Data.Double.Shaman

Documentation

data Shaman

Double-precision floating point numbers with error-bounds.

Some digits can be represented exactly and have essentially an infinitely number of significant digits:

>>> significativeDigits 1
Infinity

Some fractional numbers can also be represented exactly:

>>> significativeDigits 0.5
Infinity

Other numbers are merely approximations:

>>> significativeDigits 0.1
16.255619765854984

Pi is an irrational number so we can't represent it with infinite precision:

>>> significativeDigits pi
15.849679651557175

sin pi should theoretically be zero but we cannot do better than saying it is near zero:

>>> sin pi
1.2246467991473532e-16

The error margins are greater than value itself so we have no significant digits:

>>> significativeDigits (sin pi)
0.0

Since 'near zero' is not zero, the following fails when using Doubles:

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

Equality testing for Shaman numbers tests whether the two intervals overlap:

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

Instances

Eq Shaman

Defined in Data.Double.Shaman

Methods

(==) :: Shaman -> Shaman -> Bool

(/=) :: Shaman -> Shaman -> Bool

Floating Shaman

Defined in Data.Double.Shaman

Methods

pi :: Shaman

exp :: Shaman -> Shaman

log :: Shaman -> Shaman

sqrt :: Shaman -> Shaman

(**) :: Shaman -> Shaman -> Shaman

logBase :: Shaman -> Shaman -> Shaman

sin :: Shaman -> Shaman

cos :: Shaman -> Shaman

tan :: Shaman -> Shaman

asin :: Shaman -> Shaman

acos :: Shaman -> Shaman

atan :: Shaman -> Shaman

sinh :: Shaman -> Shaman

cosh :: Shaman -> Shaman

tanh :: Shaman -> Shaman

asinh :: Shaman -> Shaman

acosh :: Shaman -> Shaman

atanh :: Shaman -> Shaman

log1p :: Shaman -> Shaman

expm1 :: Shaman -> Shaman

log1pexp :: Shaman -> Shaman

log1mexp :: Shaman -> Shaman

Fractional Shaman

Defined in Data.Double.Shaman

Methods

(/) :: Shaman -> Shaman -> Shaman

recip :: Shaman -> Shaman

fromRational :: Rational -> Shaman

Num Shaman

Defined in Data.Double.Shaman

Methods

(+) :: Shaman -> Shaman -> Shaman

(-) :: Shaman -> Shaman -> Shaman

(*) :: Shaman -> Shaman -> Shaman

negate :: Shaman -> Shaman

abs :: Shaman -> Shaman

signum :: Shaman -> Shaman

fromInteger :: Integer -> Shaman

Ord Shaman

Defined in Data.Double.Shaman

Methods

compare :: Shaman -> Shaman -> Ordering

(<) :: Shaman -> Shaman -> Bool

(<=) :: Shaman -> Shaman -> Bool

(>) :: Shaman -> Shaman -> Bool

(>=) :: Shaman -> Shaman -> Bool

max :: Shaman -> Shaman -> Shaman

min :: Shaman -> Shaman -> Shaman

Read Shaman

Defined in Data.Double.Shaman

Methods

readsPrec :: Int -> ReadS Shaman

readList :: ReadS [Shaman]

readPrec :: ReadPrec Shaman

readListPrec :: ReadPrec [Shaman]

Real Shaman

Defined in Data.Double.Shaman

Methods

toRational :: Shaman -> Rational

RealFloat Shaman

Defined in Data.Double.Shaman

Methods

floatRadix :: Shaman -> Integer

floatDigits :: Shaman -> Int

floatRange :: Shaman -> (Int, Int)

decodeFloat :: Shaman -> (Integer, Int)

encodeFloat :: Integer -> Int -> Shaman

exponent :: Shaman -> Int

significand :: Shaman -> Shaman

scaleFloat :: Int -> Shaman -> Shaman

isNaN :: Shaman -> Bool

isInfinite :: Shaman -> Bool

isDenormalized :: Shaman -> Bool

isNegativeZero :: Shaman -> Bool

isIEEE :: Shaman -> Bool

atan2 :: Shaman -> Shaman -> Shaman

RealFrac Shaman

Defined in Data.Double.Shaman

Methods

properFraction :: Integral b => Shaman -> (b, Shaman)

truncate :: Integral b => Shaman -> b

round :: Integral b => Shaman -> b

ceiling :: Integral b => Shaman -> b

floor :: Integral b => Shaman -> b

Show Shaman

Defined in Data.Double.Shaman

Methods

showsPrec :: Int -> Shaman -> ShowS

show :: Shaman -> String

showList :: [Shaman] -> ShowS

significativeBits :: Shaman -> Double

Number of significant bits (base 2).

significativeDigits :: Shaman -> Double

Number of significant digits (base 10).

data SDouble (n :: Nat)

Double-precision floating point numbers that throw exceptions if the accumulated errors grow large enough to cause unstable branching.

If SDouble n works without throwing any exceptions, it'll be safe to use DoubleRelAbs n 0 instead for a sizable performance boost.

>>> sin pi == (0 :: SDouble 0)
*** Exception: Insufficient precision.
...

SDouble 0 failed so DoubleRelAbs 0 0 will lead to an unstable branch. In other words, it'll return False when it should have returned True:

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

Comparing to within 1 ULP stabalizes the branch:

>>> sin pi == (0 :: SDouble 1)
True

>>> sin pi == (0 :: DoubleRelAbs 1 0)
True

Instances

KnownNat n => Eq (SDouble n)

Defined in Data.Double.Shaman

Methods

(==) :: SDouble n -> SDouble n -> Bool

(/=) :: SDouble n -> SDouble n -> Bool

Floating (SDouble n)

Defined in Data.Double.Shaman

Methods

pi :: SDouble n

exp :: SDouble n -> SDouble n

log :: SDouble n -> SDouble n

sqrt :: SDouble n -> SDouble n

(**) :: SDouble n -> SDouble n -> SDouble n

logBase :: SDouble n -> SDouble n -> SDouble n

sin :: SDouble n -> SDouble n

cos :: SDouble n -> SDouble n

tan :: SDouble n -> SDouble n

asin :: SDouble n -> SDouble n

acos :: SDouble n -> SDouble n

atan :: SDouble n -> SDouble n

sinh :: SDouble n -> SDouble n

cosh :: SDouble n -> SDouble n

tanh :: SDouble n -> SDouble n

asinh :: SDouble n -> SDouble n

acosh :: SDouble n -> SDouble n

atanh :: SDouble n -> SDouble n

log1p :: SDouble n -> SDouble n

expm1 :: SDouble n -> SDouble n

log1pexp :: SDouble n -> SDouble n

log1mexp :: SDouble n -> SDouble n

Fractional (SDouble n)

Defined in Data.Double.Shaman

Methods

(/) :: SDouble n -> SDouble n -> SDouble n

recip :: SDouble n -> SDouble n

fromRational :: Rational -> SDouble n

Num (SDouble n)

Defined in Data.Double.Shaman

Methods

(+) :: SDouble n -> SDouble n -> SDouble n

(-) :: SDouble n -> SDouble n -> SDouble n

(*) :: SDouble n -> SDouble n -> SDouble n

negate :: SDouble n -> SDouble n

abs :: SDouble n -> SDouble n

signum :: SDouble n -> SDouble n

fromInteger :: Integer -> SDouble n

KnownNat n => Ord (SDouble n)

Defined in Data.Double.Shaman

Methods

compare :: SDouble n -> SDouble n -> Ordering

(<) :: SDouble n -> SDouble n -> Bool

(<=) :: SDouble n -> SDouble n -> Bool

(>) :: SDouble n -> SDouble n -> Bool

(>=) :: SDouble n -> SDouble n -> Bool

max :: SDouble n -> SDouble n -> SDouble n

min :: SDouble n -> SDouble n -> SDouble n

Read (SDouble n)

Defined in Data.Double.Shaman

Methods

readsPrec :: Int -> ReadS (SDouble n)

readList :: ReadS [SDouble n]

readPrec :: ReadPrec (SDouble n)

readListPrec :: ReadPrec [SDouble n]

KnownNat n => Real (SDouble n)

Defined in Data.Double.Shaman

Methods

toRational :: SDouble n -> Rational

KnownNat n => RealFloat (SDouble n)

Defined in Data.Double.Shaman

Methods

floatRadix :: SDouble n -> Integer

floatDigits :: SDouble n -> Int

floatRange :: SDouble n -> (Int, Int)

decodeFloat :: SDouble n -> (Integer, Int)

encodeFloat :: Integer -> Int -> SDouble n

exponent :: SDouble n -> Int

significand :: SDouble n -> SDouble n

scaleFloat :: Int -> SDouble n -> SDouble n

isNaN :: SDouble n -> Bool

isInfinite :: SDouble n -> Bool

isDenormalized :: SDouble n -> Bool

isNegativeZero :: SDouble n -> Bool

isIEEE :: SDouble n -> Bool

atan2 :: SDouble n -> SDouble n -> SDouble n

KnownNat n => RealFrac (SDouble n)

Defined in Data.Double.Shaman

Methods

properFraction :: Integral b => SDouble n -> (b, SDouble n)

truncate :: Integral b => SDouble n -> b

round :: Integral b => SDouble n -> b

ceiling :: Integral b => SDouble n -> b

floor :: Integral b => SDouble n -> b

Show (SDouble n)

Defined in Data.Double.Shaman

Methods

showsPrec :: Int -> SDouble n -> ShowS

show :: SDouble n -> String

showList :: [SDouble n] -> ShowS