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These estimators returned 1 minus the corresponding equality/match estimate, which is incorrect: we need to subtract off the fraction of nulls in the column, since those are neither equal nor not equal to the comparison value. The error only becomes obvious if the nullfrac is large, but it could be very bad in a mostly-nulls column, as reported in bug #14676 from Marko Tiikkaja. To fix the <> case, refactor eqsel() and neqsel() to call a common support routine, which can be made to account for nullfrac correctly. The pattern-match cases were already factored that way, and it was simply an oversight that patternsel() wasn't subtracting off nullfrac. neqjoinsel() has a similar problem, but since we're elsewhere discussing changing its behavior entirely, I left it alone for now. This is a very longstanding bug, but I'm hesitant to back-patch a fix for it. Given the lack of prior complaints, such cases must not come up often, so it's probably not worth the risk of destabilizing plans in stable branches. Discussion: https://postgr.es/m/20170529153847.4275.95416@wrigleys.postgresql.org
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