Safe Haskell	Safe
Language	Haskell2010

Num.Pi

Synopsis

data ExactPi
- = Exact Integer Rational
- | Approximate (forall a. Floating a => a)
approximateValue :: Floating a => ExactPi -> a
isZero :: ExactPi -> Bool
isExact :: ExactPi -> Bool
isExactZero :: ExactPi -> Bool
isExactOne :: ExactPi -> Bool
areExactlyEqual :: ExactPi -> ExactPi -> Bool
isExactInteger :: ExactPi -> Bool
toExactInteger :: ExactPi -> Maybe Integer
isExactRational :: ExactPi -> Bool
toExactRational :: ExactPi -> Maybe Rational
rationalApproximations :: ExactPi -> [Rational]

Documentation

data ExactPi #

Represents an exact or approximate real value. The exactly representable values are rational multiples of an integer power of pi.

Constructors

Exact Integer Rational	`Exact z q` = q * pi^z. Note that this means there are many representations of zero.
Approximate (forall a. Floating a => a)	An approximate value. This representation was chosen because it allows conversion to floating types using their native definition of `pi`.

Instances

Floating ExactPi
Instance details Defined in Data.ExactPi Methods pi :: ExactPi # exp :: ExactPi -> ExactPi # log :: ExactPi -> ExactPi # sqrt :: ExactPi -> ExactPi # (**) :: ExactPi -> ExactPi -> ExactPi # logBase :: ExactPi -> ExactPi -> ExactPi # sin :: ExactPi -> ExactPi # cos :: ExactPi -> ExactPi # tan :: ExactPi -> ExactPi # asin :: ExactPi -> ExactPi # acos :: ExactPi -> ExactPi # atan :: ExactPi -> ExactPi # sinh :: ExactPi -> ExactPi # cosh :: ExactPi -> ExactPi # tanh :: ExactPi -> ExactPi # asinh :: ExactPi -> ExactPi # acosh :: ExactPi -> ExactPi # atanh :: ExactPi -> ExactPi # log1p :: ExactPi -> ExactPi # expm1 :: ExactPi -> ExactPi # log1pexp :: ExactPi -> ExactPi # log1mexp :: ExactPi -> ExactPi #
Fractional ExactPi
Instance details Defined in Data.ExactPi Methods (/) :: ExactPi -> ExactPi -> ExactPi # recip :: ExactPi -> ExactPi # fromRational :: Rational -> ExactPi #
Num ExactPi
Instance details Defined in Data.ExactPi Methods (+) :: ExactPi -> ExactPi -> ExactPi # (-) :: ExactPi -> ExactPi -> ExactPi # (*) :: ExactPi -> ExactPi -> ExactPi # negate :: ExactPi -> ExactPi # abs :: ExactPi -> ExactPi # signum :: ExactPi -> ExactPi # fromInteger :: Integer -> ExactPi #
Show ExactPi
Instance details Defined in Data.ExactPi Methods showsPrec :: Int -> ExactPi -> ShowS # show :: ExactPi -> String # showList :: [ExactPi] -> ShowS #
Semigroup ExactPi	The multiplicative semigroup over `Rational`s augmented with multiples of `pi`.
Instance details Defined in Data.ExactPi Methods (<>) :: ExactPi -> ExactPi -> ExactPi # sconcat :: NonEmpty ExactPi -> ExactPi # stimes :: Integral b => b -> ExactPi -> ExactPi #
Monoid ExactPi	The multiplicative monoid over `Rational`s augmented with multiples of `pi`.
Instance details Defined in Data.ExactPi Methods mempty :: ExactPi # mappend :: ExactPi -> ExactPi -> ExactPi # mconcat :: [ExactPi] -> ExactPi #

approximateValue :: Floating a => ExactPi -> a #

Approximates an exact or approximate value, converting it to a Floating type. This uses the value of pi supplied by the destination type, to provide the appropriate precision.

isZero :: ExactPi -> Bool #

Identifies whether an ExactPi is an exact or approximate representation of zero.

isExact :: ExactPi -> Bool #

Identifies whether an ExactPi is an exact value.

isExactZero :: ExactPi -> Bool #

Identifies whether an ExactPi is an exact representation of zero.

isExactOne :: ExactPi -> Bool #

Identifies whether an ExactPi is an exact representation of one.

areExactlyEqual :: ExactPi -> ExactPi -> Bool #

Identifies whether two ExactPi values are exactly equal.

isExactInteger :: ExactPi -> Bool #

Identifies whether an ExactPi is an exact representation of an integer.

toExactInteger :: ExactPi -> Maybe Integer #

Converts an ExactPi to an exact Integer or Nothing.

isExactRational :: ExactPi -> Bool #

Identifies whether an ExactPi is an exact representation of a rational.

toExactRational :: ExactPi -> Maybe Rational #

Converts an ExactPi to an exact Rational or Nothing.

rationalApproximations :: ExactPi -> [Rational] #

Converts an ExactPi to a list of increasingly accurate rational approximations, on alternating sides of the actual value. Note that Approximate values are converted using the Real instance for Double into a singleton list. Note that exact rationals are also converted into a singleton list.

Implementation based on work by Anders Kaseorg shared at http://qr.ae/RbXl8M.