
The available number of fractional significand bits.
For fixedwidth floatingpoint types, this is the actual number of fractional significand bits.
For extensible floatingpoint types, significandBitCount
should be the
maximum allowed significand width (without counting any leading integral
bit of the significand). If there is no upper limit, then
significandBitCount
should be Int.max
.
Note that Float80.significandBitCount
is 63, even though 64 bits are
used to store the significand in the memory representation of a
Float80
(unlike other floatingpoint types, Float80
explicitly
stores the leading integral significand bit, but the
BinaryFloatingPoint
APIs provide an abstraction so that users don't
need to be aware of this detail).
Declaration
var significandBitCount: Int
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
var ulpOfOne: Double
Type Methods
Multiplies two values and produces their product, rounding to a representable value.
The multiplication operator (*
) calculates the product of its two
arguments. For example:
let x = 7.5
let y = x * 2.25
// y == 16.875
The *
operator implements the multiplication operation defined by the
IEEE 754 specification.
Declaration
public static func *(lhs: Double, rhs: Double) > Double
Multiplies two values and stores the result in the lefthandside variable, rounding to a representable value.
Declaration
public static func *=(lhs: inout Double, rhs: Double)
Adds two values and produces their sum, rounded to a representable value.
The addition operator (+
) calculates the sum of its two arguments. For
example:
let x = 1.5
let y = x + 2.25
// y == 3.75
The +
operator implements the addition operation defined by the
IEEE 754 specification.
Declaration
public static func +(lhs: Double, rhs: Double) > Double
Adds two values and stores the result in the lefthandside variable, rounded to a representable value.
Declaration
public static func +=(lhs: inout Double, rhs: Double)
Subtracts one value from another and produces their difference, rounded to a representable value.
The subtraction operator (
) calculates the difference of its two
arguments. For example:
let x = 7.5
let y = x  2.25
// y == 5.25
The 
operator implements the subtraction operation defined by the
IEEE 754 specification.
Declaration
public static func (lhs: Double, rhs: Double) > Double
Calculates the additive inverse of a value.
The unary minus operator (prefix 
) calculates the negation of its
operand. The result is always exact.
let x = 21.5
let y = x
// y == 21.5
 Parameter operand: The value to negate.
Declaration
prefix public static func (x: Double) > Double
Subtracts the second value from the first and stores the difference in the lefthandside variable, rounding to a representable value.
Declaration
public static func =(lhs: inout Double, rhs: Double)
Returns the quotient of dividing the first value by the second, rounded to a representable value.
The division operator (/
) calculates the quotient of the division if
rhs
is nonzero. If rhs
is zero, the result of the division is
infinity, with the sign of the result matching the sign of lhs
.
let x = 16.875
let y = x / 2.25
// y == 7.5
let z = x / 0
// z.isInfinite == true
The /
operator implements the division operation defined by the IEEE
754 specification.
Declaration
public static func /(lhs: Double, rhs: Double) > Double
Divides the first value by the second and stores the quotient in the lefthandside variable, rounding to a representable value.
Declaration
public static func /=(lhs: inout Double, rhs: Double)
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
.
Declaration
@inlinable public static func <(x: Self, y: Self) > Bool
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
.
Declaration
@inlinable public static func ==(x: Self, y: Self) > Bool
Declaration
public init()