-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Approximate discrete values and numbers
--   
--   This package provides approximate discrete values and numbers.
@package approximate
@version 0.3


module Data.Approximate.Type

-- | An approximate number, with a likely interval, an expected value and a
--   lower bound on the <tt>log</tt> of probability that the answer falls
--   in the interval.
--   
--   <i>NB:</i> The probabilities associated with confidence are stored in
--   the <tt>log</tt> domain.
data Approximate a
Approximate :: {-# UNPACK #-} !(Log Double) -> a -> Approximate a
class HasApproximate c_aq5z a_alY7 | c_aq5z -> a_alY7 where confidence = (.) approximate confidence estimate = (.) approximate estimate hi = (.) approximate hi lo = (.) approximate lo
approximate :: HasApproximate c_aq5z a_alY7 => Lens' c_aq5z (Approximate a_alY7)
confidence :: HasApproximate c_aq5z a_alY7 => Lens' c_aq5z (Log Double)
estimate :: HasApproximate c_aq5z a_alY7 => Lens' c_aq5z a_alY7
hi :: HasApproximate c_aq5z a_alY7 => Lens' c_aq5z a_alY7
lo :: HasApproximate c_aq5z a_alY7 => Lens' c_aq5z a_alY7
exact :: Eq a => Prism' (Approximate a) a
zero :: (Num a, Eq a) => Prism' (Approximate a) ()
one :: (Num a, Eq a) => Prism' (Approximate a) ()
withMin :: Ord a => a -> Approximate a -> Approximate a
withMax :: Ord a => a -> Approximate a -> Approximate a
instance Data.Approximate.Type.HasApproximate (Data.Approximate.Type.Approximate a0) a0
instance Data.Binary.Class.Binary a => Data.Binary.Class.Binary (Data.Approximate.Type.Approximate a)
instance Data.Serialize.Serialize a => Data.Serialize.Serialize (Data.Approximate.Type.Approximate a)
instance Data.Serialize.Serialize a => Data.SafeCopy.SafeCopy.SafeCopy (Data.Approximate.Type.Approximate a)
instance Data.Hashable.Class.Hashable a => Data.Hashable.Class.Hashable (Data.Approximate.Type.Approximate a)
instance Data.Hashable.Class.Hashable1 Data.Approximate.Type.Approximate
instance Data.Bytes.Serial.Serial a => Data.Bytes.Serial.Serial (Data.Approximate.Type.Approximate a)
instance Data.Bytes.Serial.Serial1 Data.Approximate.Type.Approximate
instance Data.Vector.Unboxed.Base.Unbox a => Data.Vector.Unboxed.Base.Unbox (Data.Approximate.Type.Approximate a)
instance Data.Vector.Unboxed.Base.Unbox a => Data.Vector.Generic.Mutable.Base.MVector Data.Vector.Unboxed.Base.MVector (Data.Approximate.Type.Approximate a)
instance Data.Vector.Unboxed.Base.Unbox a => Data.Vector.Generic.Base.Vector Data.Vector.Unboxed.Base.Vector (Data.Approximate.Type.Approximate a)
instance Control.DeepSeq.NFData a => Control.DeepSeq.NFData (Data.Approximate.Type.Approximate a)
instance GHC.Base.Functor Data.Approximate.Type.Approximate
instance Data.Foldable.Foldable Data.Approximate.Type.Approximate
instance Data.Traversable.Traversable Data.Approximate.Type.Approximate
instance Data.Copointed.Copointed Data.Approximate.Type.Approximate
instance Data.Pointed.Pointed Data.Approximate.Type.Approximate
instance Data.Functor.Bind.Class.Apply Data.Approximate.Type.Approximate
instance GHC.Base.Applicative Data.Approximate.Type.Approximate
instance (GHC.Classes.Ord a, GHC.Num.Num a) => GHC.Num.Num (Data.Approximate.Type.Approximate a)
instance GHC.Generics.Generic (Data.Approximate.Type.Approximate a)
instance Data.Data.Data a => Data.Data.Data (Data.Approximate.Type.Approximate a)
instance GHC.Read.Read a => GHC.Read.Read (Data.Approximate.Type.Approximate a)
instance GHC.Show.Show a => GHC.Show.Show (Data.Approximate.Type.Approximate a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Data.Approximate.Type.Approximate a)


-- | These functions provide wildly inaccurate but very fast approximations
--   to common transcendental functions.
--   
--   The algorithms here are based on Martin Ankerl's optimized
--   <tt>pow</tt>,
--   <a>http://martin.ankerl.com/2007/10/04/optimized-pow-approximation-for-java-and-c-c/</a>
--   which is in turn based on
--   <a>http://nic.schraudolph.org/pubs/Schraudolph99.pdf</a>
module Data.Approximate.Numerics
class Floating a => Fast a

-- | Calculate an approximate log.
flog :: Fast a => a -> a
flog_lb :: Fast a => a -> a
flog_ub :: Fast a => a -> a

-- | Calculate an approximate exp.
fexp :: Fast a => a -> a
fexp_lb :: Fast a => a -> a
fexp_ub :: Fast a => a -> a

-- | Calculate an approximate pow.
fpow :: Fast a => a -> a -> a
fpow_lb :: Fast a => a -> a -> a
fpow_ub :: Fast a => a -> a -> a

-- | Borchardt’s Algorithm from “Dead Reckoning: Calculating without
--   instruments”.
--   
--   This is a remarkably bad approximate logarithm.
--   
--   <a>flog</a> had better outperform it! It is provided merely for
--   comparison.
blog :: Floating a => a -> a
instance Data.Approximate.Numerics.Fast GHC.Types.Float
instance Data.Approximate.Numerics.Fast GHC.Types.Double


module Data.Approximate.Mass

-- | A quantity with a lower-bound on its probability mass. This represents
--   a 'probable value' as a <a>Monad</a> that you can use to calculate
--   progressively less likely consequences.
--   
--   <i>NB:</i> These probabilities are all stored in the log domain. This
--   enables us to retain accuracy despite very long multiplication chains.
--   We never add these probabilities so the additional overhead of working
--   in the log domain is never incurred, except on transitioning in and
--   out.
--   
--   This is most useful for discrete types, such as small <a>Integral</a>
--   instances or a <a>Bounded</a> <a>Enum</a> like <a>Bool</a>.
--   
--   Also note that <tt>(<a>&amp;?</a>)</tt> and <tt>(<a>|?</a>)</tt> are
--   able to use knowledge about the function to get better precision on
--   their results than naively using <tt><tt>liftA2</tt>
--   (<a>&amp;&amp;</a>)</tt>
data Mass a
Mass :: {-# UNPACK #-} !(Log Double) -> a -> Mass a

-- | Calculate the logical <tt>or</tt> of two booleans with confidence
--   lower bounds.
(|?) :: Mass Bool -> Mass Bool -> Mass Bool
infixr 2 |?

-- | Calculate the logical <tt>and</tt> of two booleans with confidence
--   lower bounds.
(&?) :: Mass Bool -> Mass Bool -> Mass Bool
infixr 3 &?

-- | Calculate the exclusive <tt>or</tt> of two booleans with confidence
--   lower bounds.
(^?) :: Mass Bool -> Mass Bool -> Mass Bool
infixl 6 ^?
instance GHC.Generics.Generic (Data.Approximate.Mass.Mass a)
instance Data.Data.Data a => Data.Data.Data (Data.Approximate.Mass.Mass a)
instance GHC.Read.Read a => GHC.Read.Read (Data.Approximate.Mass.Mass a)
instance GHC.Show.Show a => GHC.Show.Show (Data.Approximate.Mass.Mass a)
instance GHC.Classes.Ord a => GHC.Classes.Ord (Data.Approximate.Mass.Mass a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Data.Approximate.Mass.Mass a)
instance Data.Binary.Class.Binary a => Data.Binary.Class.Binary (Data.Approximate.Mass.Mass a)
instance Data.Serialize.Serialize a => Data.Serialize.Serialize (Data.Approximate.Mass.Mass a)
instance Data.Serialize.Serialize a => Data.SafeCopy.SafeCopy.SafeCopy (Data.Approximate.Mass.Mass a)
instance Data.Hashable.Class.Hashable a => Data.Hashable.Class.Hashable (Data.Approximate.Mass.Mass a)
instance Data.Hashable.Class.Hashable1 Data.Approximate.Mass.Mass
instance Data.Bytes.Serial.Serial1 Data.Approximate.Mass.Mass
instance Data.Bytes.Serial.Serial a => Data.Bytes.Serial.Serial (Data.Approximate.Mass.Mass a)
instance GHC.Base.Functor Data.Approximate.Mass.Mass
instance Data.Foldable.Foldable Data.Approximate.Mass.Mass
instance Data.Vector.Unboxed.Base.Unbox a => Data.Vector.Generic.Mutable.Base.MVector Data.Vector.Unboxed.Base.MVector (Data.Approximate.Mass.Mass a)
instance Data.Vector.Unboxed.Base.Unbox a => Data.Vector.Generic.Base.Vector Data.Vector.Unboxed.Base.Vector (Data.Approximate.Mass.Mass a)
instance Control.DeepSeq.NFData a => Control.DeepSeq.NFData (Data.Approximate.Mass.Mass a)
instance Data.Traversable.Traversable Data.Approximate.Mass.Mass
instance Data.Functor.Bind.Class.Apply Data.Approximate.Mass.Mass
instance Data.Pointed.Pointed Data.Approximate.Mass.Mass
instance Data.Copointed.Copointed Data.Approximate.Mass.Mass
instance GHC.Base.Applicative Data.Approximate.Mass.Mass
instance GHC.Base.Monoid a => GHC.Base.Monoid (Data.Approximate.Mass.Mass a)
instance Data.Semigroup.Semigroup a => Data.Semigroup.Semigroup (Data.Approximate.Mass.Mass a)
instance Data.Functor.Bind.Class.Bind Data.Approximate.Mass.Mass
instance GHC.Base.Monad Data.Approximate.Mass.Mass
instance Data.Functor.Extend.Extend Data.Approximate.Mass.Mass
instance Control.Comonad.Comonad Data.Approximate.Mass.Mass
instance Control.Comonad.ComonadApply Data.Approximate.Mass.Mass


module Data.Approximate