FindFirstFunctions

FindFirstFunctions.jl is a package for faster findfirst type functions. These are specailized to improve performance over more generic implementations.

Functions

findfirstequal

findfirstequal(x::Int64,A::DenseVector{Int64})

Finds the first value in A equal to x

bracketstrictlymontonic

bracketstrictlymontonic(v, x, guess; lt=<comparison>, by=<transform>, rev=false)

Starting from an initial guess index, find indices (lo, hi) such that v[lo] ≤ x ≤ v[hi] according to the specified order, assuming that x is actually within the range of values found in v. If x is outside that range, either lo will be firstindex(v) or hi will be lastindex(v).

Note that the results will not typically satisfy lo ≤ guess ≤ hi. If x is precisely equal to a value that is not unique in the input v, there is no guarantee that (lo, hi) will encompass all indices corresponding to that value.

This algorithm is essentially an expanding binary search, which can be used as a precursor to searchsorted and related functions, which can take lo and hi as arguments. The purpose of using this function first would be to accelerate convergence in those functions by using correlated guesses for repeated calls. The best guess for the next call of this function would be the index returned by the previous call to searchsorted.

See sort! for an explanation of the keyword arguments by, lt and rev.

searchsortedfirstcorrelated(v::AbstractVector, x, guess)

searchsortedfirstcorrelated(v::AbstractVector{T}, x, guess::T)

An accelerated findfirst on sorted vectors using a bracketed search. Requires a guess to start the search from.

Some benchmarks:

julia> x = rand(Int, 2048); s = sort(x);

julia> @btime findfirst(==($x[1011]), $x)
  266.427 ns (0 allocations: 0 bytes)
1011

julia> @btime FindFirstFunctions.findfirstequal($x[1011], $x)
  67.502 ns (0 allocations: 0 bytes)
1011

julia> @btime searchsortedfirst($s, $s[1011])
  8.897 ns (0 allocations: 0 bytes)
1011

julia> @btime FindFirstFunctions.findfirstsortedequal($s[1011], $s)
  10.896 ns (0 allocations: 0 bytes)
1011