Roy - Babylonian Square Root

This is a Markdown file. It's also literate Roy code!

We're going to define a sqrt function using the Babylonian method for approximation.

let sqrt n =

Making a good initial guess helps reduce the amount of iterations until convergence. One method is to find the highest-bit (b) and use 2^(b/2).

  let highestBit n i =
    if (1 << i) > n then
      highestBit n (i + 1)

  let guess = 1 << ((highestBit n 1) / 2)

Iteratively average the guess and the number divided by the guess until convergence with a cut-off of 0.001. The guessing is started from the initial value, calculated above.

  let nextGuess g =
    if (Math.abs (g - (n / g))) < 0.001 then
      nextGuess ((g + (n / g)) / 2)

  nextGuess guess

Now we can calculate the square root of 314 and print it.

console.log (sqrt 314)

We should get an answer of around 17.720.