// SPDX-License-Identifier: MIT
// Copyright (c) 2026 Incoprea
// Solve a nonlinear equation by bisection
// Not compiled or tested in-world
// Setup: Put in a spare prim you own. Touch to solve on the interval zero to three. Adapt equation() and the bracket together.
// Stop / restore: Disable or remove the script. It only reports to its owner and does not change prim properties. Reset clears its temporary state.
// Notes: Bisection requires a continuous function and opposite signs at the bracket endpoints. Iteration count is capped at thirty.
// License: see LICENSE in this distribution.
// Original Incoprea example. MIT. Owner-only calculation; no scene changes.
float equation(float x)
{
    return x*x*x+x-10.0;
}
default
{
    touch_start(integer detectedCount)
    {
        if (llDetectedKey(0) != llGetOwner()) return;
        float low=0.0;
        float high=3.0;
        float fLow=equation(low);
        float fHigh=equation(high);
        if (fLow*fHigh>0.0)
        {
            llOwnerSay("Bracket does not straddle a root.");
            return;
        }
        integer i;
        for (i=0; i<30; ++i)
        {
            float middle=(low+high)*0.5;
            float fMiddle=equation(middle);
            if (fLow*fMiddle<=0.0) high=middle;
            else
            {
                low=middle;
                fLow=fMiddle;
            }
        }
        float result=(low+high)*0.5;
        llOwnerSay("Root approximately "+(string)result+"; residual="+(string)equation(result));
    }
    changed(integer change)
    {
        if (change & CHANGED_OWNER) llResetScript();
    }
}