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We have a 'fast' count mode that runs in cases like a query on
{a:'c',b:'d'}
with index
{a:1,b:1}
. (Among other restrictions, all fields of the index must be present and the queried values must not be objects or numbers.) This optimization adds implementation complexity and has been a source of bugs (eg SERVER-4529). Additionally, the performance of this special counting mode has likely been degraded by changes over time (eg SERVER-3449).
Also, I'm not sure if we've actually measured the performance of fast count mode. We might consider removing it, otherwise we might refactor it out of the main query path.
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