> figuring out the magnitude of a frequency after an FFT.  I remember someone,
> like Newton, having an algorithm that gave closer and closer
> approximatations.

Newton's method is embodied in this code: translate to your favourite language:


#include        <math.h>

double
sqrt(double x)
{
        double  og, ng;
        short   niter;
        int     expon;

        if(x <= 0.0)
                return 0.0;                     /* sqrt(-ve) undefined */
        og = x;
        if(og < 1.0)
                og = 1.0/og;
        og = frexp(og, &expon);
        og = ldexp(og, expon/2);                /* make an educated guess -
 halve exponent */
        if(x < 1.0)
                og = 1.0/og;
        for(niter = 0 ; niter < 20 ; niter++) { /* iterate until value converges
 */
                ng = (x/og + og)/2.0;           /* new guess calculated as the
 average of
                                                 the old guess and the original
 value
                                                 divided by the old guess */
                if(ng == og)                    /* no change? finis! */
                        break;
                og = ng;
        }
        return og;
}


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