Safe Haskell	Safe
Language	Haskell2010

Data.Number

Contents

Description

A library for real number arithmetics

Synopsis

Classes

Continued fraction type

Represents a simple continued fraction of the form:

Supports Haskell arithmetic operators though the use of the operator function is to be preferred since provide shortcuts to calculations.

It can be an infinite sequence. Be careful with functions like show and precision: they may not terminate.

n :| x equivalent to n + 1/x

M x equivalent to -x

Constructors

Instances

Eq a => Eq (Continued a) Source
Ord a => Ord (Continued a) Source
Read a => Read (Continued a) Source
Show a => Show (Continued a) Source

Real numbers datatype (a continued fraction of naturals)

Lazy Peano numbers. Allow calculation with infinite values.

Constructors

Z	Zero
S Nat	Successor

Instances

Bounded Nat Source	The lower bound is zero, the upper bound is infinity.
Enum Nat Source	The `pred` function is bounded at Zero.
Eq Nat Source	`==` and `/=` work as long as at least one operand is finite.
Integral Nat Source	Since negative numbers are not allowed, `quot = div` and `rem = mod`. The methods `quot`, `rem`, `div`, `mod`, `quotRem` and `divMod` will terminate as long as their first argument is finite. Infinities in their second arguments are permitted and are handled as follows: n `quot` infinity = n `div` infinity = 0 n `rem` infinity = n `mod` infinity = n
Num Nat Source	Addition, multiplication, and subtraction are lazy in both arguments, meaning that, in the case of infinite values, they can produce an infinite stream of S-constructors. As long as the callers of these functions only consume a finite amount of these, the program will not hang. `fromInteger` is not injective in case of `Nat`, since negative integers are all converted to zero (`Z`).
Ord Nat Source	All methods work as long as at least one operand is finite.
Real Nat Source	Since `toRational` returns a `Ratio Integer`, it WILL NOT terminate on infinities.
Show Nat Source
Peano Nat Source	Peano class instance

Whole numbers (Z).

Constructors

Construct a whole number out of a magnitue and a sign.

Instances

Bounded Whole Source	The bounds are negative and positive infinity.
Enum Whole Source	`succ` and `pred` work according to the total order on the whole numbers, i.e. `succ n = n+1` and `pred n = n-1`.
Eq Whole Source	Positive and negative zero are considered equal.
Integral Whole Source	Integer conversions and division
Num Whole Source	Implements arithmetics for Whole numbers
Ord Whole Source	The ordering is the standard total order on Z. Positive and negative zero are equal.
Real Whole Source	Since `toRational` returns a `Ratio Integer`, it WILL NOT terminate on infinities.
Peano Whole Source	Peano class instance defines infinity (positive) and other functions handling the sign