Efficiently searching a list for the position of the closest number to a specified number

SeedRandom[42];
haystack = RandomReal[1, 6300];
AbsoluteTiming[
 f = Nearest[haystack -> Range@Length@haystack];
 {f[.3, 1], haystack[[f[.3, 1]]]}]

(*

-> {0.015625, {{3123}, {0.300033}}}

*)

Of course in this case most of the time is expended calculating the nearest function. If your points aren't changing from one use to the next, the time for calculating f[}is nil for 6K points.

The second argument of f[] specifies that Nearest[] should return only one point

In versions 10+, you can have a NearestFunction that returns multiple properties, such as the "Index" of the nearest element and the "Element" itself:

SeedRandom[42];
haystack = RandomReal[1, 1000000];
f = Nearest[haystack ->{"Index", "Element"}];

AbsoluteTiming[f[.312345]]

{0.000072, {{101999, 0.312345}}}