ex_1_07.clj

(ns sicp.chapter-1.part-1.ex-1-07
  (:require
    [sicp.chapter-1.part-1.book-1-1 :as b11]))

; Exercise 1.7
; The `good-enough?` test used in computing square roots will not be very effective
; for finding the square roots of very small numbers.
; Also, in real computers, arithmetic operations are almost always performed with limited precision.
; This makes our test inadequate for very large numbers.

; Explain these statements, with examples showing how the test fails for small and large numbers.
; An alternative strategy for implementing `good-enough?`
; is to watch how guess changes from one iteration to the next and to stop when the change
; is a very small fraction of the guess.
; Design a square-root procedure that uses this kind of end test.

; Does this work better for small and large numbers?

; Imporovments
(defn good-enough-v2?
  [guess1 guess2]
  (< (abs (- guess1 guess2)) 0.001))

(defn sqrt-iter-v2
  [guess x]
  (if (good-enough-v2? guess (b11/improve guess x))
    guess
    (sqrt-iter-v2 (b11/improve guess x) x)))