Num.Pi

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

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

Defined in Data.ExactPi

Methods

(/) :: ExactPi -> ExactPi -> ExactPi

recip :: ExactPi -> ExactPi

fromRational :: Rational -> ExactPi

Num ExactPi

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

Defined in Data.ExactPi

Methods

showsPrec :: Int -> ExactPi -> ShowS

show :: ExactPi -> String

showList :: [ExactPi] -> ShowS

Semigroup ExactPi

The multiplicative semigroup over Rationals augmented with multiples of pi.

Defined in Data.ExactPi

Methods

(<>) :: ExactPi -> ExactPi -> ExactPi

sconcat :: NonEmpty ExactPi -> ExactPi

stimes :: Integral b => b -> ExactPi -> ExactPi

Monoid ExactPi

The multiplicative monoid over Rationals augmented with multiples of pi.

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.