<div dir="ltr">Hi Patrick, <br><div><div class="gmail_extra"><br><div class="gmail_quote">On Mon, Sep 11, 2017 at 10:44 PM, PATRICK BROWNE <span dir="ltr"><<a href="mailto:patrick.browne@dit.ie" target="_blank">patrick.browne@dit.ie</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>Why is it the sqrt0 function is so much slower than sqrt1. Does the where clause allow intermediate values to be stored?</div><div>Regards,</div><div>Pat</div><div>sqrt0 :: Int -> Int</div><div>sqrt0 0 = 0 </div><div>sqrt0 1 = 1 </div><div>sqrt0 n = ((sqrt0 (n - 1)) + (n `quot` sqrt0 (n-1))) `quot` 2 </div><div>-- sqrt0 25 several minutes<br></div></div></blockquote><div> </div><div>In sqrt0, each function call with n > 1 creates two more function call, and this creates exponential blow up (factor of 2). You can make your code it faster by storing the intermediate result<br></div><div><br></div><div><div>sqrt0 :: Int -> Int</div><div>sqrt0 0 = 0 </div><div>sqrt0 1 = 1 </div><div>sqrt0 n = let k = sqrt0 (n - 1) in (k + (n `quot` k)) `quot` 2 <br></div></div><div> </div><div>This code is not blowing exponentially because of you storing intermediate result leading to faster computation.</div><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div></div><div>sqrt1 :: Int -> Int</div><div>sqrt1 n </div><div> | n == 0 = 0</div><div> | n == 1 = 1 </div><div> | otherwise = div (k + ( div n k)) 2</div><div> where k = sqrt1(n-1)</div><div>-- sqrt1 25 instant<br></div><div><br></div></div><div class="gmail_extra"><br><div class="gmail_quote">On 9 September 2017 at 05:49, KC <span dir="ltr"><<a href="mailto:kc1956@gmail.com" target="_blank">kc1956@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="auto">One approach <div dir="auto"><br></div><div dir="auto">One function to compute the next iterate</div><div dir="auto"><br></div><div dir="auto">Another function to call the computation function until results are within some tolerance </div><div dir="auto"><br></div><div dir="auto">It's usually presented as separation of control and computation 😎<br><br><div dir="auto">--<br>Sent from an expensive device which will be obsolete in a few months<br>Casey</div></div></div><div class="gmail-m_-2211523315161561755HOEnZb"><div class="gmail-m_-2211523315161561755h5"><div class="gmail_extra"><br><div class="gmail_quote">On Sep 3, 2017 1:23 AM, "mike h" <<a href="mailto:mike_k_houghton@yahoo.co.uk" target="_blank">mike_k_houghton@yahoo.co.uk</a>> wrote:<br type="attribution"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div style="overflow-wrap: break-word;">Hi,<div><br></div><div>To help me in learning Haskell I started blogging about some of the things I’ve looked at. </div><div>One such topic was calculating square roots ‘by hand’ and then deriving a Haskell algorithm. </div><div>I wrote about the well known technique here</div><div><a href="http://gitcommit.co.uk/2017/08/25/the-root-of-the-problem-part-1/" target="_blank">http://gitcommit.co.uk/2017/08<wbr>/25/the-root-of-the-problem-pa<wbr>rt-1/</a></div><div><br></div><div>and it it is really quite a simple method. </div><div><br></div><div>The second part of the post will be an implementation in Haskell. </div><div><br></div><div>I then tried implementing it and got something that works but really its not very pleasant to look at! And its something I don’t want to post! Some parts are fine but I think I locked myself into the notion that it had to be using State and really the end result is pretty poor. </div><div><br></div><div>I know this i perhaps a ‘big ask’ but I’d really appreciate any suggestions, solutions, hints etc. I will of course give full attribution. </div><div><br></div><div>I’ve created a gist of the code here</div><div><a href="https://gist.github.com/banditpig" target="_blank">https://gist.github.com/bandit<wbr>pig</a></div><div><br></div><div>Many Thanks</div><div><br></div><div>Mike</div></div><br>______________________________<wbr>_________________<br>
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