Float16

Typealiases

• typealias Exponent

  A type that can represent any written exponent.

• typealias Magnitude

  A type that can represent the absolute value of any possible value of the conforming type.

• typealias RawSignificand

  A type that represents the encoded significand of a value.

• typealias SIMDMaskScalar

Differentiation

• typealias TangentVector

  A type representing a differentiable value’s derivatives.

Initializers

• init()
• init<Source>(Source)

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

• init<Source>(Source)

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

• init(Float)

  Creates a new instance that approximates the given value.

• init?<S>(S)

  Creates a new instance from the given string.

• init<Source>(Source)

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

• init(Float16)

  Creates a new instance initialized to the given value.

• init(Double)

  Creates a new instance that approximates the given value.

• init(Float80)

  Creates a new instance that approximates the given value.

• init(Int)

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

• init?(Substring)
• init(bitPattern: UInt16)

  Creates a new value with the given bit pattern.

• init?<Source>(exactly: Source)

  Creates a new value, if the given integer can be represented exactly.

• init?<Source>(exactly: Source)

  Creates a new instance from the given value, if it can be represented exactly.

• init?(exactly: Float)

  Creates a new instance initialized to the given value, if it can be represented without rounding.

• init?(exactly: Double)

  Creates a new instance initialized to the given value, if it can be represented without rounding.

• init?(exactly: Float16)

  Creates a new instance initialized to the given value, if it can be represented without rounding.

• init?<Source>(exactly: Source)

  Creates a new value, if the given integer can be represented exactly.

• init?(exactly: Float80)

  Creates a new instance initialized to the given value, if it can be represented without rounding.

• init(floatLiteral: Float16)

  Creates an instance initialized to the specified floating-point value.

• init(from: Decoder) throws

  Creates a new instance by decoding from the given decoder.

• init(integerLiteral: Self)

  Creates an instance initialized to the specified integer value.

• init(integerLiteral: Int64)

  Creates an instance initialized to the specified integer value.

• init(nan: Float16.RawSignificand, signaling: Bool)

  Creates a NaN (“not a number”) value with the specified payload.

• init(sign: FloatingPointSign, exponent: Int, significand: Float16)

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

• init(sign: FloatingPointSign, exponentBitPattern: UInt, significandBitPattern: UInt16)

  Creates a new instance from the specified sign and bit patterns.

• init(signOf: Self, magnitudeOf: Self)

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

• init(signOf: Float16, magnitudeOf: Float16)

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

Type Properties

• static var exponentBitCount: Int

  The number of bits used to represent the type’s exponent.

• static var greatestFiniteMagnitude: Float16

  The greatest finite number representable by this type.

• static var infinity: Float16

  Positive infinity.

• static var leastNonzeroMagnitude: Float16

  The least positive number.

• static var leastNormalMagnitude: Float16

  The least positive normal number.

• static var nan: Float16

  A quiet NaN (“not a number”).

• static var pi: Float16

  The mathematical constant π, approximately equal to 3.14159.

• static var radix: Int

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

• static var signalingNaN: Float16

  A signaling NaN (“not a number”).

• static var significandBitCount: Int

  The available number of fractional significand bits.

• static var ulpOfOne: Float16

  The unit in the last place of 1.0.

• static var ulpOfOne: Self

  The unit in the last place of 1.0.

• static var zero: Self

  The zero value.

Instance Properties

• var binade: Float16

  The floating-point value with the same sign and exponent as this value, but with a significand of 1.0.

• var bitPattern: UInt16

  The bit pattern of the value’s encoding.

• var debugDescription: String

  A textual representation of the value, suitable for debugging.

• var description: String

  A textual representation of the value.

• var exponent: Int

  The exponent of the floating-point value.

• var exponentBitPattern: UInt

  The raw encoding of the value’s exponent field.

• var floatingPointClass: FloatingPointClassification

  The classification of this value.

• var isCanonical: Bool

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

• var isFinite: Bool

  A Boolean value indicating whether this instance is finite.

• var isInfinite: Bool

  A Boolean value indicating whether the instance is infinite.

• var isNaN: Bool

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

• var isNormal: Bool

  A Boolean value indicating whether this instance is normal.

• var isSignalingNaN: Bool

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

• var isSubnormal: Bool

  A Boolean value indicating whether the instance is subnormal.

• var isZero: Bool

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

• var magnitude: Float16

  The magnitude of this value.

• var nextDown: Self

  The greatest representable value that compares less than this value.

• var nextUp: Float16

  The least representable value that compares greater than this value.

• var sign: FloatingPointSign

  The sign of the floating-point value.

• var significand: Float16

  The significand of the floating-point value.

• var significandBitPattern: UInt16

  The raw encoding of the value’s significand field.

• var significandWidth: Int

  The number of bits required to represent the value’s significand.

• var ulp: Float16

  The unit in the last place of this value.

RealModule

• var reciprocal: Self?

  Implementations should be conservative with the reciprocal property; it is OK to return nil even in cases where a reciprocal could be represented. For this reason, a default implementation that simply always returns nil is correct, but conforming types should provide a better implementation if possible.

• var reciprocal: Self?

  The (approximate) reciprocal (multiplicative inverse) of this number, if it is representable.

Type Methods

• static func maximum(Self, Self) -> Self

  Returns the greater of the two given values.

• static func maximumMagnitude(Self, Self) -> Self

  Returns the value with greater magnitude.

• static func minimum(Self, Self) -> Self

  Returns the lesser of the two given values.

• static func minimumMagnitude(Self, Self) -> Self

  Returns the value with lesser magnitude.

• static func random(in: ClosedRange<Self>) -> Self

  Returns a random value within the specified range.

• static func random(in: Range<Self>) -> Self

  Returns a random value within the specified range.

• static func random<T>(in: Range<Self>, using: inout T) -> Self

  Returns a random value within the specified range, using the given generator as a source for randomness.

• static func random<T>(in: ClosedRange<Self>, using: inout T) -> Self

  Returns a random value within the specified range, using the given generator as a source for randomness.

RealModule

• static func acos(Float16) -> Float16

  The arccosine (inverse cosine) of x.

• static func acosh(Float16) -> Float16

  The inverse hyperbolic cosine of x.

• static func asin(Float16) -> Float16

  The arcsine (inverse sine) of x.

• static func asinh(Float16) -> Float16

  The inverse hyperbolic sine of x.

• static func atan(Float16) -> Float16

  The arctangent (inverse tangent) of x.

• static func atan2(y: Float16, x: Float16) -> Float16

  atan(y/x), with sign selected according to the quadrant of (x, y).

• static func atanh(Float16) -> Float16

  The inverse hyperbolic tangent of x.

• static func cos(Float16) -> Float16

  The cosine of x.

• static func cosMinusOne(Self) -> Self

  cos(x) - 1, computed in such a way as to maintain accuracy for small x.

• static func cosh(Float16) -> Float16

  The hyperbolic cosine of x.

• static func erf(Float16) -> Float16

  The error function evaluated at x.

• static func erfc(Float16) -> Float16

  The complimentary error function evaluated at x.

• static func exp(Float16) -> Float16

  The exponential function e^x whose base e is the base of the natural logarithm.

• static func exp10(Float16) -> Float16

  10^x

• static func exp10(Self) -> Self

  10^x

• static func exp2(Float16) -> Float16

  2^x

• static func expMinusOne(Float16) -> Float16

  exp(x) - 1, computed in such a way as to maintain accuracy for small x.

• static func gamma(Float16) -> Float16

  The gamma function Γ(x).

• static func hypot(Float16, Float16) -> Float16

  sqrt(x*x + y*y), computed in a manner that avoids spurious overflow or underflow.

• static func log(Float16) -> Float16

  The natural logarithm of x.

• static func log(onePlus: Float16) -> Float16

  log(1 + x), computed in such a way as to maintain accuracy for small x.

• static func log10(Float16) -> Float16

  The base-10 logarithm of x.

• static func log2(Float16) -> Float16

  The base-2 logarithm of x.

• static func logGamma(Float16) -> Float16

  The logarithm of the absolute value of the gamma function, log(|Γ(x)|).

• static func pow(Float16, Int) -> Float16

  x raised to the nth power.

• static func pow(Float16, Float16) -> Float16

  exp(y * log(x)) computed with additional internal precision.

• static func root(Float16, Int) -> Float16

  The nth root of x.

• static func signGamma(Self) -> FloatingPointSign

  The sign of the gamma function, Γ(x).

• static func sin(Float16) -> Float16

  The sine of x.

• static func sinh(Float16) -> Float16

  The hyperbolic sine of x.

• static func sqrt(Self) -> Self

  The square root of x.

• static func tan(Float16) -> Float16

  The tangent of x.

• static func tanh(Float16) -> Float16

  The hyperbolic tangent of x.

Instance Methods

• func addProduct(Float16, Float16)

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

• func addingProduct(Self, Self) -> Self

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

• func advanced(by: Float16) -> Float16

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

• func distance(to: Float16) -> Float16

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

• func encode(to: Encoder) throws

  Encodes this value into the given encoder.

• func formRemainder(dividingBy: Float16)

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

• func formSquareRoot()

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

• func formTruncatingRemainder(dividingBy: Float16)

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

• func hash(into: inout Hasher)

  Hashes the essential components of this value by feeding them into the given hasher.

• func isEqual(to: Float16) -> Bool

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

• func isLess(than: Float16) -> Bool

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

• func isLessThanOrEqualTo(Float16) -> Bool

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

• func isTotallyOrdered(belowOrEqualTo: Self) -> Bool

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

• func negate()

  Replaces this value with its additive inverse.

• func negate()

  Replaces this value with its additive inverse.

• func remainder(dividingBy: Self) -> Self

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

• func round()
• func round(FloatingPointRoundingRule)

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

• func rounded() -> Self
• func rounded(FloatingPointRoundingRule) -> Self

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

• func squareRoot() -> Self

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

• func truncatingRemainder(dividingBy: Self) -> Self

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

• func write<Target>(to: inout Target)

  Writes a textual representation of this instance into the given output stream.

Differentiation

• func move(by: Self.TangentVector)

  Moves self by the given offset. In Riemannian geometry, this is equivalent to exponential map, which moves self on the geodesic surface by the given tangent vector.

• func move(by: Float16.TangentVector)

  Moves self by the given offset. In Riemannian geometry, this is equivalent to exponential map, which moves self on the geodesic surface by the given tangent vector.

Type Operators

• static func != (Self, Self) -> Bool
• static func * (Float16, Float16) -> Float16

  Multiplies two values and produces their product, rounding to a representable value.

• static func *= (inout Float16, Float16)

  Multiplies two values and stores the result in the left-hand-side variable, rounding to a representable value.

• static func + (Self) -> Self

  Returns the given number unchanged.

• static func + (Float16, Float16) -> Float16

  Adds two values and produces their sum, rounded to a representable value.

• static func += (inout Self, Self)

  Adds two values and stores the result in the left-hand-side variable.

• static func += (inout Float16, Float16)

  Adds two values and stores the result in the left-hand-side variable, rounded to a representable value.

• static func - (Float16) -> Float16

  Calculates the additive inverse of a value.

• static func - (Self) -> Self

  Returns the additive inverse of the specified value.

• static func - (Float16, Float16) -> Float16

  Subtracts one value from another and produces their difference, rounded to a representable value.

• static func -= (inout Self, Self)

  Subtracts the second value from the first and stores the difference in the left-hand-side variable.

• static func -= (inout Float16, Float16)

  Subtracts the second value from the first and stores the difference in the left-hand-side variable, rounding to a representable value.

• static func ... (Self) -> PartialRangeFrom<Self>

  Returns a partial range extending upward from a lower bound.

• static func ... (Self) -> PartialRangeThrough<Self>

  Returns a partial range up to, and including, its upper bound.

• static func ... (Self, Self) -> ClosedRange<Self>

  Returns a closed range that contains both of its bounds.

• static func ..< (Self) -> PartialRangeUpTo<Self>

  Returns a partial range up to, but not including, its upper bound.

• static func ..< (Self, Self) -> Range<Self>

  Returns a half-open range that contains its lower bound but not its upper bound.

• static func / (Float16, Float16) -> Float16

  Returns the quotient of dividing the first value by the second, rounded to a representable value.

• static func /= (inout Float16, Float16)

  Divides the first value by the second and stores the quotient in the left-hand-side variable, rounding to a representable value.

• static func < (Self, Self) -> Bool

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

• static func < (Self, Self) -> Bool

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

• static func <= (Self, Self) -> Bool

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

• static func <= (Self, Self) -> Bool

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

• static func == (Self, Self) -> Bool

  Returns a Boolean value indicating whether two values are equal.

• static func == (Self, Self) -> Bool

  Returns a Boolean value indicating whether two values are equal.

• static func > (Self, Self) -> Bool

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

• static func > (Self, Self) -> Bool

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

• static func >= (Self, Self) -> Bool

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

• static func >= (Self, Self) -> Bool

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

RealModule

• static func / (Self, Self) -> Self

  The (approximate) quotient a/b.

Structures

• struct SIMD16Storage

  Storage for a vector of 16 floating-point values.

• struct SIMD2Storage

  Storage for a vector of two floating-point values.

• struct SIMD32Storage

  Storage for a vector of 32 floating-point values.

• struct SIMD4Storage

  Storage for a vector of four floating-point values.

• struct SIMD64Storage

  Storage for a vector of 64 floating-point values.

• struct SIMD8Storage

  Storage for a vector of eight floating-point values.