exact

A portable clojure library for doing exact arithmetic. I.e., you can write code that uses bigints and ratios and it works in CLJS too.

Note that bigdecimals are not included; though generally all bigdecimal values can be represented as integers or ratios, the arithmetic is fairly different.

Obtention

[com.gfredericks/exact "0.1.11"]

Usage

(ns my.namespace
  ;; here you can choose to exclude clojure's functions and use those
  ;; from exact if you want it to look like normal arithmetic
  (:require [com.gfredericks.exact :as e]))

(def TWO (e/native->integer 2))
(defn square [x] (e/* x x))
(defn avg [a b] (-> a (e/+ b) (e// TWO)))

(defn newtonian-square-root
  "Returns a ratio between (- (sqrt x) epsilon) and (+ (sqrt x) epsilon)"
  [x epsilon]
  (let [ee (square epsilon)]
    (loop [guess (avg x e/ZERO)]
      (if (-> guess square (e/- x) e/abs (e/< ee))
        guess
        (recur (-> x (e// guess) (avg guess)))))))

(def epsilon
  (e// (e/string->integer "1000000000000000000000000")))

(newtonian-square-root TWO epsilon)
;; => 1572584048032918633353217/1111984844349868137938112

Things in com.gfredericks.exact

• ZERO
• ONE
• +
• -
• *
• /
• zero?
• inc
• dec
• <
• >
• <=
• >=
• max
• min
• min-key
• max-key
• pos?
• neg?
• numerator
• denominator
• integer?
• ratio?
• quot
• mod
• rem
• abs
• even?
• odd?
• string->integer
• integer->string
• native->integer
• integer->native

Caveats

Most of the functions are not designed to be used with native numbers, since this can be problematic in ClojureScript. To use it portably, you must create integers with native->integer or string->integer.

License

Copyright © 2015 Gary Fredericks

Distributed under the Eclipse Public License either version 1.0 or (at your option) any later version.