diff --git a/base/float.jl b/base/float.jl
index 7b3aec3f7fe42..515c94804e896 100644
--- a/base/float.jl
+++ b/base/float.jl
@@ -807,13 +807,8 @@ precision(::Type{T}; base::Integer=2) where {T<:AbstractFloat} = _precision(T, b
 precision(::T; base::Integer=2) where {T<:AbstractFloat} = precision(T; base)
 
 
-"""
-    nextfloat(x::AbstractFloat, n::Integer)
-
-The result of `n` iterative applications of `nextfloat` to `x` if `n >= 0`, or `-n`
-applications of [`prevfloat`](@ref) if `n < 0`.
-"""
-function nextfloat(f::IEEEFloat, d::Integer)
+function _nextfloat(f::IEEEFloat, dneg::Bool, da::Integer)
+    # da must be > 0
     F = typeof(f)
     fumax = reinterpret(Unsigned, F(Inf))
     U = typeof(fumax)
@@ -823,8 +818,6 @@ function nextfloat(f::IEEEFloat, d::Integer)
     fneg = fi < 0
     fu = unsigned(fi & typemax(fi))
 
-    dneg = d < 0
-    da = uabs(d)
     if da > typemax(U)
         fneg = dneg
         fu = fumax
@@ -851,6 +844,14 @@ function nextfloat(f::IEEEFloat, d::Integer)
     reinterpret(F, fu)
 end
 
+"""
+    nextfloat(x::AbstractFloat, n::Integer)
+
+The result of `n` iterative applications of `nextfloat` to `x` if `n >= 0`, or `-n`
+applications of [`prevfloat`](@ref) if `n < 0`.
+"""
+nextfloat(f::AbstractFloat, d::Integer) = _nextfloat(f, isnegative(d), uabs(d))
+
 """
     nextfloat(x::AbstractFloat)
 
@@ -859,7 +860,7 @@ If no such `y` exists (e.g. if `x` is `Inf` or `NaN`), then return `x`.
 
 See also: [`prevfloat`](@ref), [`eps`](@ref), [`issubnormal`](@ref).
 """
-nextfloat(x::AbstractFloat) = nextfloat(x,1)
+nextfloat(x::AbstractFloat) = nextfloat(x, 1)
 
 """
     prevfloat(x::AbstractFloat, n::Integer)
@@ -867,7 +868,7 @@ nextfloat(x::AbstractFloat) = nextfloat(x,1)
 The result of `n` iterative applications of `prevfloat` to `x` if `n >= 0`, or `-n`
 applications of [`nextfloat`](@ref) if `n < 0`.
 """
-prevfloat(x::AbstractFloat, d::Integer) = nextfloat(x, -d)
+prevfloat(x::AbstractFloat, d::Integer) = _nextfloat(x, ispositive(d), uabs(d))
 
 """
     prevfloat(x::AbstractFloat)
@@ -875,7 +876,7 @@ prevfloat(x::AbstractFloat, d::Integer) = nextfloat(x, -d)
 Return the largest floating point number `y` of the same type as `x` such that `y < x`.
 If no such `y` exists (e.g. if `x` is `-Inf` or `NaN`), then return `x`.
 """
-prevfloat(x::AbstractFloat) = nextfloat(x,-1)
+prevfloat(x::AbstractFloat) = nextfloat(x, -1)
 
 for Ti in (Int8, Int16, Int32, Int64, Int128, UInt8, UInt16, UInt32, UInt64, UInt128)
     for Tf in (Float16, Float32, Float64)
diff --git a/test/numbers.jl b/test/numbers.jl
index faaa3d293626d..d2bc2317da948 100644
--- a/test/numbers.jl
+++ b/test/numbers.jl
@@ -2191,6 +2191,10 @@ end
     @test nextfloat(Inf32) === Inf32
     @test prevfloat(-Inf32) === -Inf32
     @test isequal(nextfloat(NaN32), NaN32)
+    @test nextfloat(1.0, UInt(5)) == nextfloat(1.0, 5)
+    @test prevfloat(1.0, UInt(5)) == prevfloat(1.0, 5)
+    @test nextfloat(0.0, typemax(UInt64)) == Inf
+    @test prevfloat(0.0, typemax(UInt64)) == -Inf
 end
 @testset "issue #16206" begin
     @test prevfloat(Inf) == 1.7976931348623157e308