how do calculators calculate square roots?? its just one of those things thats been bothering me for a while since i cant figure it out if anyone has a link to how its done or can tell me, ide love it :D oh and, by the way, ide also like to know how to calculate sine and cosine without a calculator

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Sam Johnston (Samith)

This works:

double sqrt( double x ) {	float	y;	float	delta;	float	maxError;	if ( x <= 0 ) {		return 0;	}	// initial guess	y = x / 2;	// refine	maxError = x * 0.001;	do {		delta = ( y * y ) - x;		y -= delta / ( 2 * y );	} while ( delta > maxError || delta < -maxError );	return y;} 

It''s from the q3 code if you''re wondering. It looks complicated, but it''s not really if you break it down.

Would that be faster than the standard sqrt function? *just curious*

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That is from the Q3 code so I''m sure it''s optimized all the way. The standard sqrt function probably looks something like that, anyhow, but I would just stick with the standard sqrt function since it''s already compiled into a library and everything.

Dont take this like I''m trying to call you a liar (as I am certainly not doing that) - but how did you get any chunk of the q3 source??

use Taylor

exp(x) = sum(k=0..inf) (x^k/k)
sin(x) = sum(k=0..inf) (-1)^k * x^(2k+1)/(2k+1)!
....

the sqrt funct is a bit harder. There isn''t one for sqrt(x)
only

(1+x)^a = 1+ax+(a(a-1)/2!)*x^2+(a(a-1)(a-2)/3!)*x^3+....

if you take a=1/2 you get sqrt(1+x)

quote:

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Original post by Xori
Dont take this like I''m trying to call you a liar (as I am certainly not doing that) - but how did you get any chunk of the q3 source??

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quote:

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Originally posted by crossbow
The standard sqrt function probably looks something like that...

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Not really - on the x86, it just uses FSQRT.

Newton and Taylor are the usual suspects.
One other way is Heron''s algorithm:
x(i+1) = ( x(i) + x/x(i) ) / 2

I''m gonna be picky about the q3a source heh

y -= delta / ( 2 * y );

you can replace (2*y) with y + y ... multiplications take quite a bit more clock cycles than additions.


I had a lot of ppl on here tell me that method was slower than what would be in the standard library...they could be wrong, though.