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

GHC.Float

Contents

Monomorphic equality operators
Orphan instances

Description

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

Synopsis

rationalToFloat :: Integer -> Integer -> Float
rationalToDouble :: Integer -> Integer -> Double
class Fractional a => Floating a where
- pi :: a
- exp, log, sqrt :: a -> a
- (**), logBase :: a -> a -> a
- sin, cos, tan :: a -> a
- asin, acos, atan :: a -> a
- sinh, cosh, tanh :: a -> a
- asinh, acosh, 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 FFFormat
- = FFExponent
- | FFFixed
- | FFGeneric
stgDoubleToWord64 :: Double# -> Word#
stgWord64ToDouble :: Word# -> Double#
stgFloatToWord32 :: Float# -> Word#
stgWord32ToFloat :: Word# -> Float#
isDoubleFinite :: Double -> Int
isDoubleNegativeZero :: Double -> Int
isDoubleDenormalized :: Double -> Int
isDoubleInfinite :: Double -> Int
isDoubleNaN :: Double -> Int
isFloatFinite :: Float -> Int
isFloatNegativeZero :: Float -> Int
isFloatDenormalized :: Float -> Int
isFloatInfinite :: Float -> Int
isFloatNaN :: Float -> Int
log1mexpOrd :: (Ord a, Floating a) => a -> a
showFloat :: RealFloat a => a -> ShowS
formatRealFloat :: RealFloat a => FFFormat -> Maybe Int -> a -> String
formatRealFloatAlt :: RealFloat a => FFFormat -> Maybe Int -> Bool -> a -> String
roundTo :: Int -> Int -> [Int] -> (Int, [Int])
floatToDigits :: RealFloat a => Integer -> a -> ([Int], Int)
fromRat :: RealFloat a => Rational -> a
fromRat' :: RealFloat a => Rational -> a
minExpt :: Int
maxExpt :: Int
expt :: Integer -> Int -> Integer
expts :: Array Int Integer
maxExpt10 :: Int
expts10 :: Array Int Integer
fromRat'' :: RealFloat a => Int -> Int -> Integer -> Integer -> a
roundingMode# :: Integer -> Int# -> Int#
plusFloat :: Float -> Float -> Float
minusFloat :: Float -> Float -> Float
timesFloat :: Float -> Float -> Float
divideFloat :: Float -> Float -> Float
negateFloat :: Float -> Float
gtFloat :: Float -> Float -> Bool
geFloat :: Float -> Float -> Bool
ltFloat :: Float -> Float -> Bool
leFloat :: Float -> Float -> Bool
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
powerFloat :: Float -> Float -> Float
plusDouble :: Double -> Double -> Double
minusDouble :: Double -> Double -> Double
timesDouble :: Double -> Double -> Double
divideDouble :: Double -> Double -> Double
negateDouble :: Double -> Double
gtDouble :: Double -> Double -> Bool
geDouble :: Double -> Double -> Bool
ltDouble :: Double -> Double -> Bool
leDouble :: Double -> Double -> Bool
double2Float :: Double -> Float
float2Double :: Float -> 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
powerDouble :: Double -> Double -> Double
word2Double :: Word -> Double
word2Float :: Word -> Float
showSignedFloat :: RealFloat a => (a -> ShowS) -> Int -> a -> ShowS
clamp :: Int -> Int -> Int
castWord32ToFloat :: Word32 -> Float
castFloatToWord32 :: Float -> Word32
castWord64ToDouble :: Word64 -> Double
castDoubleToWord64 :: Double -> Word64
data Float = F# Float#
data Double = D# Double#
data Float# :: TYPE 'FloatRep
data Double# :: TYPE 'DoubleRep
double2Int :: Double -> Int
int2Double :: Int -> Double
float2Int :: Float -> Int
int2Float :: Int -> Float
eqFloat :: Float -> Float -> Bool
eqDouble :: Double -> Double -> Bool

Documentation

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

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

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 Double #	Since: base-2.1
Instance details Defined in GHC.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.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 #
Floating CDouble #
Instance details Defined in 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 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 a => Floating (Down a) #	Since: base-4.14.0.0
Instance details Defined in 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 (Identity a) #	Since: base-4.9.0.0
Instance details Defined in 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 #
RealFloat a => Floating (Complex a) #	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 (Op a b) #
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 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 #

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 Double #	Since: base-2.1
Instance details Defined in GHC.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.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 CDouble #
Instance details Defined in 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 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 a => RealFloat (Down a) #	Since: base-4.14.0.0
Instance details Defined in 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 (Identity a) #	Since: base-4.9.0.0
Instance details Defined in 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 (Const a b) #	Since: base-4.9.0.0
Instance details Defined in 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 #

data FFFormat Source #

Constructors

FFExponent
FFFixed
FFGeneric

stgDoubleToWord64 :: Double# -> Word# Source #

stgWord64ToDouble :: Word# -> Double# Source #

stgFloatToWord32 :: Float# -> Word# Source #

stgWord32ToFloat :: Word# -> Float# Source #

isDoubleFinite :: Double -> Int Source #

isDoubleNegativeZero :: Double -> Int Source #

isDoubleDenormalized :: Double -> Int Source #

isDoubleInfinite :: Double -> Int Source #

isDoubleNaN :: Double -> Int Source #

isFloatFinite :: Float -> Int Source #

isFloatNegativeZero :: Float -> Int Source #

isFloatDenormalized :: Float -> Int Source #

isFloatInfinite :: Float -> Int Source #

isFloatNaN :: Float -> Int Source #

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.

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.

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

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

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

```
n >= 1
```
```
x = 0.d1d2...dn * (base**e)
```
```
0 <= di <= base-1
```

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

Converts a Rational value into any type in class RealFloat.

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

minExpt :: Int Source #

maxExpt :: Int Source #

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

expts :: Array Int Integer Source #

maxExpt10 :: Int Source #

expts10 :: Array Int Integer Source #

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

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

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

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

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

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

negateFloat :: Float -> Float Source #

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

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

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

leFloat :: Float -> Float -> Bool 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 #

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

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

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

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

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

negateDouble :: Double -> Double Source #

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

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

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

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

double2Float :: Double -> Float Source #

float2Double :: Float -> 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 #

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

word2Double :: Word -> Double Source #

word2Float :: Word -> Float 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

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

castWord32ToFloat :: Word32 -> Float Source #

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

Since: base-4.10.0.0

castFloatToWord32 :: Float -> Word32 Source #

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

Since: base-4.10.0.0

castWord64ToDouble :: Word64 -> Double Source #

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

Since: base-4.10.0.0

castDoubleToWord64 :: Double -> Word64 Source #

castFloatToWord64 f does a bit-for-bit copy from a floating-point value to an integral value.

Since: base-4.10.0.0

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

Enum Float #	Since: base-2.1
Instance details Defined in GHC.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 #
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 substitutivity: `>>>` `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 #
Floating Float #	Since: base-2.1
Instance details Defined in GHC.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 #
Fractional Float #	Note that due to the presence of `NaN`, not all elements of `Float` have an multiplicative inverse. `>>>` *`0/0 (recip 0/0 :: Float)`*NaN Since: base-2.1*
Instance details Defined in GHC.Float Methods (/) :: Float -> Float -> Float Source # recip :: Float -> Float Source # fromRational :: Rational -> Float Source #
Data Float #	Since: base-4.0.0.0
Instance details Defined in 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 #
Num Float #	Note that due to the presence of `NaN`, not all elements of `Float` have an additive inverse. `>>>` `0/0 + (negate 0/0 :: Float)`NaN Also note that due to the presence of -0, `Float`'s `Num` instance doesn't have an additive identity `>>>` `0 + (-0 :: Float)`0.0 Since: base-2.1
Instance details Defined in GHC.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 #
Ord Float	Note that due to the presence of `NaN`, `Float`'s `Ord` instance does not satisfy reflexivity. `>>>` `0/0 <= (0/0 :: Float)`False Also note that, due to the same, `Ord`'s operator interactions are not respected by `Float`'s instance: `>>>` `(0/0 :: Float) > 1`False `>>>` `compare (0/0 :: Float) 1`GT
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 #
Read Float #	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Float Source # readList :: ReadS [Float] Source # readPrec :: ReadPrec Float Source # readListPrec :: ReadPrec [Float] Source #
Real Float #	Since: base-2.1
Instance details Defined in GHC.Float Methods toRational :: Float -> Rational Source #
RealFloat Float #	Since: base-2.1
Instance details Defined in GHC.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 #
RealFrac Float #	Since: base-2.1
Instance details Defined in GHC.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.Float Methods showsPrec :: Int -> Float -> ShowS Source # show :: Float -> String Source # showList :: [Float] -> ShowS Source #
Storable Float #	Since: base-2.1
Instance details Defined in 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 #
PrintfArg Float #	Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Float -> FieldFormatter Source # parseFormat :: Float -> ModifierParser Source #
Generic1 (URec Float :: k -> Type) #
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Float) :: k -> Type Source # Methods from1 :: forall (a :: k0). URec Float a -> Rep1 (URec Float) a Source # to1 :: forall (a :: k0). Rep1 (URec Float) a -> URec Float a Source #
Foldable (UFloat :: Type -> Type) #	Since: base-4.9.0.0
Instance details Defined in 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 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.Generics Methods fmap :: (a -> b) -> URec Float a -> URec Float b Source # (<$) :: a -> URec Float b -> URec Float a Source #
Eq (URec Float p) #
Instance details Defined in GHC.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.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 #
Show (URec Float p) #
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Float p -> ShowS Source # show :: URec Float p -> String Source # showList :: [URec Float p] -> ShowS Source #
Generic (URec Float p) #
Instance details Defined in GHC.Generics Associated Types type Rep (URec Float p) :: Type -> Type Source # Methods from :: URec Float p -> Rep (URec Float p) x Source # to :: Rep (URec Float p) x -> 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.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.Generics type Rep1 (URec Float :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" '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.Generics type Rep (URec Float p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: Type -> Type)))

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

Enum Double #	Since: base-2.1
Instance details Defined in GHC.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 #
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 #
Floating Double #	Since: base-2.1
Instance details Defined in GHC.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 #
Fractional Double #	Note that due to the presence of `NaN`, not all elements of `Double` have an multiplicative inverse. `>>>` *`0/0 (recip 0/0 :: Double)`*NaN Since: base-2.1*
Instance details Defined in GHC.Float Methods (/) :: Double -> Double -> Double Source # recip :: Double -> Double Source # fromRational :: Rational -> Double Source #
Data Double #	Since: base-4.0.0.0
Instance details Defined in 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 #
Num Double #	Note that due to the presence of `NaN`, not all elements of `Double` have an additive inverse. `>>>` `0/0 + (negate 0/0 :: Double)`NaN Also note that due to the presence of -0, `Double`'s `Num` instance doesn't have an additive identity `>>>` `0 + (-0 :: Double)`0.0 Since: base-2.1
Instance details Defined in GHC.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 #
Ord Double	Note that due to the presence of `NaN`, `Double`'s `Ord` instance does not satisfy reflexivity. `>>>` `0/0 <= (0/0 :: Double)`False Also note that, due to the same, `Ord`'s operator interactions are not respected by `Double`'s instance: `>>>` `(0/0 :: Double) > 1`False `>>>` `compare (0/0 :: Double) 1`GT
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 #
Read Double #	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Double Source # readList :: ReadS [Double] Source # readPrec :: ReadPrec Double Source # readListPrec :: ReadPrec [Double] Source #
Real Double #	Since: base-2.1
Instance details Defined in GHC.Float Methods toRational :: Double -> Rational Source #
RealFloat Double #	Since: base-2.1
Instance details Defined in GHC.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 #
RealFrac Double #	Since: base-2.1
Instance details Defined in GHC.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.Float Methods showsPrec :: Int -> Double -> ShowS Source # show :: Double -> String Source # showList :: [Double] -> ShowS Source #
Storable Double #	Since: base-2.1
Instance details Defined in 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 #
PrintfArg Double #	Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Double -> FieldFormatter Source # parseFormat :: Double -> ModifierParser Source #
Generic1 (URec Double :: k -> Type) #
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Double) :: k -> Type Source # Methods from1 :: forall (a :: k0). URec Double a -> Rep1 (URec Double) a Source # to1 :: forall (a :: k0). Rep1 (URec Double) a -> URec Double a Source #
Foldable (UDouble :: Type -> Type) #	Since: base-4.9.0.0
Instance details Defined in 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 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.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b Source # (<$) :: a -> URec Double b -> URec Double a Source #
Eq (URec Double p) #	Since: base-4.9.0.0
Instance details Defined in GHC.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.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 #
Show (URec Double p) #	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Double p -> ShowS Source # show :: URec Double p -> String Source # showList :: [URec Double p] -> ShowS Source #
Generic (URec Double p) #
Instance details Defined in GHC.Generics Associated Types type Rep (URec Double p) :: Type -> Type Source # Methods from :: URec Double p -> Rep (URec Double p) x Source # to :: Rep (URec Double p) x -> 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.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.Generics type Rep1 (URec Double :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" '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.Generics type Rep (URec Double p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: Type -> Type)))

data Float# :: TYPE 'FloatRep Source #

data Double# :: TYPE 'DoubleRep Source #

double2Int :: Double -> Int Source #

int2Double :: Int -> Double Source #

float2Int :: Float -> Int Source #

int2Float :: Int -> Float Source #

Monomorphic equality operators

See GHC.Classes#matching_overloaded_methods_in_rules

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

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

Orphan instances

Enum Double #	Since: base-2.1
Instance details 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 #
Enum Float #	Since: base-2.1
Instance details 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 #
Fractional Double #	Note that due to the presence of `NaN`, not all elements of `Double` have an multiplicative inverse. `>>>` *`0/0 (recip 0/0 :: Double)`*NaN Since: base-2.1*
Instance details Methods (/) :: Double -> Double -> Double Source # recip :: Double -> Double Source # fromRational :: Rational -> Double Source #
Fractional Float #	Note that due to the presence of `NaN`, not all elements of `Float` have an multiplicative inverse. `>>>` *`0/0 (recip 0/0 :: Float)`*NaN Since: base-2.1*
Instance details Methods (/) :: Float -> Float -> Float Source # recip :: Float -> Float Source # fromRational :: Rational -> Float Source #
Num Double #	Note that due to the presence of `NaN`, not all elements of `Double` have an additive inverse. `>>>` `0/0 + (negate 0/0 :: Double)`NaN Also note that due to the presence of -0, `Double`'s `Num` instance doesn't have an additive identity `>>>` `0 + (-0 :: Double)`0.0 Since: base-2.1
Instance details 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 #
Num Float #	Note that due to the presence of `NaN`, not all elements of `Float` have an additive inverse. `>>>` `0/0 + (negate 0/0 :: Float)`NaN Also note that due to the presence of -0, `Float`'s `Num` instance doesn't have an additive identity `>>>` `0 + (-0 :: Float)`0.0 Since: base-2.1
Instance details 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 #
Real Double #	Since: base-2.1
Instance details Methods toRational :: Double -> Rational Source #
Real Float #	Since: base-2.1
Instance details Methods toRational :: Float -> Rational Source #
RealFrac Double #	Since: base-2.1
Instance details 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 #
RealFrac Float #	Since: base-2.1
Instance details 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 Double #	Since: base-2.1
Instance details Methods showsPrec :: Int -> Double -> ShowS Source # show :: Double -> String Source # showList :: [Double] -> ShowS Source #
Show Float #	Since: base-2.1
Instance details Methods showsPrec :: Int -> Float -> ShowS Source # show :: Float -> String Source # showList :: [Float] -> ShowS Source #