Incorrect IDF in MultiPhraseQuery and SpanOrQuery

I recently stumbled across a very old bug in the IDF computation for MultiPhraseQuery and SpanOrQuery.

BM25Similarity and TFIDFSimilarity / ClassicSimilarity have a method for combining IDF values from more than on term / TermStatistics.

I mean the method:

Explanation idfExplain(CollectionStatistics collectionStats, TermStatistics termStats[])

It simply adds up the IDFs from all termStats[].

This method is used e.g. in PhraseQuery where it makes sense. If we assume that for the phrase "New York" the occurrences of both words are independent, we can multiply their probabilitis and since IDFs are logarithmic we add them up. Seems to be a reasonable approximation. However, this method is also used to add up the IDFs of all terms in a MultiPhraseQuery as can be seen in:

Similarity.SimScorer getStats(IndexSearcher searcher)

A MultiPhraseQuery is actually a PhraseQuery with alternatives at individual positions. IDFs of alternative terms for one position should not be added up. Instead we should use the minimum value as an approcimation because this corresponds to the docFreq of the most frequent term and we know that this is a lower bound for the docFreq for this position.

In SpanOrQuerry we have the same problem It uses buildSimWeight(...) from SpanWeight and adds up all IDFs of all OR-clauses.

If my arguments are not convincing, look at SynonymQuery / SynonymWeight in the constructor:

SynonymWeight(Query query, IndexSearcher searcher, ScoreMode scoreMode, float boost)

A SynonymQuery is also a kind of OR-query and it uses the maximum of the docFreq of all its alternative terms. I think this is how it should be.