diff --git a/base/array.jl b/base/array.jl
index 3811e717211c3..2830a85d715de 100644
--- a/base/array.jl
+++ b/base/array.jl
@@ -1653,7 +1653,7 @@ CartesianIndex(2, 1)
 """
 function findnext(A, start)
     l = last(keys(A))
-    i = start
+    i = oftype(l, start)
     i > l && return nothing
     while true
         A[i] && return i
@@ -1735,7 +1735,7 @@ CartesianIndex(1, 1)
 """
 function findnext(testf::Function, A, start)
     l = last(keys(A))
-    i = start
+    i = oftype(l, start)
     i > l && return nothing
     while true
         testf(A[i]) && return i
@@ -1839,8 +1839,8 @@ CartesianIndex(2, 1)
 ```
 """
 function findprev(A, start)
-    i = start
     f = first(keys(A))
+    i = oftype(f, start)
     i < f && return nothing
     while true
         A[i] && return i
@@ -1930,8 +1930,8 @@ CartesianIndex(2, 1)
 ```
 """
 function findprev(testf::Function, A, start)
-    i = start
     f = first(keys(A))
+    i = oftype(f, start)
     i < f && return nothing
     while true
         testf(A[i]) && return i
diff --git a/base/bitarray.jl b/base/bitarray.jl
index 2bbb138c1d7e5..b5d47000f84a5 100644
--- a/base/bitarray.jl
+++ b/base/bitarray.jl
@@ -1374,7 +1374,7 @@ end
 
 count(B::BitArray) = bitcount(B.chunks)
 
-function unsafe_bitfindnext(Bc::Vector{UInt64}, start::Integer)
+function unsafe_bitfindnext(Bc::Vector{UInt64}, start::Int)
     chunk_start = _div64(start-1)+1
     within_chunk_start = _mod64(start-1)
     mask = _msk64 << within_chunk_start
@@ -1397,13 +1397,14 @@ end
 function findnext(B::BitArray, start::Integer)
     start > 0 || throw(BoundsError(B, start))
     start > length(B) && return nothing
-    unsafe_bitfindnext(B.chunks, start)
+    unsafe_bitfindnext(B.chunks, Int(start))
 end
 
 #findfirst(B::BitArray) = findnext(B, 1)  ## defined in array.jl
 
 # aux function: same as findnext(~B, start), but performed without temporaries
 function findnextnot(B::BitArray, start::Integer)
+    start = Int(start)
     start > 0 || throw(BoundsError(B, start))
     start > length(B) && return nothing
 
@@ -1458,7 +1459,7 @@ function findnext(testf::Function, B::BitArray, start::Integer)
 end
 #findfirst(testf::Function, B::BitArray) = findnext(testf, B, 1)  ## defined in array.jl
 
-function unsafe_bitfindprev(Bc::Vector{UInt64}, start::Integer)
+function unsafe_bitfindprev(Bc::Vector{UInt64}, start::Int)
     chunk_start = _div64(start-1)+1
     mask = _msk_end(start)
 
@@ -1480,10 +1481,11 @@ end
 function findprev(B::BitArray, start::Integer)
     start > 0 || return nothing
     start > length(B) && throw(BoundsError(B, start))
-    unsafe_bitfindprev(B.chunks, start)
+    unsafe_bitfindprev(B.chunks, Int(start))
 end
 
 function findprevnot(B::BitArray, start::Integer)
+    start = Int(start)
     start > 0 || return nothing
     start > length(B) && throw(BoundsError(B, start))
 
diff --git a/base/sort.jl b/base/sort.jl
index fa102c1eba3c5..ff8edf15bd645 100644
--- a/base/sort.jl
+++ b/base/sort.jl
@@ -10,7 +10,7 @@ using .Base: copymutable, LinearIndices, length, (:),
     AbstractVector, @inbounds, AbstractRange, @eval, @inline, Vector, @noinline,
     AbstractMatrix, AbstractUnitRange, isless, identity, eltype, >, <, <=, >=, |, +, -, *, !,
     extrema, sub_with_overflow, add_with_overflow, oneunit, div, getindex, setindex!,
-    length, resize!, fill, Missing, require_one_based_indexing
+    length, resize!, fill, Missing, require_one_based_indexing, keytype
 
 using .Base: >>>, !==
 
@@ -174,7 +174,7 @@ midpoint(lo::Integer, hi::Integer) = midpoint(promote(lo, hi)...)
 
 # index of the first value of vector a that is greater than or equal to x;
 # returns length(v)+1 if x is greater than all values in v.
-function searchsortedfirst(v::AbstractVector, x, lo::T, hi::T, o::Ordering) where T<:Integer
+function searchsortedfirst(v::AbstractVector, x, lo::T, hi::T, o::Ordering)::keytype(v) where T<:Integer
     u = T(1)
     lo = lo - u
     hi = hi + u
@@ -191,7 +191,7 @@ end
 
 # index of the last value of vector a that is less than or equal to x;
 # returns 0 if x is less than all values of v.
-function searchsortedlast(v::AbstractVector, x, lo::T, hi::T, o::Ordering) where T<:Integer
+function searchsortedlast(v::AbstractVector, x, lo::T, hi::T, o::Ordering)::keytype(v) where T<:Integer
     u = T(1)
     lo = lo - u
     hi = hi + u
@@ -209,7 +209,7 @@ end
 # returns the range of indices of v equal to x
 # if v does not contain x, returns a 0-length range
 # indicating the insertion point of x
-function searchsorted(v::AbstractVector, x, ilo::T, ihi::T, o::Ordering) where T<:Integer
+function searchsorted(v::AbstractVector, x, ilo::T, ihi::T, o::Ordering)::UnitRange{keytype(v)} where T<:Integer
     u = T(1)
     lo = ilo - u
     hi = ihi + u
@@ -228,7 +228,7 @@ function searchsorted(v::AbstractVector, x, ilo::T, ihi::T, o::Ordering) where T
     return (lo + 1) : (hi - 1)
 end
 
-function searchsortedlast(a::AbstractRange{<:Real}, x::Real, o::DirectOrdering)
+function searchsortedlast(a::AbstractRange{<:Real}, x::Real, o::DirectOrdering)::keytype(a)
     require_one_based_indexing(a)
     if step(a) == 0
         lt(o, x, first(a)) ? 0 : length(a)
@@ -238,7 +238,7 @@ function searchsortedlast(a::AbstractRange{<:Real}, x::Real, o::DirectOrdering)
     end
 end
 
-function searchsortedfirst(a::AbstractRange{<:Real}, x::Real, o::DirectOrdering)
+function searchsortedfirst(a::AbstractRange{<:Real}, x::Real, o::DirectOrdering)::keytype(a)
     require_one_based_indexing(a)
     if step(a) == 0
         lt(o, first(a), x) ? length(a) + 1 : 1
@@ -248,7 +248,7 @@ function searchsortedfirst(a::AbstractRange{<:Real}, x::Real, o::DirectOrdering)
     end
 end
 
-function searchsortedlast(a::AbstractRange{<:Integer}, x::Real, o::DirectOrdering)
+function searchsortedlast(a::AbstractRange{<:Integer}, x::Real, o::DirectOrdering)::keytype(a)
     require_one_based_indexing(a)
     h = step(a)
     if h == 0
@@ -270,7 +270,7 @@ function searchsortedlast(a::AbstractRange{<:Integer}, x::Real, o::DirectOrderin
     end
 end
 
-function searchsortedfirst(a::AbstractRange{<:Integer}, x::Real, o::DirectOrdering)
+function searchsortedfirst(a::AbstractRange{<:Integer}, x::Real, o::DirectOrdering)::keytype(a)
     require_one_based_indexing(a)
     h = step(a)
     if h == 0
@@ -285,14 +285,14 @@ function searchsortedfirst(a::AbstractRange{<:Integer}, x::Real, o::DirectOrderi
         lastindex(a) + 1
     else
         if o isa ForwardOrdering
-            -fld(floor(Integer, -x) + first(a), h) + 1
+            -fld(floor(Integer, -x) + Signed(first(a)), h) + 1
         else
-            -fld(ceil(Integer, -x) + first(a), h) + 1
+            -fld(ceil(Integer, -x) + Signed(first(a)), h) + 1
         end
     end
 end
 
-function searchsortedfirst(a::AbstractRange{<:Integer}, x::Unsigned, o::DirectOrdering)
+function searchsortedfirst(a::AbstractRange{<:Integer}, x::Unsigned, o::DirectOrdering)::keytype(a)
     require_one_based_indexing(a)
     if lt(o, first(a), x)
         if step(a) == 0
@@ -305,7 +305,7 @@ function searchsortedfirst(a::AbstractRange{<:Integer}, x::Unsigned, o::DirectOr
     end
 end
 
-function searchsortedlast(a::AbstractRange{<:Integer}, x::Unsigned, o::DirectOrdering)
+function searchsortedlast(a::AbstractRange{<:Integer}, x::Unsigned, o::DirectOrdering)::keytype(a)
     require_one_based_indexing(a)
     if lt(o, x, first(a))
         0
diff --git a/base/strings/search.jl b/base/strings/search.jl
index dbc572dc948fa..9dec4f1db66cc 100644
--- a/base/strings/search.jl
+++ b/base/strings/search.jl
@@ -125,6 +125,7 @@ findfirst(ch::AbstractChar, string::AbstractString) = findfirst(==(ch), string)
 
 # AbstractString implementation of the generic findnext interface
 function findnext(testf::Function, s::AbstractString, i::Integer)
+    i = Int(i)
     z = ncodeunits(s) + 1
     1 ≤ i ≤ z || throw(BoundsError(s, i))
     @inbounds i == z || isvalid(s, i) || string_index_err(s, i)
@@ -272,7 +273,7 @@ julia> findnext("Lang", "JuliaLang", 2)
 6:9
 ```
 """
-findnext(t::AbstractString, s::AbstractString, i::Integer) = _search(s, t, i)
+findnext(t::AbstractString, s::AbstractString, i::Integer) = _search(s, t, Int(i))
 
 """
     findnext(ch::AbstractChar, string::AbstractString, start::Integer)
@@ -484,7 +485,7 @@ julia> findprev("Julia", "JuliaLang", 6)
 1:5
 ```
 """
-findprev(t::AbstractString, s::AbstractString, i::Integer) = _rsearch(s, t, i)
+findprev(t::AbstractString, s::AbstractString, i::Integer) = _rsearch(s, t, Int(i))
 
 """
     findprev(ch::AbstractChar, string::AbstractString, start::Integer)
diff --git a/stdlib/SparseArrays/test/sparse.jl b/stdlib/SparseArrays/test/sparse.jl
index 9449895f16b66..8e50e8c8428bf 100644
--- a/stdlib/SparseArrays/test/sparse.jl
+++ b/stdlib/SparseArrays/test/sparse.jl
@@ -2462,6 +2462,22 @@ end
         @test findnext(!iszero, z,i) == findnext(!iszero, z_sp,i)
         @test findprev(!iszero, z,i) == findprev(!iszero, z_sp,i)
     end
+
+    # issue 32568
+    for T = (UInt, BigInt)
+        @test findnext(!iszero, x_sp, T(4)) isa keytype(x_sp)
+        @test findnext(!iszero, x_sp, T(5)) isa keytype(x_sp)
+        @test findprev(!iszero, x_sp, T(5)) isa keytype(x_sp)
+        @test findprev(!iszero, x_sp, T(6)) isa keytype(x_sp)
+        @test findnext(iseven, x_sp, T(4)) isa keytype(x_sp)
+        @test findnext(iseven, x_sp, T(5)) isa keytype(x_sp)
+        @test findprev(iseven, x_sp, T(4)) isa keytype(x_sp)
+        @test findprev(iseven, x_sp, T(5)) isa keytype(x_sp)
+        @test findnext(!iszero, z_sp, T(4)) isa keytype(z_sp)
+        @test findnext(!iszero, z_sp, T(5)) isa keytype(z_sp)
+        @test findprev(!iszero, z_sp, T(4)) isa keytype(z_sp)
+        @test findprev(!iszero, z_sp, T(5)) isa keytype(z_sp)
+    end
 end
 
 # #20711
diff --git a/test/arrayops.jl b/test/arrayops.jl
index 667ca080034f8..3a2b31b094b79 100644
--- a/test/arrayops.jl
+++ b/test/arrayops.jl
@@ -564,6 +564,18 @@ end
     @test findlast(isequal(0x00), [0x01, 0x00]) == 2
     @test findnext(isequal(0x00), [0x00, 0x01, 0x00], 2) == 3
     @test findprev(isequal(0x00), [0x00, 0x01, 0x00], 2) == 1
+
+    @testset "issue 32568" for T = (UInt, BigInt)
+        @test findnext(!iszero, a, T(1)) isa keytype(a)
+        @test findnext(!iszero, a, T(2)) isa keytype(a)
+        @test findprev(!iszero, a, T(4)) isa keytype(a)
+        @test findprev(!iszero, a, T(5)) isa keytype(a)
+        b = [true, false, true]
+        @test findnext(b, T(2)) isa keytype(b)
+        @test findnext(b, T(3)) isa keytype(b)
+        @test findprev(b, T(1)) isa keytype(b)
+        @test findprev(b, T(2)) isa keytype(b)
+    end
 end
 @testset "find with Matrix" begin
     A = [1 2 0; 3 4 0]
diff --git a/test/bitarray.jl b/test/bitarray.jl
index 3b66359823eb4..a12d93cbef5b0 100644
--- a/test/bitarray.jl
+++ b/test/bitarray.jl
@@ -1307,6 +1307,21 @@ timesofar("find")
     @test_throws BoundsError findprev(x->true, b1, 11)
     @test_throws BoundsError findnext(x->true, b1, -1)
 
+    @testset "issue 32568" for T = (UInt, BigInt)
+        for x = (1, 2)
+            @test findnext(evens, T(x)) isa keytype(evens)
+            @test findnext(iseven, evens, T(x)) isa keytype(evens)
+            @test findnext(isequal(true), evens, T(x)) isa keytype(evens)
+            @test findnext(isequal(false), evens, T(x)) isa keytype(evens)
+        end
+        for x = (3, 4)
+            @test findprev(evens, T(x)) isa keytype(evens)
+            @test findprev(iseven, evens, T(x)) isa keytype(evens)
+            @test findprev(isequal(true), evens, T(x)) isa keytype(evens)
+            @test findprev(isequal(false), evens, T(x)) isa keytype(evens)
+        end
+    end
+
     for l = [1, 63, 64, 65, 127, 128, 129]
         f = falses(l)
         t = trues(l)
diff --git a/test/sorting.jl b/test/sorting.jl
index 37d294a6d962e..07d7eb5741016 100644
--- a/test/sorting.jl
+++ b/test/sorting.jl
@@ -141,6 +141,20 @@ end
         @test searchsortedlast(500:1.0:600, -1.0e20) == 0
         @test searchsortedlast(500:1.0:600, 1.0e20) == 101
     end
+
+    @testset "issue 32568" begin
+        for R in numTypes, T in numTypes
+            for arr in [R[1:5;], R(1):R(5), R(1):2:R(5)]
+                @test eltype(searchsorted(arr, T(2))) == keytype(arr)
+                @test eltype(searchsorted(arr, T(2), big(1), big(4), Forward)) == keytype(arr)
+                @test searchsortedfirst(arr, T(2)) isa keytype(arr)
+                @test searchsortedfirst(arr, T(2), big(1), big(4), Forward) isa keytype(arr)
+                @test searchsortedlast(arr, T(2)) isa keytype(arr)
+                @test searchsortedlast(arr, T(2), big(1), big(4), Forward) isa keytype(arr)
+            end
+        end
+    end
+
     @testset "issue #34157" begin
         @test searchsorted(1:2.0, -Inf) === 1:0
         @test searchsorted([1,2], -Inf) === 1:0
@@ -173,7 +187,6 @@ end
                 @test searchsortedlast(reverse(coll), -huge, rev=true) === lastindex(coll)
                 @test searchsorted(reverse(coll), huge, rev=true) === firstindex(coll):firstindex(coll) - 1
                 @test searchsorted(reverse(coll), -huge, rev=true) === lastindex(coll)+1:lastindex(coll)
-
             end
         end
     end
diff --git a/test/strings/search.jl b/test/strings/search.jl
index 92fc03177dc76..f952229afdfe2 100644
--- a/test/strings/search.jl
+++ b/test/strings/search.jl
@@ -389,3 +389,22 @@ s_18109 = "fooα🐨βcd3"
     @test findall("aa", "aaaaaa") == [1:2, 3:4, 5:6]
     @test findall("aa", "aaaaaa", overlap=true) == [1:2, 2:3, 3:4, 4:5, 5:6]
 end
+
+# issue 32568
+for T = (UInt, BigInt)
+    for x = (4, 5)
+        @test eltype(findnext(r"l", astr, T(x))) == Int
+        @test findnext(isequal('l'), astr, T(x)) isa Int
+        @test findprev(isequal('l'), astr, T(x)) isa Int
+        @test findnext('l', astr, T(x)) isa Int
+        @test findprev('l', astr, T(x)) isa Int
+    end
+    for x = (5, 6)
+        @test eltype(findprev(",b", "foo,bar,baz", T(x))) == Int
+    end
+    for x = (7, 8)
+        @test eltype(findnext(",b", "foo,bar,baz", T(x))) == Int
+        @test findnext(isletter, astr, T(x)) isa Int
+        @test findprev(isletter, astr, T(x)) isa Int
+    end
+end
diff --git a/test/tuple.jl b/test/tuple.jl
index d0985537addff..c8df66c94bc41 100644
--- a/test/tuple.jl
+++ b/test/tuple.jl
@@ -479,6 +479,13 @@ end
     @test findprev(isequal(1), (1, 1), 1) == 1
     @test findnext(isequal(1), (2, 3), 1) === nothing
     @test findprev(isequal(1), (2, 3), 2) === nothing
+
+    @testset "issue 32568" begin
+        @test findnext(isequal(1), (1, 2), big(1)) isa Int
+        @test findprev(isequal(1), (1, 2), big(2)) isa Int
+        @test findnext(isequal(1), (1, 1), UInt(2)) isa Int
+        @test findprev(isequal(1), (1, 1), UInt(1)) isa Int
+    end
 end
 
 @testset "properties" begin