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Roy - Literate Roy

Brian McKenna2012-01-01

I added some literate programming support to Roy. You can write Markdown files with an extension of .lroy and the roy executable will accept them.

I've also written a shell script that will run it through Pandoc to give you nice-looking HTML output, using Kevin Burke's Markdown.css:

The above was generated using the following Markdown:

% 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.

[Babylonian method]:

Happy New Year!

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