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Compute Square Root - using Scheme

 
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Compute Square Root - using Scheme, Cannot compute square root
LionessHeadstrong
post 9 Mar, 2007 - 01:21 AM
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Hello

I am trying to write a program in Dr Scheme (Lisp - scheme) that will compute a square root for me. This is what I have so far:

(define value (lambda (x) (- x 0.00000001) (* x x))
(if (lambda (= x value) x)))

But this doesn't work, anyone have any ideas?

Thanks for your help

Linda
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Programmist
post 9 Mar, 2007 - 09:47 AM
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numerical_jerome
post 15 Aug, 2008 - 07:14 PM
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if this was a school assignment, this might be a little far from what your professor wanted, but

[math]
sqrt(x) == x^0.5
x == e^(ln(x))
x^0.5 == e^(0.5*ln(x))
sqrt(x) == e^(0.5*ln(x))
[/math]

this is actually very fast, as your floating point unit has an optimized natural log / natural exponent

in common lisp this looks like:

CODE

(defun my_sqrt (a)
    (exp (* 0.5 (log a))))


in scheme this would be something like:

CODE

(define my_sqrt (lambda (a)
    (exp (* 0.5 (log a)))))


If your instructor complains, demonstrate the great speed at which your function evaluates, and point out how the fancier bits of the FPU can be developed from ln, e using a similar technique
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NickDMax
post 15 Aug, 2008 - 07:55 PM
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The posts are old but thanks for the responses. I used to try to answer scheme and lisp questions but it really hurts my head... welcome to DIC!
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