Safe Haskell	Safe
Language	Haskell98

Data.Number.FixedPrec

Contents

Type-level integers for precision
Fixed-precision numbers
Static and dynamic casts
Other operations

Description

A reasonably efficient implementation of arbitrary-but-fixed precision real numbers. This is inspired by, and partly based on, Data.Number.Fixed and Data.Number.CReal, but more efficient.

Synopsis

class Precision e
data P0
data P1
data P10
data P100
data P1000
data P2000
data PPlus1 e
data PPlus3 e
data PPlus10 e
data PPlus100 e
data PPlus1000 e
data FixedPrec e
getprec :: Precision e => FixedPrec e -> Int
cast :: (Precision e, Precision f) => FixedPrec e -> FixedPrec f
upcast :: Precision e => FixedPrec e -> FixedPrec (PPlus3 e)
downcast :: Precision e => FixedPrec (PPlus3 e) -> FixedPrec e
with_added_digits :: forall a f. Precision f => Int -> (forall e. Precision e => FixedPrec e -> a) -> FixedPrec f -> a
fractional :: Precision e => FixedPrec e -> FixedPrec e
solve_quadratic :: Precision e => FixedPrec e -> FixedPrec e -> Maybe (FixedPrec e, FixedPrec e)
log_double :: (Floating a, Real a) => a -> Double

Type-level integers for precision

class Precision e Source #

A type class for type-level integers, capturing a precision parameter. Precision is measured in decimal digits.

Minimal complete definition

digits

Instances

Precision P2000 Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: P2000 -> Int
Precision P1000 Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: P1000 -> Int
Precision P100 Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: P100 -> Int
Precision P10 Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: P10 -> Int
Precision P1 Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: P1 -> Int
Precision P0 Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: P0 -> Int
Precision e => Precision (PPlus1000 e) Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: PPlus1000 e -> Int
Precision e => Precision (PPlus100 e) Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: PPlus100 e -> Int
Precision e => Precision (PPlus10 e) Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: PPlus10 e -> Int
Precision e => Precision (PPlus3 e) Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: PPlus3 e -> Int
Precision e => Precision (PPlus1 e) Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: PPlus1 e -> Int

data P0 Source #

Precision of 0 digits.

Instances

Precision P0 Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: P0 -> Int

data P1 Source #

Precision of 1 digit.

Instances

Precision P1 Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: P1 -> Int

data P10 Source #

Precision of 10 digits.

Instances

Precision P10 Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: P10 -> Int

data P100 Source #

Precision of 100 digits.

Instances

Precision P100 Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: P100 -> Int

data P1000 Source #

Precision of 1000 digits.

Instances

Precision P1000 Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: P1000 -> Int

data P2000 Source #

Precision of 2000 digits.

Instances

Precision P2000 Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: P2000 -> Int

data PPlus1 e Source #

Add 1 digit to the given precision.

Instances

Precision e => Precision (PPlus1 e) Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: PPlus1 e -> Int

data PPlus3 e Source #

Add 3 digits to the given precision.

Instances

Precision e => Precision (PPlus3 e) Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: PPlus3 e -> Int

data PPlus10 e Source #

Add 10 digits to the given precision.

Instances

Precision e => Precision (PPlus10 e) Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: PPlus10 e -> Int

data PPlus100 e Source #

Add 100 digits to the given precision.

Instances

Precision e => Precision (PPlus100 e) Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: PPlus100 e -> Int

data PPlus1000 e Source #

Add 1000 digits to the given precision.

Instances

Precision e => Precision (PPlus1000 e) Source #
Instance details Defined in Data.Number.FixedPrec Methods digits :: PPlus1000 e -> Int

Fixed-precision numbers

data FixedPrec e Source #

The type of fixed-precision numbers.

Instances

Eq (FixedPrec e) Source #
Instance details Defined in Data.Number.FixedPrec Methods (==) :: FixedPrec e -> FixedPrec e -> Bool # (/=) :: FixedPrec e -> FixedPrec e -> Bool #
Precision e => Floating (FixedPrec e) Source #
Instance details Defined in Data.Number.FixedPrec Methods pi :: FixedPrec e # exp :: FixedPrec e -> FixedPrec e # log :: FixedPrec e -> FixedPrec e # sqrt :: FixedPrec e -> FixedPrec e # (**) :: FixedPrec e -> FixedPrec e -> FixedPrec e # logBase :: FixedPrec e -> FixedPrec e -> FixedPrec e # sin :: FixedPrec e -> FixedPrec e # cos :: FixedPrec e -> FixedPrec e # tan :: FixedPrec e -> FixedPrec e # asin :: FixedPrec e -> FixedPrec e # acos :: FixedPrec e -> FixedPrec e # atan :: FixedPrec e -> FixedPrec e # sinh :: FixedPrec e -> FixedPrec e # cosh :: FixedPrec e -> FixedPrec e # tanh :: FixedPrec e -> FixedPrec e # asinh :: FixedPrec e -> FixedPrec e # acosh :: FixedPrec e -> FixedPrec e # atanh :: FixedPrec e -> FixedPrec e # log1p :: FixedPrec e -> FixedPrec e # expm1 :: FixedPrec e -> FixedPrec e # log1pexp :: FixedPrec e -> FixedPrec e # log1mexp :: FixedPrec e -> FixedPrec e #
Precision e => Fractional (FixedPrec e) Source #
Instance details Defined in Data.Number.FixedPrec Methods (/) :: FixedPrec e -> FixedPrec e -> FixedPrec e # recip :: FixedPrec e -> FixedPrec e # fromRational :: Rational -> FixedPrec e #
Precision e => Num (FixedPrec e) Source #
Instance details Defined in Data.Number.FixedPrec Methods (+) :: FixedPrec e -> FixedPrec e -> FixedPrec e # (-) :: FixedPrec e -> FixedPrec e -> FixedPrec e # (*) :: FixedPrec e -> FixedPrec e -> FixedPrec e # negate :: FixedPrec e -> FixedPrec e # abs :: FixedPrec e -> FixedPrec e # signum :: FixedPrec e -> FixedPrec e # fromInteger :: Integer -> FixedPrec e #
Ord (FixedPrec e) Source #
Instance details Defined in Data.Number.FixedPrec Methods compare :: FixedPrec e -> FixedPrec e -> Ordering # (<) :: FixedPrec e -> FixedPrec e -> Bool # (<=) :: FixedPrec e -> FixedPrec e -> Bool # (>) :: FixedPrec e -> FixedPrec e -> Bool # (>=) :: FixedPrec e -> FixedPrec e -> Bool # max :: FixedPrec e -> FixedPrec e -> FixedPrec e # min :: FixedPrec e -> FixedPrec e -> FixedPrec e #
Precision e => Real (FixedPrec e) Source #
Instance details Defined in Data.Number.FixedPrec Methods toRational :: FixedPrec e -> Rational #
Precision e => RealFrac (FixedPrec e) Source #
Instance details Defined in Data.Number.FixedPrec Methods properFraction :: Integral b => FixedPrec e -> (b, FixedPrec e) # truncate :: Integral b => FixedPrec e -> b # round :: Integral b => FixedPrec e -> b # ceiling :: Integral b => FixedPrec e -> b # floor :: Integral b => FixedPrec e -> b #
Precision e => Show (FixedPrec e) Source #
Instance details Defined in Data.Number.FixedPrec Methods showsPrec :: Int -> FixedPrec e -> ShowS # show :: FixedPrec e -> String # showList :: [FixedPrec e] -> ShowS #
Precision e => Random (FixedPrec e) Source #
Instance details Defined in Data.Number.FixedPrec Methods randomR :: RandomGen g => (FixedPrec e, FixedPrec e) -> g -> (FixedPrec e, g) # random :: RandomGen g => g -> (FixedPrec e, g) # randomRs :: RandomGen g => (FixedPrec e, FixedPrec e) -> g -> [FixedPrec e] # randoms :: RandomGen g => g -> [FixedPrec e] # randomRIO :: (FixedPrec e, FixedPrec e) -> IO (FixedPrec e) # randomIO :: IO (FixedPrec e) #

getprec :: Precision e => FixedPrec e -> Int Source #

Get the precision of a fixed-precision number, in decimal digits.

Static and dynamic casts

cast :: (Precision e, Precision f) => FixedPrec e -> FixedPrec f Source #

Cast from any FixedPrec type to another.

upcast :: Precision e => FixedPrec e -> FixedPrec (PPlus3 e) Source #

Cast to a fixed-point type with three additional digits of accuracy.

downcast :: Precision e => FixedPrec (PPlus3 e) -> FixedPrec e Source #

Cast to a fixed-point type with three fewer digits of accuracy.

with_added_digits :: forall a f. Precision f => Int -> (forall e. Precision e => FixedPrec e -> a) -> FixedPrec f -> a Source #

The function with_added_digits d f x evaluates f(x), adding d digits of accuracy to x during the computation.

Other operations

fractional :: Precision e => FixedPrec e -> FixedPrec e Source #

Return the positive fractional part of a fixed-precision number. The result is always in [0,1), regardless of the sign of the input.

solve_quadratic :: Precision e => FixedPrec e -> FixedPrec e -> Maybe (FixedPrec e, FixedPrec e) Source #

Solve the quadratic equation x^2 + bx + c = 0 with maximal possible precision, using a numerically stable method. Return the pair (x1, x2) of solutions with x1 <= x2, or Nothing if no solution exists.

This is far more precise, and probably more efficient, than naively using the quadratic formula.

log_double :: (Floating a, Real a) => a -> Double Source #

A version of the natural logarithm that returns a Double. The logarithm of just about any value can fit into a Double; so if not a lot of precision is required in the mantissa, this function is often faster than log.