public void b1(object sender, EventArgs e)
{
   for(int i = 0; i < 1000000; ++i)
   {
      ...
   }
}

public void b2(object sender, EventArgs e)
{
   ???
}

CancellationTokenSource cts;

public async void b1(object sender, EventArgs e)
{
    using (cts = new CancellationTokenSource())
        await Calculate(cts.Token);
}

public void b2(object sender, EventArgs e)
{
    cts.Cancel();
}

Task Calculate(CancellationToken ct)
{
    return Task.Run(() => CalculateImpl(ct));
}

void CalculateImpl(CancellationToken ct)
{
    for (int i = 0; i < 1000000; ++i)
    {
        if (ct.IsCancellationRequested)
            return;
        // ...
    }
}

private BackgroundWorker bw;

public void b1(object sender, EventArgs e)
{
    bw = new BackgroundWorker { WorkerSupportsCancellation = true };
    bw.DoWork += (obj, args) =>
         {
             BackgroundWorker lbw = (BackgroundWorker)obj;
             for (int i = 0; i < 1000000 && !lbw.CancellationPending; ++i)
             {
                ...
             }
         };
    bw.RunWorkerAsync();
}

public void b2(object sender, EventArgs e)
{
    if (bw != null && bw.IsBusy && !bw.CancellationPending)
        bw.CancelAsync();
}

private volatile bool _isRunning;

private void buttonStart_Click (object sender, EventArgs e)
{
    Task.Run(() => {
        _isRunning = true;
        for (int i = 0; i < 10000; i++) {
            Invoke((Action)(() => Text = i.ToString()));
            if (!_isRunning)
                break;
        }
    });
}

private void buttonStop_Click (object sender, EventArgs e)
{
    _isRunning = false;
}

private volatile bool _stop_cycle;

public void b1(object sender, EventArgs e)
{
    _stop_cycle = false;
    for(int i = 0; i < 1000000 && !_stop_cycle; ++i)
    {
         ...
    }
}

public void b2(object sender, EventArgs e)
{
     _stop_cycle = true;
}