.map() function

I'd like to implement .map(IntToIntFunction f) that returns new RoaringBitmap as a result of mapping.
Example:

RoaringBitmap r1 = RoaringBitmap.bitmapOf(1, 3, 6, 8, 9, 14)
RoaringBitmap r2 = r1.map(i -> (i*7)%13)
r2 // {7, 8, 3, 4, 11}

I would like to gather ideas how to solve problem with performance of inserting new values in non-ordered way.

Currently I can see that using java.util.BitSet as a temporary buffer gives me speed-up 6x. I assume it is because of skipping binary-search part.

public class Main {
  public static void main(String[] args) {
    RoaringBitmap b = new RoaringBitmap();
    Random r = new Random(1333);
    for (int i = 0; i < 120_000_000; i++) {
      b.add(r.nextInt(200_000_000));
    }
    b.runOptimize();

    for (int i = 0; i < 100; i++) { //naive benchmark
      Instant s = Instant.now();
      //RoaringBitmap res = new RoaringBitmap();
      BitSet altRes = new java.util.BitSet(77_333_333);
      b.forEach((IntConsumer) value -> altRes.set((value * 3) % 77_333_333));
      RoaringBitmap altResAsBitmap = BitSetUtil.bitmapOf(altRes);
      Instant e = Instant.now();
      System.out.println("res:" + altResAsBitmap.getCardinality() + " time: " + Duration.between(s, e).toMillis());
    }
  }
}

Start with the proposed RoaringBitmap.map(IntToIntFunction) entry point and review the existing bitmap insertion and iteration APIs. Use the benchmark in the issue to understand the non-ordered insertion concern. Done means an agreed mapping API and implementation strategy with performance and result-cardinality behavior validated.