Benchmarking some different implementations of sqrt. Requires <https://github.com/hugoduncan/criterium> to run the benchmarks.

square_roots.clj

(ns square-roots
  (:require [criterium.core :refer [bench]]))

(defn square [x] (* x x))

(defn abs [x] (if (< 0 x) (- x) x))

(defn sqrt-repeated-average
  [x lo hi tolerance]
  (if (<= (- hi lo) tolerance)
    lo
    (let [y (/ (+ lo hi) 2)]
      (if (> (square y) x)
        (recur x lo y tolerance)
        (recur x y hi tolerance)))))

(defn sqrt-inc
  [x lo hi tolerance]
  (if (> (square lo) x)
    lo
    (recur x (+ lo tolerance) hi tolerance)))

(defn sqrt-newton
  [x g tolerance]
  (let [g' (- g (/ (square g) (* 2.0 g)))]
    (if (< (abs (- g g')) tolerance)
      g'
      (recur x g' tolerance))))

(comment
  (bench #(sqrt-repeated-average (rand) 0.0 1.0 0.00000001))

  (bench #(sqrt-inc (rand) 0.0 1.0 0.00000001))

  (bench #(sqrt-newton (rand) 0.5 0.00000001)))