## Overview

• Double represents a 64-bit floating-point number.
• Double has a precision of at least 15 decimal digits, whereas the precision of Float can be as little as 6 decimal digits.
• Swift always chooses Double (rather than Float) when inferring the type of floating-point numbers.If you combine integer and floating-point literals in an expression, a type of Double will be inferred.

## 1. Converting Floating-Point Values

#### 1.1 init(_:)

• Creates a new instance initialized to the given value.
``````let x: Double = 21.25
let y = Double(x)
print(x, y)
//prints 21.25 21.25
``````

#### 1.2 init(sign:exponent:significand:)

• Creates a new value from the given sign, exponent, and significand.
``````let z = Double(sign: .plus, exponent: -2, significand: 1.5)
print(z)
//prints 0.375
``````

#### 1.3 init(signOf:magnitudeOf:)

• Creates a new floating-point value using the sign of one value and the magnitude of another.
``````let a = -21.5
let b = 305.15
let c = Double(signOf: a, magnitudeOf: b)
print(c)
//prints -305.15
``````

## 2. Performing Calculations

#### 2.1 Floating-Point Operators for Double

• Perform arithmetic and bitwise operations or compare values.
Framework
``````print(a + b)
//prints 283.65

print(a - b)
//prints -326.65

print(a * b)
//prints -6560.725

print(a / b)
//prints -0.0704571522202196

a += b
print(a)
//prints 283.65

a -= b
print(a)
//prints -21.5

a *= b
print(a)
//prints -6560.725

a /= b
print(a)
//prints -21.5
``````

#### 2.2 squareRoot()

• Returns the square root of the value, rounded to a representable value.
``````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)
print(distance)
//prints 5.0
``````

#### 2.3 remainder(dividingBy:)

• Returns the remainder of this value divided by the given value.
``````let q = (x / 0.75).rounded(.toNearestOrEven)
let r = x.remainder(dividingBy: 0.75)
print(q,r)
//prints 28.0 0.25
``````

#### 2.4 negate()

• Replaces this value with its additive inverse.
``````var k = 21.003
k.negate()
print(k)
//prints -21.003
``````

## 3. Querying a Double's State

#### 3.1 isZero

• A Boolean value indicating whether the instance is equal to zero.
``````let m = -0.0
print(m.isZero)
//prints true
``````

#### 3.2 isFinite

• A Boolean value indicating whether this instance is finite.
``````let m = -0.0
print(m.isFinite)
//prints true
``````

#### 3.3 isInfinite

• A Boolean value indicating whether the instance is infinite.
``````let m = -0.0
print(m.isInfinite)
//prints false
``````

#### 3.4 isNaN

• A Boolean value indicating whether the instance is NaN (“not a number”).
``````let x1 = 0.0
let y1 = x1 * .infinity
print(x1 == Double.nan)
//prints false
print(y1 == Double.nan)
//prints false
``````

#### 3.5 isSignalingNaN

• A Boolean value indicating whether the instance is a signaling NaN.
``````let x1 = 0.0
let y1 = x1 * .infinity
print(x1.isSignalingNaN)
//prints false
print(y1.isSignalingNaN)
//prints false
``````

#### 3.6 isNormal

• A Boolean value indicating whether this instance is normal.
``````let x1 = 0.0
let y1 = x1 * .infinity
print(x1.isNormal)
//prints false
print(y1.isNormal)
//prints false
``````

#### 3.7 isSubnormal

• A Boolean value indicating whether the instance is subnormal.
``````let x1 = 0.0
let y1 = x1 * .infinity
print(x1.isSubnormal)
//prints false
print(y1.isSubnormal)
//prints false
``````

#### 3.8 isCanonical

• A Boolean value indicating whether the instance’s representation is in the canonical form.
``````let x1 = 0.0
let y1 = x1 * .infinity
print(x1.isCanonical)
//prints true
print(y1.isCanonical)
//prints true
``````

#### 3.9 floatingPointClass

• The classification of this value.
``````let x1 = 0.0
let y1 = x1 * .infinity
print(x1.floatingPointClass)
//prints positiveZero
print(y1.floatingPointClass)
//prints quietNaN
``````

## 4. Rounding

#### 4.1 rounded()

• Returns this value rounded to an integral value using “schoolbook rounding.”
``````let m1: Double = 6.5
print(m1.rounded(.toNearestOrAwayFromZero))
//prints 7.0
print(m1.rounded(.towardZero))
//prints 6.0
print(m1.rounded(.up))
//prints 7.0
print(m1.rounded(.down))
//prints 6.0
``````

#### 4.2 round()

• Rounds this value to an integral value using “schoolbook rounding.”
``````var j = 5.2
j.round()
print(j)
//prints 5.0

var h = 5.5
h.round()
print(h)
//prints 6.0

var g = -5.5
g.round()
print(g)
//prints -6.0
``````

## 5. Comparing Doubles

#### 5.1 Floating-Point Operators for Double - comparison

• Perform arithmetic and bitwise operations or compare values.
``````print(a > b)
//prints false

print(a < b)
//prints true

print(a <= b)
//prints true

print(a >= b)
//prints false

print(a == b)
//prints false
``````

#### 5.2 isEqual(to:)

• Returns a Boolean value indicating whether this instance is equal to the given value.
``````var a = -21.5
var b = 305.15
if(a.isEqual(to: b)){
print(a)
}else{
print(b)
}
//prints 305.15
``````

#### 5.3 isLess(than:)

• Returns a Boolean value indicating whether this instance is less than the given value.
``````var a = -21.5
var b = 305.15
if(a.isLess(than: b)){
print(a)
}else{
print(b)
}
//prints -21.5
``````

#### 5.4 isLessThanOrEqualTo(_:)

• Returns a Boolean value indicating whether this instance is less than or equal to the given value.
``````var a = -21.5
var b = 305.15
if(a.isLessThanOrEqualTo(b)){
print(a)
}else{
print(b)
}
//prints -21.5
``````

#### 5.5 isTotallyOrdered(belowOrEqualTo:)

• Returns a Boolean value indicating whether this instance should precede or tie positions with the given value in an ascending sort.
``````var a = -21.5
var b = 305.15
if(a.isTotallyOrdered(belowOrEqualTo: b)){
print(a)
}else{
print(b)
}
//prints -21.5
``````

#### 5.6 minimum(::)

• Returns the lesser of the two given values.
``````print(Double.minimum(10.0, -25.0))
//prints -25.0
``````

#### 5.7 maximum(::)

• Returns the lesser of the two given values.
``````print(Double.maximum(10.0, -25.0))
//prints 10.0
``````

#### 5.8 minimumMagnitude(::)

• Returns the value with lesser magnitude.
``````print(Double.minimumMagnitude(-10.0, 2.0))
//prints 2.0
``````

#### 5.9 maximumMagnitude(::)

• Returns the value with greater magnitude.
``````print(Double.maximumMagnitude(-10.0, 2.0))
//prints -10.0
``````

## 6. Finding the Sign and Magnitude

#### 6.1 magnitude

• The magnitude of this value.
``````let num1 = -259.0001
print(num1.magnitude)
//prints 259.0001
``````

#### 6.2 sign

• The sign of the floating-point value.
``````let num1 = -259.0001
print(num1.sign)
//prints minus
``````

## 7. Querying a Double

#### 7.1 ulp

• The unit in the last place of this value.
``````let num2 = 0.23
print(num2.ulp)
//prints 2.77555756156289e-17
``````

#### 7.2 significand

• The significand of the floating-point value.
``````let num3 = 9.91
print(num3.significand)
//prints 1.23875
``````

#### 7.3 exponent

• The exponent of the floating-point value.
``````let num3 = 9.91
print(num3.exponent)
//prints 3
``````

#### 7.4 nextUp

• The least representable value that compares greater than this value.
``````let num4 = 10.0
print(num4.nextUp)
//prints 10.0
``````

#### 7.5 nextDown

• The greatest representable value that compares less than this value.
``````let num4 = 10.0
print(num4.nextDown)
//prints 10.0
``````

• The floating-point value with the same sign and exponent as this value, but with a significand of 1.0.
``````print(num4.binade)
//prints 8.0
``````

## 8. Accessing Numeric Constants

#### 8.1 pi

• The mathematical constant pi.
``````print(Double.pi)
//prints 3.14159265358979
``````

#### 8.2 infinity

• Positive infinity.
``````let x1 = Double.greatestFiniteMagnitude
let y1 = x1 * 2
print(y1)
//prints nan
``````

#### 8.3 greatestFiniteMagnitude

• The greatest finite number representable by this type.
``````let x1 = Double.greatestFiniteMagnitude
print(x1)
//prints 0.0
``````

#### 8.4 nan

• A quiet NaN (“not a number”).
``````let x1 = Double.greatestFiniteMagnitude
print(x1 > Double.nan)
//prints false
``````

#### 8.5 signalingNaN

• A signaling NaN (“not a number”).
``````let x1 = Double.greatestFiniteMagnitude
print(x1 > Double.signalingNaN)
//prints false
``````

#### 8.6 ulpOfOne

• The unit in the last place of 1.0.
``````let x1 = Double.greatestFiniteMagnitude
print(x1 > Double.ulpOfOne)
//prints false
``````

## 9. Working with Binary Representation

#### 9.1 bitPattern

• The bit pattern of the value’s encoding.
``````let num5 = 3000.00000
print(num5.bitPattern)
//prints 4658815484840378368
``````

#### 9.2 significandBitPattern

• The raw encoding of the value’s significand field.
``````let num5 = 3000.00000
print(num5.significandBitPattern)
//prints 2093470139285504
``````

#### 9.3 exponentBitPattern

• The raw encoding of the value’s exponent field.
``````let num5 = 3000.00000
print(num5.exponentBitPattern)
//prints 1034
``````

#### 9.4 significandWidth

• The number of bits required to represent the value’s significand.
``````let num5 = 3000.00000
print(num5.significandWidth)
//prints 8
``````

## 10. Describing a Double

#### 10.1 description

• A textual representation of the value.
``````let num5 = 3000.00000
print(num5.description)
//prints 3000.0
``````

#### 10.2 debugDescription

• A textual representation of the value, suitable for debugging.
``````let num5 = 3000.00000
print(num5.debugDescription)
//prints 3000.0
``````

#### 10.3 customMirror

• A mirror that reflects the Float instance.
``````let num5 = 3000.00000
print(num5.customMirror)
//prints Mirror for Double
``````

#### 10.4 hashValue

• The number’s hash value.
``````print(num5.hashValue)
//prints 4658815484840378368
``````

## 11. Infrequently Used Functionality

#### 11.1 distance(to:)

• Returns the distance from this value to the specified value.
``````let x2 = 21.5
let d2 = x2.distance(to: 15.0)
print(d2)
//prints -6.5
``````

Returns a new value advanced by the given distance.

``````let x2 = 21.5
let d2 = -6.5
//prints 15.0
``````

#### 11.3 init(floatLiteral:)

• Creates a new value from the given floating-point literal.
``````let x3: Double = 21.25
print(x3)
//prints 21.25
``````

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