Safe Haskell	None
Language	Haskell2010

Data.Double.Approximate

Description

Synopsis

type SafeDouble = DoubleRelAbs 10 10
newtype DoubleRelAbs (abs :: Nat) (rel :: Nat) = DoubleRelAbs Double

Documentation

type SafeDouble = DoubleRelAbs 10 10 Source #

Relatively safe double floating-point type with a relative error margin of 10 ULPs and an absolute margin around zero of 10*epsilon.

Warning: All numbers within 10*epsilon of zero will be considered zero.

>>> m_epsilon * 10
2.220446049250313e-15

>>> realToFrac (m_epsilon * 10) == (0::SafeDouble)
False

>>> realToFrac (m_epsilon * 9) == (0::SafeDouble)
True

>>> 1e-20 == (5e-20 :: Double)
False
>>> 1e-20 == (5e-20 :: SafeDouble)
True

pi and sin are approximations:

>>> sin pi
1.2246467991473532e-16

>>> sin pi == (0 :: Double)
False

>>> sin pi == (0 :: SafeDouble)
True

newtype DoubleRelAbs (abs :: Nat) (rel :: Nat) Source #

Custom double floating-point type with a relative error margin of rel number of ULPs and an absolute error margin of abs times epsilon.

The relative error margin is the primary tool for good numerical robustness and can relatively safely be set to a high number such as 100. The absolute error margin is a last ditch attempt at fixing broken algorithms and dramatically limits the resolution around zero. If possible, use a low absolute error margin.

Constructors

DoubleRelAbs Double

Instances

Instances details

Enum (DoubleRelAbs abs rel) Source #
Instance details Defined in Data.Double.Approximate Methods succ :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # pred :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # toEnum :: Int -> DoubleRelAbs abs rel # fromEnum :: DoubleRelAbs abs rel -> Int # enumFrom :: DoubleRelAbs abs rel -> [DoubleRelAbs abs rel] # enumFromThen :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> [DoubleRelAbs abs rel] # enumFromTo :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> [DoubleRelAbs abs rel] # enumFromThenTo :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> [DoubleRelAbs abs rel] #
(KnownNat abs, KnownNat rel) => Eq (DoubleRelAbs abs rel) Source #
Instance details Defined in Data.Double.Approximate Methods (==) :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> Bool # (/=) :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> Bool #
Floating (DoubleRelAbs abs rel) Source #
Instance details Defined in Data.Double.Approximate Methods pi :: DoubleRelAbs abs rel # exp :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # log :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # sqrt :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # (**) :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> DoubleRelAbs abs rel # logBase :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> DoubleRelAbs abs rel # sin :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # cos :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # tan :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # asin :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # acos :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # atan :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # sinh :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # cosh :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # tanh :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # asinh :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # acosh :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # atanh :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # log1p :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # expm1 :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # log1pexp :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # log1mexp :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel #
Fractional (DoubleRelAbs abs rel) Source #
Instance details Defined in Data.Double.Approximate Methods (/) :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> DoubleRelAbs abs rel # recip :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # fromRational :: Rational -> DoubleRelAbs abs rel #
Num (DoubleRelAbs abs rel) Source #
Instance details Defined in Data.Double.Approximate Methods (+) :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> DoubleRelAbs abs rel # (-) :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> DoubleRelAbs abs rel # (*) :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> DoubleRelAbs abs rel # negate :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # abs :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # signum :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # fromInteger :: Integer -> DoubleRelAbs abs rel #
(KnownNat abs, KnownNat rel) => Ord (DoubleRelAbs abs rel) Source #
Instance details Defined in Data.Double.Approximate Methods compare :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> Ordering # (<) :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> Bool # (<=) :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> Bool # (>) :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> Bool # (>=) :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> Bool # max :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> DoubleRelAbs abs rel # min :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> DoubleRelAbs abs rel #
Read (DoubleRelAbs abs rel) Source #
Instance details Defined in Data.Double.Approximate Methods readsPrec :: Int -> ReadS (DoubleRelAbs abs rel) # readList :: ReadS [DoubleRelAbs abs rel] # readPrec :: ReadPrec (DoubleRelAbs abs rel) # readListPrec :: ReadPrec [DoubleRelAbs abs rel] #
(KnownNat abs, KnownNat rel) => Real (DoubleRelAbs abs rel) Source #
Instance details Defined in Data.Double.Approximate Methods toRational :: DoubleRelAbs abs rel -> Rational #
(KnownNat abs, KnownNat rel) => RealFloat (DoubleRelAbs abs rel) Source #
Instance details Defined in Data.Double.Approximate Methods floatRadix :: DoubleRelAbs abs rel -> Integer # floatDigits :: DoubleRelAbs abs rel -> Int # floatRange :: DoubleRelAbs abs rel -> (Int, Int) # decodeFloat :: DoubleRelAbs abs rel -> (Integer, Int) # encodeFloat :: Integer -> Int -> DoubleRelAbs abs rel # exponent :: DoubleRelAbs abs rel -> Int # significand :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel # scaleFloat :: Int -> DoubleRelAbs abs rel -> DoubleRelAbs abs rel # isNaN :: DoubleRelAbs abs rel -> Bool # isInfinite :: DoubleRelAbs abs rel -> Bool # isDenormalized :: DoubleRelAbs abs rel -> Bool # isNegativeZero :: DoubleRelAbs abs rel -> Bool # isIEEE :: DoubleRelAbs abs rel -> Bool # atan2 :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> DoubleRelAbs abs rel #
(KnownNat abs, KnownNat rel) => RealFrac (DoubleRelAbs abs rel) Source #
Instance details Defined in Data.Double.Approximate Methods properFraction :: Integral b => DoubleRelAbs abs rel -> (b, DoubleRelAbs abs rel) # truncate :: Integral b => DoubleRelAbs abs rel -> b # round :: Integral b => DoubleRelAbs abs rel -> b # ceiling :: Integral b => DoubleRelAbs abs rel -> b # floor :: Integral b => DoubleRelAbs abs rel -> b #
Show (DoubleRelAbs abs rel) Source #
Instance details Defined in Data.Double.Approximate Methods showsPrec :: Int -> DoubleRelAbs abs rel -> ShowS # show :: DoubleRelAbs abs rel -> String # showList :: [DoubleRelAbs abs rel] -> ShowS #
Random (DoubleRelAbs abs rel) Source #
Instance details Defined in Data.Double.Approximate Methods randomR :: RandomGen g => (DoubleRelAbs abs rel, DoubleRelAbs abs rel) -> g -> (DoubleRelAbs abs rel, g) # random :: RandomGen g => g -> (DoubleRelAbs abs rel, g) # randomRs :: RandomGen g => (DoubleRelAbs abs rel, DoubleRelAbs abs rel) -> g -> [DoubleRelAbs abs rel] # randoms :: RandomGen g => g -> [DoubleRelAbs abs rel] #
NFData (DoubleRelAbs abs rel) Source #
Instance details Defined in Data.Double.Approximate Methods rnf :: DoubleRelAbs abs rel -> () #