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lang-mma
circDist = Compile[{{t1, _Real}, {t2, _Real}}, With[{d = Abs[t1 - t2]}, Min[{d, 1 - d}]]]is a little faster. $\endgroup$Last@midpoint[{0.9,0.1}]is0.9, but it's obviously0or1$\endgroup$midpoint[{t1_, t2_}] := With[{dist = Abs[t1 - t2]}, Which[dist <= 1 - dist, {dist, Mean[{t1, t2}]}, True, {1 - dist, Mean[{t1, t2}] + 1/2}]]is the correct way. It fullfillsLast@midpoint[{0.9,0.1}]==1as lesobrod mentions. $\endgroup$