Data.Double.Approximate

Documentation

type SafeDouble = DoubleRelAbs 10 10

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)

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

Enum (DoubleRelAbs abs rel)

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)

Defined in Data.Double.Approximate

Methods

(==) :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> Bool

(/=) :: DoubleRelAbs abs rel -> DoubleRelAbs abs rel -> Bool

Floating (DoubleRelAbs abs rel)

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)

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)

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)

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)

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)

Defined in Data.Double.Approximate

Methods

toRational :: DoubleRelAbs abs rel -> Rational

(KnownNat abs, KnownNat rel) => RealFloat (DoubleRelAbs abs rel)

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)

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)

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)

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)

Defined in Data.Double.Approximate

Methods

rnf :: DoubleRelAbs abs rel -> ()