Sign-aware computation of midpoint for sorting (fixes JuliaLang#33977) (

JuliaLang#34106)

base/sort.jl

@@ -164,6 +164,10 @@ same thing as `partialsort!` but leaving `v` unmodified.
 partialsort(v::AbstractVector, k::Union{Integer,OrdinalRange}; kws...) =
  partialsort!(copymutable(v), k; kws...)
 
+# This implementation of `midpoint` is performance-optimized but safe
+# only if `lo <= hi`.
+midpoint(lo::T, hi::T) where T<:Integer = lo + ((hi - lo) >>> 0x01)
+midpoint(lo::Integer, hi::Integer) = midpoint(promote(lo, hi)...)
 
 # reference on sorted binary search:
 # https://www.tbray.org/ongoing/When/200x/2003/03/22/Binary
@@ -175,7 +179,7 @@ function searchsortedfirst(v::AbstractVector, x, lo::T, hi::T, o::Ordering) wher
  lo = lo - u
  hi = hi + u
  @inbounds while lo < hi - u
- m = (lo + hi) >>> 1
+ m = midpoint(lo, hi)
  if lt(o, v[m], x)
  lo = m
  else
@@ -192,7 +196,7 @@ function searchsortedlast(v::AbstractVector, x, lo::T, hi::T, o::Ordering) where
  lo = lo - u
  hi = hi + u
  @inbounds while lo < hi - u
- m = (lo + hi) >>> 1
+ m = midpoint(lo, hi)
  if lt(o, x, v[m])
  hi = m
  else
@@ -210,7 +214,7 @@ function searchsorted(v::AbstractVector, x, ilo::T, ihi::T, o::Ordering) where T
  lo = ilo - u
  hi = ihi + u
  @inbounds while lo < hi - u
- m = (lo + hi) >>> 1
+ m = midpoint(lo, hi)
  if lt(o, v[m], x)
  lo = m
  elseif lt(o, x, v[m])
@@ -487,7 +491,7 @@ end
 
 @inline function selectpivot!(v::AbstractVector, lo::Integer, hi::Integer, o::Ordering)
  @inbounds begin
- mi = (lo+hi)>>>1
+ mi = midpoint(lo, hi)
 
  # sort v[mi] <= v[lo] <= v[hi] such that the pivot is immediately in place
  if lt(o, v[lo], v[mi])
@@ -552,7 +556,7 @@ function sort!(v::AbstractVector, lo::Integer, hi::Integer, a::MergeSortAlg, o::
  @inbounds if lo < hi
  hi-lo <= SMALL_THRESHOLD && return sort!(v, lo, hi, SMALL_ALGORITHM, o)
 
- m = (lo+hi)>>>1
+ m = midpoint(lo, hi)
  (length(t) < m-lo+1) && resize!(t, m-lo+1)
 
  sort!(v, lo, m, a, o, t)

test/offsetarray.jl

@@ -475,6 +475,19 @@ v = OffsetArray(rand(8), (-2,))
 @test sortslices(A, dims=2) == OffsetArray(sortslices(parent(A), dims=2), A.offsets)
 @test sort(A, dims=1) == OffsetArray(sort(parent(A), dims=1), A.offsets)
 @test sort(A, dims=2) == OffsetArray(sort(parent(A), dims=2), A.offsets)
+# Issue #33977
+soa = OffsetArray([2,2,3], -2)
+@test searchsorted(soa, 1) == -1:-2
+@test searchsortedfirst(soa, 1) == -1
+@test searchsortedlast(soa, 1) == -2
+@test first(sort!(soa; alg=QuickSort)) == 2
+@test first(sort!(soa; alg=MergeSort)) == 2
+soa = OffsetArray([2,2,3], typemax(Int)-4)
+@test searchsorted(soa, 1) == typemax(Int)-3:typemax(Int)-4
+@test searchsortedfirst(soa, 2) == typemax(Int) - 3
+@test searchsortedlast(soa, 2) == typemax(Int) - 2
+@test first(sort!(soa; alg=QuickSort)) == 2
+@test first(sort!(soa; alg=MergeSort)) == 2
 
 @test mapslices(sort, A, dims=1) == OffsetArray(mapslices(sort, parent(A), dims=1), A.offsets)
 @test mapslices(sort, A, dims=2) == OffsetArray(mapslices(sort, parent(A), dims=2), A.offsets)

test/sorting.jl

@@ -11,6 +11,21 @@ using Test
  @test ReverseOrdering(Forward) == ReverseOrdering() == Reverse
 end
 
+@testset "midpoint" begin
+ @test Base.Sort.midpoint(1, 3) === 2
+ @test Base.Sort.midpoint(2, 4) === 3
+ @test 2 <= Base.Sort.midpoint(1, 4) <= 3
+ @test Base.Sort.midpoint(-3, -1) === -2
+ @test Base.Sort.midpoint(-4, -2) === -3
+ @test -3 <= Base.Sort.midpoint(-4, -1) <= -2
+ @test Base.Sort.midpoint(-1, 1) === 0
+ @test -1 <= Base.Sort.midpoint(-2, 1) <= 0
+ @test 0 <= Base.Sort.midpoint(-1, 2) <= 1
+ @test Base.Sort.midpoint(-2, 2) === 0
+ @test Base.Sort.midpoint(typemax(Int)-2, typemax(Int)) === typemax(Int)-1
+ @test Base.Sort.midpoint(typemin(Int), typemin(Int)+2) === typemin(Int)+1
+ @test -1 <= Base.Sort.midpoint(typemin(Int), typemax(Int)) <= 0
+end
 
 @testset "sort" begin
  @test sort([2,3,1]) == [1,2,3] == sort([2,3,1]; order=Forward)