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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
let highestBit n i = if (1 << i) > n then i else 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 g else 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.