License	MIT
Maintainer	douglas.mcclean@gmail.com
Stability	experimental
Safe Haskell	Safe-Inferred
Language	Haskell2010
Extensions	RankNTypes ExplicitForAll

Data.ExactPi

Description

This type is sufficient to exactly express the closure of Q ∪ {π} under multiplication and division. As a result it is useful for representing conversion factors between physical units. Approximate values are included both to close the remainder of the arithmetic operations in the Num typeclass and to encode conversion factors defined experimentally.

Synopsis

Documentation

data ExactPi Source

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
Fractional ExactPi
Num ExactPi
Show ExactPi
Monoid ExactPi	The multiplicative monoid over augmented rationals.
Group ExactPi	The multiplicative group over augmented rationals.
Abelian ExactPi

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

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.

isExactZero :: ExactPi -> Bool Source

Identifies whether an ExactPi is an exact representation of zero.

isExactOne :: ExactPi -> Bool Source

Identifies whether an ExactPi is an exact representation of one.