// SPDX-License-Identifier: MIT
// Copyright (c) 2026 Incoprea
// Newton iteration with a convergence check
// Not compiled or tested in-world
// Setup: Place in a spare owned prim. Set VALUE positive. Touch to run; output is private to the owner.
// Stop / restore: Disable/remove. No scene changes or external calls.
// Notes: Stops on a relative change threshold or after thirty steps; llSqrt is printed as a reference, not used in the iteration.
// License: see LICENSE in this distribution.
// Original Incoprea. MIT.
float VALUE=37.0;
default
{
    touch_start(integer detectedCount)
    {
        if(llDetectedKey(0)!=llGetOwner())return;
        if(VALUE<=0.0)
        {
            llOwnerSay("Positive value required.");
            return;
        }
        float guess=VALUE;
        if(guess<1.0)guess=1.0;
        integer i;
        integer done;
        for(i=0;i<30&&!done;++i)
        {
            float next=0.5*(guess+VALUE/guess);
            done=(llFabs(next-guess)<0.000001*(1.0+llFabs(next)));
            guess=next;
        }
        llOwnerSay("Root="+(string)guess+" reference="+(string)llSqrt(VALUE)+" iterations="+(string)i);
    }
}