rational

Rational numbers (a.k.a fractions) for Carp.

Fractions are expressed as pairs of integers. Mathematical operations and conversion primitives to and from integers and floating point numbers are provided.

Installation

(load "git@github.com:carpentry-org/rational@0.7.0")

Usage

(load "git@github.com:carpentry-org/rational@0.7.0")

(Rational.new 22 12) ; => (Rational 11/6)
(Rational.mul (Rational.new 22 12) (Rational.new 1 6)) ; => (Rational 2/1)
(Rational.to-int (Rational.new 2 1)) ; => 2
(Rational.to-float (Rational.new 1 4)) ; => 0.25
(Rational.rationalize 3.14159 300) ; => (Rational 355/113)
(Rational.floor (Rational.new 7 2)) ; => (Rational 3/1)
(Rational.ceil (Rational.new 7 2)) ; => (Rational 4/1)
(Rational.round (Rational.new 7 2)) ; => (Rational 4/1)
(Rational.reciprocal (Rational.new 3 4)) ; => (Rational 4/3)
(Rational.pow (Rational.new 2 3) 3) ; => (Rational 8/27)
(Rational.pow (Rational.new 2 3) -2) ; => (Rational 9/4)
(Rational.sign (Rational.new -3 4)) ; => (Rational -1/1)
(Rational.pos? (Rational.new -3 4)) ; => false
(Rational.neg? (Rational.new -3 4)) ; => true
(Rational.zero? (Rational.new 0 5)) ; => true
(Rational.<= (Rational.new 1 2) (Rational.new 2 3)) ; => true
(Rational.min (Rational.new 1 2) (Rational.new 2 3)) ; => (Rational 1/2)
(Rational.max (Rational.new 1 2) (Rational.new 2 3)) ; => (Rational 2/3)
(Rational.clamp (Rational.new 0 1) (Rational.new 1 1) (Rational.new 3 2)) ; => (Rational 1/1)

Please note that conversion can be lossy, because conversion to integer throws away any non-real value and conversion to floating point values is only as accurate as floating point numbers are.

Comparisons — and everything built on them, such as min, max, clamp and Array.sorted — are exact for every representable fraction. Arithmetic is not: add, sub, mul, div and pow cancel common factors first, but they still overflow when the result in lowest terms does not fit into an Int.

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Have fun!