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:Re: Question about a numerical computation

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  :Re: Question about a numerical computation "Robert L." <No_spamming@noWhere_7073.org> - 2016-11-29 09:31 +0000

#52948 — :Re: Question about a numerical computation

Paul Foley wrote:

> Forget epsilon; just look to see whether tmp changed at all.  When you
> run out of bits, it won't change:
> 
>   (defun heron-sqrt (x)
>     (let ((val 1l0))
>       (loop
>         (let ((next (* 0.5l0 (+ val (/ x val)))))
>           (if (= next val)
>               (return val)
>               (setq val next))))))

Ruby:

def heron_sqrt x
  Enumerator.new{|y| guess = 1
    loop{y.yield guess; guess = (x.fdiv(guess) + guess) * 0.5}
  }.each_cons(2).find{|a,b| a==b}.first
end

(2..22).each{|n| p [n, heron_sqrt(n)]}
[2, 1.414213562373095]
[3, 1.7320508075688772]
[4, 2.0]
[5, 2.23606797749979]
[6, 2.449489742783178]
[7, 2.6457513110645907]
[8, 2.82842712474619]
[9, 3.0]
[10, 3.162277660168379]
[11, 3.3166247903554]
[12, 3.4641016151377544]
[13, 3.6055512754639896]
[14, 3.7416573867739413]
[15, 3.872983346207417]
[16, 4.0]
[17, 4.123105625617661]
[18, 4.242640687119286]
[19, 4.358898943540673]
[20, 4.47213595499958]
[21, 4.58257569495584]
[22, 4.69041575982343]

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