base-4.20.2.0: Core data structures and operations

Copyright | (c) The University of Glasgow 1994-2002 Portions obtained from hbc (c) Lennart Augusstson
License | see libraries/base/LICENSE
Maintainer | ghc-devs@haskell.org
Stability | internal
Portability | non-portable (GHC Extensions)
Safe Haskell | Safe
Language | Haskell2010

GHC.Float

Contents

- Classes
- `Float`
  - Conversion
  - Operations
  - Predicate
  - Comparison
  - Arithmetic
- `Double`
  - Conversion
  - Operations
  - Predicate
  - Comparison
  - Arithmetic
- Formatting
- Operations
- Monomorphic equality operators
- Internal

Description

The types `Float` and `Double`, the classes `Floating` and `RealFloat` and casting between Word32 and Float and Word64 and Double.

Synopsis

- class Fractional a => Floating a where
  - pi :: a
  - exp :: a -> a
  - log :: a -> a
  - sqrt :: a -> a
  - (**) :: a -> a -> a
  - logBase :: a -> a -> a
  - sin :: a -> a
  - cos :: a -> a
  - tan :: a -> a
  - asin :: a -> a
  - acos :: a -> a
  - atan :: a -> a
  - sinh :: a -> a
  - cosh :: a -> a
  - tanh :: a -> a
  - asinh :: a -> a
  - acosh :: a -> a
  - atanh :: a -> a
  - log1p :: a -> a
  - expm1 :: a -> a
  - log1pexp :: a -> a
  - log1mexp :: a -> a
- class (RealFrac a, Floating a) => RealFloat a where
  - floatRadix :: a -> Integer
  - floatDigits :: a -> Int
  - floatRange :: a -> (Int, Int)
  - decodeFloat :: a -> (Integer, Int)
  - encodeFloat :: Integer -> Int -> a
  - exponent :: a -> Int
  - significand :: a -> a
  - scaleFloat :: Int -> a -> a
  - isNaN :: a -> Bool
  - isInfinite :: a -> Bool
  - isDenormalized :: a -> Bool
  - isNegativeZero :: a -> Bool
  - isIEEE :: a -> Bool
  - atan2 :: a -> a -> a
- data Float = F# Float#
- data Float# :: TYPE 'FloatRep
- float2Int :: Float -> Int
- int2Float :: Int -> Float
- word2Float :: Word -> Float
- integerToFloat# :: Integer -> Float#
- naturalToFloat# :: Natural -> Float#
- rationalToFloat :: Integer -> Integer -> Float
- castWord32ToFloat :: Word32 -> Float
- castFloatToWord32 :: Float -> Word32
- castWord32ToFloat# :: Word32# -> Float#
- castFloatToWord32# :: Float# -> Word32#
- float2Double :: Float -> Double
- floorFloat :: Integral b => Float -> b
- ceilingFloat :: Integral b => Float -> b
- truncateFloat :: Integral b => Float -> b
- roundFloat :: Integral b => Float -> b
- properFractionFloat :: Integral b => Float -> (b, Float)
- isFloatDenormalized :: Float -> Int
- isFloatFinite :: Float -> Int
- isFloatInfinite :: Float -> Int
- isFloatNaN :: Float -> Int
- isFloatNegativeZero :: Float -> Int
- gtFloat :: Float -> Float -> Bool
- geFloat :: Float -> Float -> Bool
- leFloat :: Float -> Float -> Bool
- ltFloat :: Float -> Float -> Bool
- plusFloat :: Float -> Float -> Float
- minusFloat :: Float -> Float -> Float
- timesFloat :: Float -> Float -> Float
- divideFloat :: Float -> Float -> Float
- negateFloat :: Float -> Float
- expFloat :: Float -> Float
- expm1Float :: Float -> Float
- logFloat :: Float -> Float
- log1pFloat :: Float -> Float
- sqrtFloat :: Float -> Float
- fabsFloat :: Float -> Float
- sinFloat :: Float -> Float
- cosFloat :: Float -> Float
- tanFloat :: Float -> Float
- asinFloat :: Float -> Float
- acosFloat :: Float -> Float
- atanFloat :: Float -> Float
- sinhFloat :: Float -> Float
- coshFloat :: Float -> Float
- tanhFloat :: Float -> Float
- asinhFloat :: Float -> Float
- acoshFloat :: Float -> Float
- atanhFloat :: Float -> Float
- data Double = D# Double#
- data Double# :: TYPE 'DoubleRep
- double2Int :: Double -> Int
- int2Double :: Int -> Double
- word2Double :: Word -> Double
- integerToDouble# :: Integer -> Double#
- naturalToDouble# :: Natural -> Double#
- rationalToDouble :: Integer -> Integer -> Double
- castWord64ToDouble :: Word64 -> Double
- castDoubleToWord64 :: Double -> Word64
- castWord64ToDouble# :: Word64# -> Double#
- castDoubleToWord64# :: Double# -> Word64#
- double2Float :: Double -> Float
- floorDouble :: Integral b => Double -> b
- ceilingDouble :: Integral b => Double -> b
- truncateDouble :: Integral b => Double -> b
- roundDouble :: Integral b => Double -> b
- properFractionDouble :: Integral b => Double -> (b, Double)
- isDoubleDenormalized :: Double -> Int
- isDoubleFinite :: Double -> Int
- isDoubleInfinite :: Double -> Int
- isDoubleNaN :: Double -> Int
- isDoubleNegativeZero :: Double -> Int
- gtDouble :: Double -> Double -> Bool
- geDouble :: Double -> Double -> Bool
- leDouble :: Double -> Double -> Bool
- ltDouble :: Double -> Double -> Bool
- plusDouble :: Double -> Double -> Double
- minusDouble :: Double -> Double -> Double
- timesDouble :: Double -> Double -> Double
- divideDouble :: Double -> Double -> Double
- negateDouble :: Double -> Double
- expDouble :: Double -> Double
- expm1Double :: Double -> Double
- logDouble :: Double -> Double
- log1pDouble :: Double -> Double
- sqrtDouble :: Double -> Double
- fabsDouble :: Double -> Double
- sinDouble :: Double -> Double
- cosDouble :: Double -> Double
- tanDouble :: Double -> Double
- asinDouble :: Double -> Double
- acosDouble :: Double -> Double
- atanDouble :: Double -> Double
- sinhDouble :: Double -> Double
- coshDouble :: Double -> Double
- tanhDouble :: Double -> Double
- asinhDouble :: Double -> Double
- acoshDouble :: Double -> Double
- atanhDouble :: Double -> Double
- showFloat :: RealFloat a => a -> ShowS
- data FFFormat
  - = FFExponent
  - | FFFixed
  - | FFGeneric
- formatRealFloat :: RealFloat a => FFFormat -> Maybe Int -> a -> String
- formatRealFloatAlt :: RealFloat a => FFFormat -> Maybe Int -> Bool -> a -> String
- showSignedFloat :: RealFloat a => (a -> ShowS) -> Int -> a -> ShowS
- log1mexpOrd :: (Ord a, Floating a) => a -> a
- roundTo :: Int -> Int -> [Int] -> (Int, [Int])
- floatToDigits :: RealFloat a => Integer -> a -> ([Int], Int)
- integerToBinaryFloat' :: RealFloat a => Integer -> a
- fromRat :: RealFloat a => Rational -> a
- fromRat' :: RealFloat a => Rational -> a
- roundingMode# :: Integer -> Int# -> Int#
- eqFloat :: Float -> Float -> Bool
- eqDouble :: Double -> Double -> Bool
- clamp :: Int -> Int -> Int
- expt :: Integer -> Int -> Integer
- expts :: Array Int Integer
- expts10 :: Array Int Integer
- fromRat'' :: RealFloat a => Int -> Int -> Integer -> Integer -> a
- maxExpt :: Int
- maxExpt10 :: Int
- minExpt :: Int
- powerDouble :: Double -> Double -> Double
- powerFloat :: Float -> Float -> Float
- stgDoubleToWord64 :: Double# -> Word64#
- stgFloatToWord32 :: Float# -> Word32#
- stgWord64ToDouble :: Word64# -> Double#
- stgWord32ToFloat :: Word32# -> Float#

# Classes

class Fractional a => Floating a where Source #

Trigonometric and hyperbolic functions and related functions.

The Haskell Report defines no laws for `Floating`. However, `(`+`)`, `(`*`)` and `exp` are customarily expected to define an exponential field and have the following properties:

- `exp (a + b)` = `exp a * exp b`
- `exp (fromInteger 0)` = `fromInteger 1`

Minimal complete definition

pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Methods

pi :: a Source #

exp :: a -> a Source #

log :: a -> a Source #

sqrt :: a -> a Source #

(**) :: a -> a -> a infixr 8 Source #

logBase :: a -> a -> a Source #

sin :: a -> a Source #

cos :: a -> a Source #

tan :: a -> a Source #

asin :: a -> a Source #

acos :: a -> a Source #

atan :: a -> a Source #

sinh :: a -> a Source #

cosh :: a -> a Source #

tanh :: a -> a Source #

asinh :: a -> a Source #

acosh :: a -> a Source #

atanh :: a -> a Source #

log1p :: a -> a Source #

``log1p` x` computes ``log` (1 + x)`, but provides more precise results for small (absolute) values of `x` if possible.

Since: base-4.9.0.0

expm1 :: a -> a Source #

``expm1` x` computes ``exp` x - 1`, but provides more precise results for small (absolute) values of `x` if possible.

Since: base-4.9.0.0

log1pexp :: a -> a Source #

``log1pexp` x` computes ``log` (1 + `exp` x)`, but provides more precise results if possible.

Examples:

- if `x` is a large negative number, ``log` (1 + `exp` x)` will be imprecise for the reasons given in `log1p`.
- if ``exp` x` is close to `-1`, ``log` (1 + `exp` x)` will be imprecise for the reasons given in `expm1`.

Since: base-4.9.0.0

log1mexp :: a -> a Source #

``log1mexp` x` computes ``log` (1 - `exp` x)`, but provides more precise results if possible.

Examples:

- if `x` is a large negative number, ``log` (1 - `exp` x)` will be imprecise for the reasons given in `log1p`.
- if ``exp` x` is close to `1`, ``log` (1 - `exp` x)` will be imprecise for the reasons given in `expm1`.

Since: base-4.9.0.0

#### Instances

Instances details

Floating CDouble |

Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

pi :: CDouble Source #

exp :: CDouble -> CDouble Source #

log :: CDouble -> CDouble Source #

sqrt :: CDouble -> CDouble Source #

(**) :: CDouble -> CDouble -> CDouble Source #

logBase :: CDouble -> CDouble -> CDouble Source #

sin :: CDouble -> CDouble Source #

cos :: CDouble -> CDouble Source #

tan :: CDouble -> CDouble Source #

asin :: CDouble -> CDouble Source #

acos :: CDouble -> CDouble Source #

atan :: CDouble -> CDouble Source #

sinh :: CDouble -> CDouble Source #

cosh :: CDouble -> CDouble Source #

tanh :: CDouble -> CDouble Source #

asinh :: CDouble -> CDouble Source #

acosh :: CDouble -> CDouble Source #

atanh :: CDouble -> CDouble Source #

log1p :: CDouble -> CDouble Source #

expm1 :: CDouble -> CDouble Source #

log1pexp :: CDouble -> CDouble Source #

log1mexp :: CDouble -> CDouble Source #

Floating CFloat |

Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

pi :: CFloat Source #

exp :: CFloat -> CFloat Source #

log :: CFloat -> CFloat Source #

sqrt :: CFloat -> CFloat Source #

(**) :: CFloat -> CFloat -> CFloat Source #

logBase :: CFloat -> CFloat -> CFloat Source #

sin :: CFloat -> CFloat Source #

cos :: CFloat -> CFloat Source #

tan :: CFloat -> CFloat Source #

asin :: CFloat -> CFloat Source #

acos :: CFloat -> CFloat Source #

atan :: CFloat -> CFloat Source #

sinh :: CFloat -> CFloat Source #

cosh :: CFloat -> CFloat Source #

tanh :: CFloat -> CFloat Source #

asinh :: CFloat -> CFloat Source #

acosh :: CFloat -> CFloat Source #

atanh :: CFloat -> CFloat Source #

log1p :: CFloat -> CFloat Source #

expm1 :: CFloat -> CFloat Source #

log1pexp :: CFloat -> CFloat Source #

log1mexp :: CFloat -> CFloat Source #

Floating Double | Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Methods

pi :: Double Source #

exp :: Double -> Double Source #

log :: Double -> Double Source #

sqrt :: Double -> Double Source #

(**) :: Double -> Double -> Double Source #

logBase :: Double -> Double -> Double Source #

sin :: Double -> Double Source #

cos :: Double -> Double Source #

tan :: Double -> Double Source #

asin :: Double -> Double Source #

acos :: Double -> Double Source #

atan :: Double -> Double Source #

sinh :: Double -> Double Source #

cosh :: Double -> Double Source #

tanh :: Double -> Double Source #

asinh :: Double -> Double Source #

acosh :: Double -> Double Source #

atanh :: Double -> Double Source #

log1p :: Double -> Double Source #

expm1 :: Double -> Double Source #

log1pexp :: Double -> Double Source #

log1mexp :: Double -> Double Source #

Floating Float | Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Methods

pi :: Float Source #

exp :: Float -> Float Source #

log :: Float -> Float Source #

sqrt :: Float -> Float Source #

(**) :: Float -> Float -> Float Source #

logBase :: Float -> Float -> Float Source #

sin :: Float -> Float Source #

cos :: Float -> Float Source #

tan :: Float -> Float Source #

asin :: Float -> Float Source #

acos :: Float -> Float Source #

atan :: Float -> Float Source #

sinh :: Float -> Float Source #

cosh :: Float -> Float Source #

tanh :: Float -> Float Source #

asinh :: Float -> Float Source #

acosh :: Float -> Float Source #

atanh :: Float -> Float Source #

log1p :: Float -> Float Source #

expm1 :: Float -> Float Source #

log1pexp :: Float -> Float Source #

log1mexp :: Float -> Float Source #

RealFloat a => Floating (Complex a) Source # | Since: base-2.1

Instance details

Defined in Data.Complex

Methods

pi :: Complex a Source #

exp :: Complex a -> Complex a Source #

log :: Complex a -> Complex a Source #

sqrt :: Complex a -> Complex a Source #

(**) :: Complex a -> Complex a -> Complex a Source #

logBase :: Complex a -> Complex a -> Complex a Source #

sin :: Complex a -> Complex a Source #

cos :: Complex a -> Complex a Source #

tan :: Complex a -> Complex a Source #

asin :: Complex a -> Complex a Source #

acos :: Complex a -> Complex a Source #

atan :: Complex a -> Complex a Source #

sinh :: Complex a -> Complex a Source #

cosh :: Complex a -> Complex a Source #

tanh :: Complex a -> Complex a Source #

asinh :: Complex a -> Complex a Source #

acosh :: Complex a -> Complex a Source #

atanh :: Complex a -> Complex a Source #

log1p :: Complex a -> Complex a Source #

expm1 :: Complex a -> Complex a Source #

log1pexp :: Complex a -> Complex a Source #

log1mexp :: Complex a -> Complex a Source #

Floating a => Floating (Identity a) | Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Methods

pi :: Identity a Source #

exp :: Identity a -> Identity a Source #

log :: Identity a -> Identity a Source #

sqrt :: Identity a -> Identity a Source #

(**) :: Identity a -> Identity a -> Identity a Source #

logBase :: Identity a -> Identity a -> Identity a Source #

sin :: Identity a -> Identity a Source #

cos :: Identity a -> Identity a Source #

tan :: Identity a -> Identity a Source #

asin :: Identity a -> Identity a Source #

acos :: Identity a -> Identity a Source #

atan :: Identity a -> Identity a Source #

sinh :: Identity a -> Identity a Source #

cosh :: Identity a -> Identity a Source #

tanh :: Identity a -> Identity a Source #

asinh :: Identity a -> Identity a Source #

acosh :: Identity a -> Identity a Source #

atanh :: Identity a -> Identity a Source #

log1p :: Identity a -> Identity a Source #

expm1 :: Identity a -> Identity a Source #

log1pexp :: Identity a -> Identity a Source #

log1mexp :: Identity a -> Identity a Source #

Floating a => Floating (Down a) | Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

pi :: Down a Source #

exp :: Down a -> Down a Source #

log :: Down a -> Down a Source #

sqrt :: Down a -> Down a Source #

(**) :: Down a -> Down a -> Down a Source #

logBase :: Down a -> Down a -> Down a Source #

sin :: Down a -> Down a Source #

cos :: Down a -> Down a Source #

tan :: Down a -> Down a Source #

asin :: Down a -> Down a Source #

acos :: Down a -> Down a Source #

atan :: Down a -> Down a Source #

sinh :: Down a -> Down a Source #

cosh :: Down a -> Down a Source #

tanh :: Down a -> Down a Source #

asinh :: Down a -> Down a Source #

acosh :: Down a -> Down a Source #

atanh :: Down a -> Down a Source #

log1p :: Down a -> Down a Source #

expm1 :: Down a -> Down a Source #

log1pexp :: Down a -> Down a Source #

log1mexp :: Down a -> Down a Source #

Floating a => Floating (Op a b) Source # |

Instance details

Defined in Data.Functor.Contravariant

Methods

pi :: Op a b Source #

exp :: Op a b -> Op a b Source #

log :: Op a b -> Op a b Source #

sqrt :: Op a b -> Op a b Source #

(**) :: Op a b -> Op a b -> Op a b Source #

logBase :: Op a b -> Op a b -> Op a b Source #

sin :: Op a b -> Op a b Source #

cos :: Op a b -> Op a b Source #

tan :: Op a b -> Op a b Source #

asin :: Op a b -> Op a b Source #

acos :: Op a b -> Op a b Source #

atan :: Op a b -> Op a b Source #

sinh :: Op a b -> Op a b Source #

cosh :: Op a b -> Op a b Source #

tanh :: Op a b -> Op a b Source #

asinh :: Op a b -> Op a b Source #

acosh :: Op a b -> Op a b Source #

atanh :: Op a b -> Op a b Source #

log1p :: Op a b -> Op a b Source #

expm1 :: Op a b -> Op a b Source #

log1pexp :: Op a b -> Op a b Source #

log1mexp :: Op a b -> Op a b Source #

Floating a => Floating (Const a b) | Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

pi :: Const a b Source #

exp :: Const a b -> Const a b Source #

log :: Const a b -> Const a b Source #

sqrt :: Const a b -> Const a b Source #

(**) :: Const a b -> Const a b -> Const a b Source #

logBase :: Const a b -> Const a b -> Const a b Source #

sin :: Const a b -> Const a b Source #

cos :: Const a b -> Const a b Source #

tan :: Const a b -> Const a b Source #

asin :: Const a b -> Const a b Source #

acos :: Const a b -> Const a b Source #

atan :: Const a b -> Const a b Source #

sinh :: Const a b -> Const a b Source #

cosh :: Const a b -> Const a b Source #

tanh :: Const a b -> Const a b Source #

asinh :: Const a b -> Const a b Source #

acosh :: Const a b -> Const a b Source #

atanh :: Const a b -> Const a b Source #

log1p :: Const a b -> Const a b Source #

expm1 :: Const a b -> Const a b Source #

log1pexp :: Const a b -> Const a b Source #

log1mexp :: Const a b -> Const a b Source #

Floating (f (g a)) => Floating (Compose f g a) Source # | Since: base-4.20.0.0

Instance details

Defined in Data.Functor.Compose

Methods

pi :: Compose f g a Source #

exp :: Compose f g a -> Compose f g a Source #

log :: Compose f g a -> Compose f g a Source #

sqrt :: Compose f g a -> Compose f g a Source #

(**) :: Compose f g a -> Compose f g a -> Compose f g a Source #

logBase :: Compose f g a -> Compose f g a -> Compose f g a Source #

sin :: Compose f g a -> Compose f g a Source #

cos :: Compose f g a -> Compose f g a Source #

tan :: Compose f g a -> Compose f g a Source #

asin :: Compose f g a -> Compose f g a Source #

acos :: Compose f g a -> Compose f g a Source #

atan :: Compose f g a -> Compose f g a Source #

sinh :: Compose f g a -> Compose f g a Source #

cosh :: Compose f g a -> Compose f g a Source #

tanh :: Compose f g a -> Compose f g a Source #

asinh :: Compose f g a -> Compose f g a Source #

acosh :: Compose f g a -> Compose f g a Source #

atanh :: Compose f g a -> Compose f g a Source #

log1p :: Compose f g a -> Compose f g a Source #

expm1 :: Compose f g a -> Compose f g a Source #

log1pexp :: Compose f g a -> Compose f g a Source #

log1mexp :: Compose f g a -> Compose f g a Source #

class (RealFrac a, Floating a) => RealFloat a where Source #

Efficient, machine-independent access to the components of a floating-point number.

Minimal complete definition

floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE

Methods

floatRadix :: a -> Integer Source #

a constant function, returning the radix of the representation (often `2`)

floatDigits :: a -> Int Source #

a constant function, returning the number of digits of `floatRadix` in the significand

floatRange :: a -> (Int, Int) Source #

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: a -> (Integer, Int) Source #

The function `decodeFloat` applied to a real floating-point number returns the significand expressed as an `Integer` and an appropriately scaled exponent (an `Int`). If ``decodeFloat` x` yields `(m,n)`, then `x` is equal in value to `m*b^^n`, where `b` is the floating-point radix, and furthermore, either `m` and `n` are both zero or else `b^(d-1) <= `abs` m < b^d`, where `d` is the value of ``floatDigits` x`. In particular, ``decodeFloat` 0 = (0,0)`. If the type contains a negative zero, also ``decodeFloat` (-0.0) = (0,0)`. The result of ``decodeFloat` x` is unspecified if either of ``isNaN` x` or ``isInfinite` x` is `True`.

encodeFloat :: Integer -> Int -> a Source #

`encodeFloat` performs the inverse of `decodeFloat` in the sense that for finite `x` with the exception of `-0.0`, ``uncurry` `encodeFloat` (`decodeFloat` x) = x`. ``encodeFloat` m n` is one of the two closest representable floating-point numbers to `m*b^^n` (or `±Infinity` if overflow occurs); usually the closer, but if `m` contains too many bits, the result may be rounded in the wrong direction.

exponent :: a -> Int Source #

`exponent` corresponds to the second component of `decodeFloat`. ``exponent` 0 = 0` and for finite nonzero `x`, ``exponent` x = snd (`decodeFloat` x) + `floatDigits` x`. If `x` is a finite floating-point number, it is equal in value to ``significand` x * b ^^ `exponent` x`, where `b` is the floating-point radix. The behaviour is unspecified on infinite or `NaN` values.

significand :: a -> a Source #

The first component of `decodeFloat`, scaled to lie in the open interval (`-1`,`1`), either `0.0` or of absolute value `>= 1/b`, where `b` is the floating-point radix. The behaviour is unspecified on infinite or `NaN` values.

scaleFloat :: Int -> a -> a Source #

multiplies a floating-point number by an integer power of the radix

isNaN :: a -> Bool Source #

`True` if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: a -> Bool Source #

`True` if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool Source #

`True` if the argument is too small to be represented in normalized format

isNegativeZero :: a -> Bool Source #

`True` if the argument is an IEEE negative zero

isIEEE :: a -> Bool Source #

`True` if the argument is an IEEE floating point number

atan2 :: a -> a -> a Source #

a version of arctangent taking two real floating-point arguments. For real floating `x` and `y`, ``atan2` y x` computes the angle (from the positive x-axis) of the vector from the origin to the point `(x,y)`. ``atan2` y x` returns a value in the range [`-pi`, `pi`]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. ``atan2` y 1`, with `y` in a type that is `RealFloat`, should return the same value as ``atan` y`. A default definition of `atan2` is provided, but implementors can provide a more accurate implementation.

#### Instances

Instances details

RealFloat CDouble |

Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

floatRadix :: CDouble -> Integer Source #

floatDigits :: CDouble -> Int Source #

floatRange :: CDouble -> (Int, Int) Source #

decodeFloat :: CDouble -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> CDouble Source #

exponent :: CDouble -> Int Source #

significand :: CDouble -> CDouble Source #

scaleFloat :: Int -> CDouble -> CDouble Source #

isNaN :: CDouble -> Bool Source #

isInfinite :: CDouble -> Bool Source #

isDenormalized :: CDouble -> Bool Source #

isNegativeZero :: CDouble -> Bool Source #

isIEEE :: CDouble -> Bool Source #

atan2 :: CDouble -> CDouble -> CDouble Source #

RealFloat CFloat |

Instance details

Defined in GHC.Internal.Foreign.C.Types

Methods

floatRadix :: CFloat -> Integer Source #

floatDigits :: CFloat -> Int Source #

floatRange :: CFloat -> (Int, Int) Source #

decodeFloat :: CFloat -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> CFloat Source #

exponent :: CFloat -> Int Source #

significand :: CFloat -> CFloat Source #

scaleFloat :: Int -> CFloat -> CFloat Source #

isNaN :: CFloat -> Bool Source #

isInfinite :: CFloat -> Bool Source #

isDenormalized :: CFloat -> Bool Source #

isNegativeZero :: CFloat -> Bool Source #

isIEEE :: CFloat -> Bool Source #

atan2 :: CFloat -> CFloat -> CFloat Source #

RealFloat Double | Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Methods

floatRadix :: Double -> Integer Source #

floatDigits :: Double -> Int Source #

floatRange :: Double -> (Int, Int) Source #

decodeFloat :: Double -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> Double Source #

exponent :: Double -> Int Source #

significand :: Double -> Double Source #

scaleFloat :: Int -> Double -> Double Source #

isNaN :: Double -> Bool Source #

isInfinite :: Double -> Bool Source #

isDenormalized :: Double -> Bool Source #

isNegativeZero :: Double -> Bool Source #

isIEEE :: Double -> Bool Source #

atan2 :: Double -> Double -> Double Source #

RealFloat Float | Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Methods

floatRadix :: Float -> Integer Source #

floatDigits :: Float -> Int Source #

floatRange :: Float -> (Int, Int) Source #

decodeFloat :: Float -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> Float Source #

exponent :: Float -> Int Source #

significand :: Float -> Float Source #

scaleFloat :: Int -> Float -> Float Source #

isNaN :: Float -> Bool Source #

isInfinite :: Float -> Bool Source #

isDenormalized :: Float -> Bool Source #

isNegativeZero :: Float -> Bool Source #

isIEEE :: Float -> Bool Source #

atan2 :: Float -> Float -> Float Source #

RealFloat a => RealFloat (Identity a) | Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Methods

floatRadix :: Identity a -> Integer Source #

floatDigits :: Identity a -> Int Source #

floatRange :: Identity a -> (Int, Int) Source #

decodeFloat :: Identity a -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> Identity a Source #

exponent :: Identity a -> Int Source #

significand :: Identity a -> Identity a Source #

scaleFloat :: Int -> Identity a -> Identity a Source #

isNaN :: Identity a -> Bool Source #

isInfinite :: Identity a -> Bool Source #

isDenormalized :: Identity a -> Bool Source #

isNegativeZero :: Identity a -> Bool Source #

isIEEE :: Identity a -> Bool Source #

atan2 :: Identity a -> Identity a -> Identity a Source #

RealFloat a => RealFloat (Down a) | Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

floatRadix :: Down a -> Integer Source #

floatDigits :: Down a -> Int Source #

floatRange :: Down a -> (Int, Int) Source #

decodeFloat :: Down a -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> Down a Source #

exponent :: Down a -> Int Source #

significand :: Down a -> Down a Source #

scaleFloat :: Int -> Down a -> Down a Source #

isNaN :: Down a -> Bool Source #

isInfinite :: Down a -> Bool Source #

isDenormalized :: Down a -> Bool Source #

isNegativeZero :: Down a -> Bool Source #

isIEEE :: Down a -> Bool Source #

atan2 :: Down a -> Down a -> Down a Source #

RealFloat a => RealFloat (Const a b) | Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

floatRadix :: Const a b -> Integer Source #

floatDigits :: Const a b -> Int Source #

floatRange :: Const a b -> (Int, Int) Source #

decodeFloat :: Const a b -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> Const a b Source #

exponent :: Const a b -> Int Source #

significand :: Const a b -> Const a b Source #

scaleFloat :: Int -> Const a b -> Const a b Source #

isNaN :: Const a b -> Bool Source #

isInfinite :: Const a b -> Bool Source #

isDenormalized :: Const a b -> Bool Source #

isNegativeZero :: Const a b -> Bool Source #

isIEEE :: Const a b -> Bool Source #

atan2 :: Const a b -> Const a b -> Const a b Source #

RealFloat (f (g a)) => RealFloat (Compose f g a) Source # | Since: base-4.20.0.0

Instance details

Defined in Data.Functor.Compose

Methods

floatRadix :: Compose f g a -> Integer Source #

floatDigits :: Compose f g a -> Int Source #

floatRange :: Compose f g a -> (Int, Int) Source #

decodeFloat :: Compose f g a -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> Compose f g a Source #

exponent :: Compose f g a -> Int Source #

significand :: Compose f g a -> Compose f g a Source #

scaleFloat :: Int -> Compose f g a -> Compose f g a Source #

isNaN :: Compose f g a -> Bool Source #

isInfinite :: Compose f g a -> Bool Source #

isDenormalized :: Compose f g a -> Bool Source #

isNegativeZero :: Compose f g a -> Bool Source #

isIEEE :: Compose f g a -> Bool Source #

atan2 :: Compose f g a -> Compose f g a -> Compose f g a Source #

# `Float`

data Float Source #

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

Constructors

F# Float# |

#### Instances

Instances details

PrintfArg Float Source # | Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Float -> FieldFormatter Source # parseFormat :: Float -> ModifierParser Source #
Data Float | Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Float -> c Float Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Float Source #

toConstr :: Float -> Constr Source #

dataTypeOf :: Float -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Float) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Float) Source #

gmapT :: (forall b. Data b => b -> b) -> Float -> Float Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Float -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Float -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Float -> m Float Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source #

Enum Float

`fromEnum` just truncates its argument, beware of all sorts of overflows.

List generators have extremely peculiar behavior, mandated by Haskell Report 2010:

    >>> [0..1.5 :: Float]
    [0.0,1.0,2.0]

Since: base-2.1

Instance details Defined in GHC.Internal.Float Methods succ :: Float -> Float Source # pred :: Float -> Float Source # toEnum :: Int -> Float Source # fromEnum :: Float -> Int Source # enumFrom :: Float -> [Float] Source # enumFromThen :: Float -> Float -> [Float] Source # enumFromTo :: Float -> Float -> [Float] Source # enumFromThenTo :: Float -> Float -> Float -> [Float] Source #
Floating Float | Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Methods

pi :: Float Source #

exp :: Float -> Float Source #

log :: Float -> Float Source #

sqrt :: Float -> Float Source #

(**) :: Float -> Float -> Float Source #

logBase :: Float -> Float -> Float Source #

sin :: Float -> Float Source #

cos :: Float -> Float Source #

tan :: Float -> Float Source #

asin :: Float -> Float Source #

acos :: Float -> Float Source #

atan :: Float -> Float Source #

sinh :: Float -> Float Source #

cosh :: Float -> Float Source #

tanh :: Float -> Float Source #

asinh :: Float -> Float Source #

acosh :: Float -> Float Source #

atanh :: Float -> Float Source #

log1p :: Float -> Float Source #

expm1 :: Float -> Float Source #

log1pexp :: Float -> Float Source #

log1mexp :: Float -> Float Source #

RealFloat Float | Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Methods

floatRadix :: Float -> Integer Source #

floatDigits :: Float -> Int Source #

floatRange :: Float -> (Int, Int) Source #

decodeFloat :: Float -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> Float Source #

exponent :: Float -> Int Source #

significand :: Float -> Float Source #

scaleFloat :: Int -> Float -> Float Source #

isNaN :: Float -> Bool Source #

isInfinite :: Float -> Bool Source #

isDenormalized :: Float -> Bool Source #

isNegativeZero :: Float -> Bool Source #

isIEEE :: Float -> Bool Source #

atan2 :: Float -> Float -> Float Source #

Storable Float | Since: base-2.1

Instance details

Defined in GHC.Internal.Foreign.Storable

Methods

sizeOf :: Float -> Int Source #

alignment :: Float -> Int Source #

peekElemOff :: Ptr Float -> Int -> IO Float Source #

pokeElemOff :: Ptr Float -> Int -> Float -> IO () Source #

peekByteOff :: Ptr b -> Int -> IO Float Source #

pokeByteOff :: Ptr b -> Int -> Float -> IO () Source #

peek :: Ptr Float -> IO Float Source #

poke :: Ptr Float -> Float -> IO () Source #

Num Float

This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. Neither addition nor multiplication are associative or distributive:

    >>> (0.1 + 0.1 :: Float) + 0.5 == 0.1 + (0.1 + 0.5)
    False
    >>> (0.1 + 0.2 :: Float) * 0.9 == 0.1 * 0.9 + 0.2 * 0.9
    False
    >>> (0.1 * 0.1 :: Float) * 0.9 == 0.1 * (0.1 * 0.9)
    False

Since: base-2.1

Instance details Defined in GHC.Internal.Float Methods (+) :: Float -> Float -> Float Source # (-) :: Float -> Float -> Float Source # (*) :: Float -> Float -> Float Source # negate :: Float -> Float Source # abs :: Float -> Float Source # signum :: Float -> Float Source # fromInteger :: Integer -> Float Source #
Read Float | Since: base-2.1
Instance details Defined in GHC.Internal.Read Methods readsPrec :: Int -> ReadS Float Source # readList :: ReadS [Float] Source # readPrec :: ReadPrec Float Source # readListPrec :: ReadPrec [Float] Source #

Fractional Float

This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero.

    >>> 0 == (-0 :: Float)
    True
    >>> recip 0 == recip (-0 :: Float)
    False
    >>> map (/ 0) [-1, 0, 1 :: Float]
    [-Infinity,NaN,Infinity]
    >>> map (* 0) $ map (/ 0) [-1, 0, 1 :: Float]
    [NaN,NaN,NaN]

Since: base-2.1

Instance details Defined in GHC.Internal.Float Methods (/) :: Float -> Float -> Float Source # recip :: Float -> Float Source # fromRational :: Rational -> Float Source #

Real Float

Beware that `toRational` generates garbage for non-finite arguments:

    >>> toRational (1/0 :: Float)
    340282366920938463463374607431768211456 % 1
    >>> toRational (0/0 :: Float)
    510423550381407695195061911147652317184 % 1

Since: base-2.1

Instance details Defined in GHC.Internal.Float Methods toRational :: Float -> Rational Source #

RealFrac Float

Beware that results for non-finite arguments are garbage:

    >>> [ f x | f <- [round, floor, ceiling], x <- [-1/0, 0/0, 1/0 :: Float] ] :: [Int]
    [0,0,0,0,0,0,0,0,0]
    >>> map properFraction [-1/0, 0/0, 1/0] :: [(Int, Float)]
    [(0,0.0),(0,0.0),(0,0.0)]

and get even more non-sensical if you ask for `Integer` instead of `Int`.

Since: base-2.1

Instance details Defined in GHC.Internal.Float Methods properFraction :: Integral b => Float -> (b, Float) Source # truncate :: Integral b => Float -> b Source # round :: Integral b => Float -> b Source # ceiling :: Integral b => Float -> b Source # floor :: Integral b => Float -> b Source #
Show Float | Since: base-2.1
Instance details Defined in GHC.Internal.Float Methods showsPrec :: Int -> Float -> ShowS Source # show :: Float -> String Source # showList :: [Float] -> ShowS Source #

Eq Float

Note that due to the presence of `NaN`, `Float`'s `Eq` instance does not satisfy reflexivity.

    >>> 0/0 == (0/0 :: Float)
    False

Also note that `Float`'s `Eq` instance does not satisfy extensionality:

    >>> 0 == (-0 :: Float)
    True
    >>> recip 0 == recip (-0 :: Float)
    False

Instance details Defined in GHC.Classes Methods (==) :: Float -> Float -> Bool Source # (/=) :: Float -> Float -> Bool Source #
Ord Float | See `instance` `Ord` `Double` for discussion of deviations from IEEE 754 standard.
Instance details Defined in GHC.Classes Methods compare :: Float -> Float -> Ordering Source # (<) :: Float -> Float -> Bool Source # (<=) :: Float -> Float -> Bool Source # (>) :: Float -> Float -> Bool Source # (>=) :: Float -> Float -> Bool Source # max :: Float -> Float -> Float Source # min :: Float -> Float -> Float Source #
Generic1 (URec Float :: k -> Type) |

Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep1 (URec Float :: k -> Type) | Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics type Rep1 (URec Float :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: k -> Type)))

Methods

from1 :: forall (a :: k). URec Float a -> Rep1 (URec Float :: k -> Type) a Source #

to1 :: forall (a :: k). Rep1 (URec Float :: k -> Type) a -> URec Float a Source #

Foldable (UFloat :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UFloat m -> m Source #

foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source #

foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source #

foldr :: (a -> b -> b) -> b -> UFloat a -> b Source #

foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source #

foldl :: (b -> a -> b) -> b -> UFloat a -> b Source #

foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source #

foldr1 :: (a -> a -> a) -> UFloat a -> a Source #

foldl1 :: (a -> a -> a) -> UFloat a -> a Source #

toList :: UFloat a -> [a] Source #

null :: UFloat a -> Bool Source #

length :: UFloat a -> Int Source #

elem :: Eq a => a -> UFloat a -> Bool Source #

maximum :: Ord a => UFloat a -> a Source #

minimum :: Ord a => UFloat a -> a Source #

sum :: Num a => UFloat a -> a Source #

product :: Num a => UFloat a -> a Source #

Traversable (UFloat :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UFloat a -> f (UFloat b) Source # sequenceA :: Applicative f => UFloat (f a) -> f (UFloat a) Source # mapM :: Monad m => (a -> m b) -> UFloat a -> m (UFloat b) Source # sequence :: Monad m => UFloat (m a) -> m (UFloat a) Source #
Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods fmap :: (a -> b) -> URec Float a -> URec Float b Source # (<$) :: a -> URec Float b -> URec Float a Source #
Generic (URec Float p) |

Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep (URec Float p) |
Instance details Defined in GHC.Internal.Generics type Rep (URec Float p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: Type -> Type)))

Methods

from :: URec Float p -> Rep (URec Float p) x Source #

to :: Rep (URec Float p) x -> URec Float p Source #

Show (URec Float p) |
Instance details Defined in GHC.Internal.Generics Methods showsPrec :: Int -> URec Float p -> ShowS Source # show :: URec Float p -> String Source # showList :: [URec Float p] -> ShowS Source #
Eq (URec Float p) |
Instance details Defined in GHC.Internal.Generics Methods (==) :: URec Float p -> URec Float p -> Bool Source # (/=) :: URec Float p -> URec Float p -> Bool Source #
Ord (URec Float p) |

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: URec Float p -> URec Float p -> Ordering Source #

(<) :: URec Float p -> URec Float p -> Bool Source #

(<=) :: URec Float p -> URec Float p -> Bool Source #

(>) :: URec Float p -> URec Float p -> Bool Source #

(>=) :: URec Float p -> URec Float p -> Bool Source #

max :: URec Float p -> URec Float p -> URec Float p Source #

min :: URec Float p -> URec Float p -> URec Float p Source #

data URec Float (p :: k) | Used for marking occurrences of `Float#` Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

data URec Float (p :: k) = UFloat {

- uFloat# :: Float#

}

type Rep1 (URec Float :: k -> Type) | Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics type Rep1 (URec Float :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: k -> Type)))
type Rep (URec Float p) |
Instance details Defined in GHC.Internal.Generics type Rep (URec Float p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: Type -> Type)))

data Float# :: TYPE 'FloatRep Source #

## Conversion

float2Int :: Float -> Int Source #

int2Float :: Int -> Float Source #

word2Float :: Word -> Float Source #

integerToFloat# :: Integer -> Float# Source #

Convert an Integer to a Float#

naturalToFloat# :: Natural -> Float# Source #

Convert a Natural to a Float#

rationalToFloat :: Integer -> Integer -> Float Source #

castWord32ToFloat :: Word32 -> Float Source #

``castWord32ToFloat` w` does a bit-for-bit copy from an integral value to a floating-point value.

Since: base-4.11.0.0

castFloatToWord32 :: Float -> Word32 Source #

``castFloatToWord32` f` does a bit-for-bit copy from a floating-point value to an integral value.

Since: base-4.11.0.0

castWord32ToFloat# :: Word32# -> Float# Source #

Bitcast a `Word32#` into a `Float#`

castFloatToWord32# :: Float# -> Word32# Source #

Bitcast a `Float#` into a `Word32#`

float2Double :: Float -> Double Source #

## Operations

floorFloat :: Integral b => Float -> b Source #

ceilingFloat :: Integral b => Float -> b Source #

truncateFloat :: Integral b => Float -> b Source #

roundFloat :: Integral b => Float -> b Source #

properFractionFloat :: Integral b => Float -> (b, Float) Source #

## Predicate

isFloatDenormalized :: Float -> Int Source #

isFloatFinite :: Float -> Int Source #

isFloatInfinite :: Float -> Int Source #

isFloatNaN :: Float -> Int Source #

isFloatNegativeZero :: Float -> Int Source #

## Comparison

gtFloat :: Float -> Float -> Bool Source #

geFloat :: Float -> Float -> Bool Source #

leFloat :: Float -> Float -> Bool Source #

ltFloat :: Float -> Float -> Bool Source #

## Arithmetic

plusFloat :: Float -> Float -> Float Source #

minusFloat :: Float -> Float -> Float Source #

timesFloat :: Float -> Float -> Float Source #

divideFloat :: Float -> Float -> Float Source #

negateFloat :: Float -> Float Source #

expFloat :: Float -> Float Source #

expm1Float :: Float -> Float Source #

logFloat :: Float -> Float Source #

log1pFloat :: Float -> Float Source #

sqrtFloat :: Float -> Float Source #

fabsFloat :: Float -> Float Source #

sinFloat :: Float -> Float Source #

cosFloat :: Float -> Float Source #

tanFloat :: Float -> Float Source #

asinFloat :: Float -> Float Source #

acosFloat :: Float -> Float Source #

atanFloat :: Float -> Float Source #

sinhFloat :: Float -> Float Source #

coshFloat :: Float -> Float Source #

tanhFloat :: Float -> Float Source #

asinhFloat :: Float -> Float Source #

acoshFloat :: Float -> Float Source #

atanhFloat :: Float -> Float Source #

# `Double`

data Double Source #

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

Constructors

D# Double# |

#### Instances

Instances details

PrintfArg Double Source # | Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Double -> FieldFormatter Source # parseFormat :: Double -> ModifierParser Source #
Data Double | Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Double -> c Double Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Double Source #

toConstr :: Double -> Constr Source #

dataTypeOf :: Double -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Double) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Double) Source #

gmapT :: (forall b. Data b => b -> b) -> Double -> Double Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Double -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Double -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Double -> m Double Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double Source #

Enum Double

`fromEnum` just truncates its argument, beware of all sorts of overflows.

List generators have extremely peculiar behavior, mandated by Haskell Report 2010:

    >>> [0..1.5]
    [0.0,1.0,2.0]

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Methods

succ :: Double -> Double Source #

pred :: Double -> Double Source #

toEnum :: Int -> Double Source #

fromEnum :: Double -> Int Source #

enumFrom :: Double -> [Double] Source #

enumFromThen :: Double -> Double -> [Double] Source #

enumFromTo :: Double -> Double -> [Double] Source #

enumFromThenTo :: Double -> Double -> Double -> [Double] Source #

Floating Double | Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Methods

pi :: Double Source #

exp :: Double -> Double Source #

log :: Double -> Double Source #

sqrt :: Double -> Double Source #

(**) :: Double -> Double -> Double Source #

logBase :: Double -> Double -> Double Source #

sin :: Double -> Double Source #

cos :: Double -> Double Source #

tan :: Double -> Double Source #

asin :: Double -> Double Source #

acos :: Double -> Double Source #

atan :: Double -> Double Source #

sinh :: Double -> Double Source #

cosh :: Double -> Double Source #

tanh :: Double -> Double Source #

asinh :: Double -> Double Source #

acosh :: Double -> Double Source #

atanh :: Double -> Double Source #

log1p :: Double -> Double Source #

expm1 :: Double -> Double Source #

log1pexp :: Double -> Double Source #

log1mexp :: Double -> Double Source #

RealFloat Double | Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Methods

floatRadix :: Double -> Integer Source #

floatDigits :: Double -> Int Source #

floatRange :: Double -> (Int, Int) Source #

decodeFloat :: Double -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> Double Source #

exponent :: Double -> Int Source #

significand :: Double -> Double Source #

scaleFloat :: Int -> Double -> Double Source #

isNaN :: Double -> Bool Source #

isInfinite :: Double -> Bool Source #

isDenormalized :: Double -> Bool Source #

isNegativeZero :: Double -> Bool Source #

isIEEE :: Double -> Bool Source #

atan2 :: Double -> Double -> Double Source #

Storable Double | Since: base-2.1

Instance details

Defined in GHC.Internal.Foreign.Storable

Methods

sizeOf :: Double -> Int Source #

alignment :: Double -> Int Source #

peekElemOff :: Ptr Double -> Int -> IO Double Source #

pokeElemOff :: Ptr Double -> Int -> Double -> IO () Source #

peekByteOff :: Ptr b -> Int -> IO Double Source #

pokeByteOff :: Ptr b -> Int -> Double -> IO () Source #

peek :: Ptr Double -> IO Double Source #

poke :: Ptr Double -> Double -> IO () Source #

Num Double

This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. Neither addition nor multiplication are associative or distributive:

    >>> (0.1 + 0.1) + 0.4 == 0.1 + (0.1 + 0.4)
    False
    >>> (0.1 + 0.2) * 0.3 == 0.1 * 0.3 + 0.2 * 0.3
    False
    >>> (0.1 * 0.1) * 0.3 == 0.1 * (0.1 * 0.3)
    False

Since: base-2.1

Instance details Defined in GHC.Internal.Float Methods (+) :: Double -> Double -> Double Source # (-) :: Double -> Double -> Double Source # (*) :: Double -> Double -> Double Source # negate :: Double -> Double Source # abs :: Double -> Double Source # signum :: Double -> Double Source # fromInteger :: Integer -> Double Source #
Read Double | Since: base-2.1
Instance details Defined in GHC.Internal.Read Methods readsPrec :: Int -> ReadS Double Source # readList :: ReadS [Double] Source # readPrec :: ReadPrec Double Source # readListPrec :: ReadPrec [Double] Source #

Fractional Double

This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero.

    >>> 0 == (-0 :: Double)
    True
    >>> recip 0 == recip (-0 :: Double)
    False
    >>> map (/ 0) [-1, 0, 1]
    [-Infinity,NaN,Infinity]
    >>> map (* 0) $ map (/ 0) [-1, 0, 1]
    [NaN,NaN,NaN]

Since: base-2.1

Instance details Defined in GHC.Internal.Float Methods (/) :: Double -> Double -> Double Source # recip :: Double -> Double Source # fromRational :: Rational -> Double Source #

Real Double

Beware that `toRational` generates garbage for non-finite arguments:

    >>> toRational (1/0)
    179769313 (and 300 more digits...) % 1
    >>> toRational (0/0)
    269653970 (and 300 more digits...) % 1

Since: base-2.1

Instance details Defined in GHC.Internal.Float Methods toRational :: Double -> Rational Source #

RealFrac Double

Beware that results for non-finite arguments are garbage:

    >>> [ f x | f <- [round, floor, ceiling], x <- [-1/0, 0/0, 1/0] ] :: [Int]
    [0,0,0,0,0,0,0,0,0]
    >>> map properFraction [-1/0, 0/0, 1/0] :: [(Int, Double)]
    [(0,0.0),(0,0.0),(0,0.0)]

and get even more non-sensical if you ask for `Integer` instead of `Int`.

Since: base-2.1

Instance details Defined in GHC.Internal.Float Methods properFraction :: Integral b => Double -> (b, Double) Source # truncate :: Integral b => Double -> b Source # round :: Integral b => Double -> b Source # ceiling :: Integral b => Double -> b Source # floor :: Integral b => Double -> b Source #
Show Double | Since: base-2.1
Instance details Defined in GHC.Internal.Float Methods showsPrec :: Int -> Double -> ShowS Source # show :: Double -> String Source # showList :: [Double] -> ShowS Source #

Eq Double

Note that due to the presence of `NaN`, `Double`'s `Eq` instance does not satisfy reflexivity.

    >>> 0/0 == (0/0 :: Double)
    False

Also note that `Double`'s `Eq` instance does not satisfy substitutivity:

    >>> 0 == (-0 :: Double)
    True
    >>> recip 0 == recip (-0 :: Double)
    False

Instance details Defined in GHC.Classes Methods (==) :: Double -> Double -> Bool Source # (/=) :: Double -> Double -> Bool Source #

Ord Double

IEEE 754 `Double`-precision type includes not only numbers, but also positive and negative infinities and a special element called `NaN` (which can be quiet or signal).

IEEE 754-2008, section 5.11 requires that if at least one of arguments of `<=`, `<`, `>`, `>=` is `NaN` then the result of the comparison is `False`, and `instance` `Ord` `Double` complies with this requirement. This violates the reflexivity: both `NaN` `<=` `NaN` and `NaN` `>=` `NaN` are `False`.

IEEE 754-2008, section 5.10 defines `totalOrder` predicate. Unfortunately, `compare` on `Double`s violates the IEEE standard and does not define a total order. More specifically, both `compare` `NaN` `x` and `compare` `x` `NaN` always return `GT`.

Thus, users must be extremely cautious when using `instance` `Ord` `Double`. For instance, one should avoid ordered containers with keys represented by `Double`, because data loss and corruption may happen. An IEEE-compliant `compare` is available in `fp-ieee` package as `TotallyOrdered` newtype.

Moving further, the behaviour of `min` and `max` with regards to `NaN` is also non-compliant. IEEE 754-2008, section 5.3.1 defines that quiet `NaN` should be treated as a missing data by `minNum` and `maxNum` functions, for example, `minNum(NaN, 1) = minNum(1, NaN) = 1`. Some languages such as Java deviate from the standard implementing `minNum(NaN, 1) = minNum(1, NaN) = NaN`. However, `min` / `max` in `base` are even worse: `min` `NaN` 1 is 1, but `min` 1 `NaN` is `NaN`.

IEEE 754-2008 compliant `min` / `max` can be found in `ieee754` package under `minNum` / `maxNum` names. Implementations compliant with `minimumNumber` / `maximumNumber` from a newer IEEE 754-2019, section 9.6 are available from `fp-ieee` package.

Instance details Defined in GHC.Classes Methods compare :: Double -> Double -> Ordering Source # (<) :: Double -> Double -> Bool Source # (<=) :: Double -> Double -> Bool Source # (>) :: Double -> Double -> Bool Source # (>=) :: Double -> Double -> Bool Source # max :: Double -> Double -> Double Source # min :: Double -> Double -> Double Source #
Generic1 (URec Double :: k -> Type) |

Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep1 (URec Double :: k -> Type) | Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics type Rep1 (URec Double :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: k -> Type)))

Methods

from1 :: forall (a :: k). URec Double a -> Rep1 (URec Double :: k -> Type) a Source #

to1 :: forall (a :: k). Rep1 (URec Double :: k -> Type) a -> URec Double a Source #

Foldable (UDouble :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UDouble m -> m Source #

foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source #

foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source #

foldr :: (a -> b -> b) -> b -> UDouble a -> b Source #

foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source #

foldl :: (b -> a -> b) -> b -> UDouble a -> b Source #

foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source #

foldr1 :: (a -> a -> a) -> UDouble a -> a Source #

foldl1 :: (a -> a -> a) -> UDouble a -> a Source #

toList :: UDouble a -> [a] Source #

null :: UDouble a -> Bool Source #

length :: UDouble a -> Int Source #

elem :: Eq a => a -> UDouble a -> Bool Source #

maximum :: Ord a => UDouble a -> a Source #

minimum :: Ord a => UDouble a -> a Source #

sum :: Num a => UDouble a -> a Source #

product :: Num a => UDouble a -> a Source #

Traversable (UDouble :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> UDouble a -> f (UDouble b) Source # sequenceA :: Applicative f => UDouble (f a) -> f (UDouble a) Source # mapM :: Monad m => (a -> m b) -> UDouble a -> m (UDouble b) Source # sequence :: Monad m => UDouble (m a) -> m (UDouble a) Source #
Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b Source # (<$) :: a -> URec Double b -> URec Double a Source #
Generic (URec Double p) |

Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep (URec Double p) | Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics type Rep (URec Double p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: Type -> Type)))

Methods

from :: URec Double p -> Rep (URec Double p) x Source #

to :: Rep (URec Double p) x -> URec Double p Source #

Show (URec Double p) | Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods showsPrec :: Int -> URec Double p -> ShowS Source # show :: URec Double p -> String Source # showList :: [URec Double p] -> ShowS Source #
Eq (URec Double p) | Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods (==) :: URec Double p -> URec Double p -> Bool Source # (/=) :: URec Double p -> URec Double p -> Bool Source #
Ord (URec Double p) | Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: URec Double p -> URec Double p -> Ordering Source #

(<) :: URec Double p -> URec Double p -> Bool Source #

(<=) :: URec Double p -> URec Double p -> Bool Source #

(>) :: URec Double p -> URec Double p -> Bool Source #

(>=) :: URec Double p -> URec Double p -> Bool Source #

max :: URec Double p -> URec Double p -> URec Double p Source #

min :: URec Double p -> URec Double p -> URec Double p Source #

data URec Double (p :: k) | Used for marking occurrences of `Double#` Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

data URec Double (p :: k) = UDouble {

- uDouble# :: Double#

}

type Rep1 (URec Double :: k -> Type) | Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics type Rep1 (URec Double :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: k -> Type)))
type Rep (URec Double p) | Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics type Rep (URec Double p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: Type -> Type)))

data Double# :: TYPE 'DoubleRep Source #

## Conversion

double2Int :: Double -> Int Source #

int2Double :: Int -> Double Source #

word2Double :: Word -> Double Source #

integerToDouble# :: Integer -> Double# Source #

Convert an Integer to a Double#

naturalToDouble# :: Natural -> Double# Source #

Encode a Natural (mantissa) into a Double#

rationalToDouble :: Integer -> Integer -> Double Source #

castWord64ToDouble :: Word64 -> Double Source #

``castWord64ToDouble` w` does a bit-for-bit copy from an integral value to a floating-point value.

Since: base-4.11.0.0

castDoubleToWord64 :: Double -> Word64 Source #

``castDoubleToWord64` f` does a bit-for-bit copy from a floating-point value to an integral value.

Since: base-4.11.0.0

castWord64ToDouble# :: Word64# -> Double# Source #

Bitcast a `Word64#` into a `Double#`

castDoubleToWord64# :: Double# -> Word64# Source #

Bitcast a `Double#` into a `Word64#`

double2Float :: Double -> Float Source #

## Operations

floorDouble :: Integral b => Double -> b Source #

ceilingDouble :: Integral b => Double -> b Source #

truncateDouble :: Integral b => Double -> b Source #

roundDouble :: Integral b => Double -> b Source #

properFractionDouble :: Integral b => Double -> (b, Double) Source #

## Predicate

isDoubleDenormalized :: Double -> Int Source #

isDoubleFinite :: Double -> Int Source #

isDoubleInfinite :: Double -> Int Source #

isDoubleNaN :: Double -> Int Source #

isDoubleNegativeZero :: Double -> Int Source #

## Comparison

gtDouble :: Double -> Double -> Bool Source #

geDouble :: Double -> Double -> Bool Source #

leDouble :: Double -> Double -> Bool Source #

ltDouble :: Double -> Double -> Bool Source #

## Arithmetic

plusDouble :: Double -> Double -> Double Source #

minusDouble :: Double -> Double -> Double Source #

timesDouble :: Double -> Double -> Double Source #

divideDouble :: Double -> Double -> Double Source #

negateDouble :: Double -> Double Source #

expDouble :: Double -> Double Source #

expm1Double :: Double -> Double Source #

logDouble :: Double -> Double Source #

log1pDouble :: Double -> Double Source #

sqrtDouble :: Double -> Double Source #

fabsDouble :: Double -> Double Source #

sinDouble :: Double -> Double Source #

cosDouble :: Double -> Double Source #

tanDouble :: Double -> Double Source #

asinDouble :: Double -> Double Source #

acosDouble :: Double -> Double Source #

atanDouble :: Double -> Double Source #

sinhDouble :: Double -> Double Source #

coshDouble :: Double -> Double Source #

tanhDouble :: Double -> Double Source #

asinhDouble :: Double -> Double Source #

acoshDouble :: Double -> Double Source #

atanhDouble :: Double -> Double Source #

# Formatting

showFloat :: RealFloat a => a -> ShowS Source #

Show a signed `RealFloat` value to full precision using standard decimal notation for arguments whose absolute value lies between `0.1` and `9,999,999`, and scientific notation otherwise.

data FFFormat Source #

Constructors

FFExponent |
FFFixed |
FFGeneric |

formatRealFloat :: RealFloat a => FFFormat -> Maybe Int -> a -> String Source #

formatRealFloatAlt :: RealFloat a => FFFormat -> Maybe Int -> Bool -> a -> String Source #

showSignedFloat Source #

Arguments

:: RealFloat a |
=> (a -> ShowS) | a function that can show unsigned values
-> Int | the precedence of the enclosing context
-> a | the value to show
-> ShowS |

# Operations

log1mexpOrd :: (Ord a, Floating a) => a -> a Source #

Default implementation for ``log1mexp`` requiring ``Ord`` to test against a threshold to decide which implementation variant to use.

roundTo :: Int -> Int -> [Int] -> (Int, [Int]) Source #

floatToDigits :: RealFloat a => Integer -> a -> ([Int], Int) Source #

`floatToDigits` takes a base and a non-negative `RealFloat` number, and returns a list of digits and an exponent. In particular, if `x>=0`, and

    floatToDigits base x = ([d1,d2,...,dn], e)

then

1.     n >= 1

2.     x = 0.d1d2...dn * (base**e)

3.     0 <= di <= base-1

integerToBinaryFloat' :: RealFloat a => Integer -> a Source #

Converts a positive integer to a floating-point value.

The value nearest to the argument will be returned. If there are two such values, the one with an even significand will be returned (i.e. IEEE roundTiesToEven).

The argument must be strictly positive, and `floatRadix (undefined :: a)` must be 2.

fromRat :: RealFloat a => Rational -> a Source #

Converts a `Rational` value into any type in class `RealFloat`.

fromRat' :: RealFloat a => Rational -> a Source #

roundingMode# :: Integer -> Int# -> Int# Source #

# Monomorphic equality operators

See GHC.Classes#matching_overloaded_methods_in_rules

eqFloat :: Float -> Float -> Bool Source #

eqDouble :: Double -> Double -> Bool Source #

# Internal

These may vanish in a future release

clamp :: Int -> Int -> Int Source #

Used to prevent exponent over/underflow when encoding floating point numbers. This is also the same as

    \(x,y) -> max (-x) (min x y)

#### Example

Expand

    >>> clamp (-10) 5
    10

Since: base-4.13.0.0

expt :: Integer -> Int -> Integer Source #

expts :: Array Int Integer Source #

expts10 :: Array Int Integer Source #

fromRat'' :: RealFloat a => Int -> Int -> Integer -> Integer -> a Source #

maxExpt :: Int Source #

maxExpt10 :: Int Source #

minExpt :: Int Source #

powerDouble :: Double -> Double -> Double Source #

powerFloat :: Float -> Float -> Float Source #

stgDoubleToWord64 :: Double# -> Word64# Source #

stgFloatToWord32 :: Float# -> Word32# Source #

stgWord64ToDouble :: Word64# -> Double# Source #

stgWord32ToFloat :: Word32# -> Float# Source #