diff --git a/base/float.jl b/base/float.jl
index f93fee64796fd..8844acd3e0f61 100644
--- a/base/float.jl
+++ b/base/float.jl
@@ -216,6 +216,24 @@ const NaN32 = box(Float32,unbox(Uint32,0x7fc00000))
 const Inf = box(Float64,unbox(Uint64,0x7ff0000000000000))
 const NaN = box(Float64,unbox(Uint64,0x7ff8000000000000))
 
+function float_lex_order(f::Integer, delta::Integer)
+    # convert from signed magnitude to 2's complement and back
+    if f < 0
+        f = oftype(f, -(f & typemax(f)))
+    end
+    f = oftype(f, f + delta)
+    f < 0 ? oftype(f, -(f & typemax(f))) : f
+end
+
+nextfloat(x::Float16, i::Integer) =
+    reinterpret(Float16,float_lex_order(reinterpret(Int16,x), i))
+nextfloat(x::Float32, i::Integer) =
+    reinterpret(Float32,float_lex_order(reinterpret(Int32,x), i))
+nextfloat(x::Float64, i::Integer) =
+    reinterpret(Float64,float_lex_order(reinterpret(Int64,x), i))
+nextfloat(x::FloatingPoint) = nextfloat(x,1)
+prevfloat(x::FloatingPoint) = nextfloat(x,-1)
+
 @eval begin
     inf(::Type{Float16}) = $Inf16
     nan(::Type{Float16}) = $NaN16
@@ -249,12 +267,6 @@ const NaN = box(Float64,unbox(Uint64,0x7ff8000000000000))
     realmin() = realmin(Float64)
     realmax() = realmax(Float64)
 
-    nextfloat(x::Float16, i::Integer) = box(Float16,add_int(reinterpret(Int16,x),unbox(Int16,int16(i))))
-    nextfloat(x::Float32, i::Integer) = box(Float32,add_int(unbox(Float32,x),unbox(Int32,int32(i))))
-    nextfloat(x::Float64, i::Integer) = box(Float64,add_int(unbox(Float64,x),unbox(Int64,int64(i))))
-    nextfloat(x::FloatingPoint) = nextfloat(x,1)
-    prevfloat(x::FloatingPoint) = nextfloat(x,-1)
-
     eps(x::FloatingPoint) = isfinite(x) ? abs(nextfloat(x)-x) : nan(x)
     eps(::Type{Float16}) = $(box(Float16,unbox(Uint16,0x1400)))
     eps(::Type{Float32}) = $(box(Float32,unbox(Uint32,0x34000000)))
diff --git a/test/numbers.jl b/test/numbers.jl
index 475a1309db12c..882e46778795e 100644
--- a/test/numbers.jl
+++ b/test/numbers.jl
@@ -1162,22 +1162,22 @@ end
 @test iround(Int, 0.5) == 1
 @test iround(Int, prevfloat(0.5)) == 0
 @test iround(Int, -0.5) == -1
-@test iround(Int, prevfloat(-0.5)) == 0
+@test iround(Int, nextfloat(-0.5)) == 0
 
 @test iround(Uint, 0.5) == 1
 @test iround(Uint, prevfloat(0.5)) == 0
 @test_throws iround(Uint, -0.5)
-@test iround(Uint, prevfloat(-0.5)) == 0
+@test iround(Uint, nextfloat(-0.5)) == 0
 
 @test iround(Int, 0.5f0) == 1
 @test iround(Int, prevfloat(0.5f0)) == 0
 @test iround(Int, -0.5f0) == -1
-@test iround(Int, prevfloat(-0.5f0)) == 0
+@test iround(Int, nextfloat(-0.5f0)) == 0
 
 @test iround(Uint, 0.5f0) == 1
 @test iround(Uint, prevfloat(0.5f0)) == 0
 @test_throws iround(Uint, -0.5f0)
-@test iround(Uint, prevfloat(-0.5f0)) == 0
+@test iround(Uint, nextfloat(-0.5f0)) == 0
 
 # numbers that can't be rounded by trunc(x+0.5)
 @test iround(Int64, 2.0^52 + 1) == 4503599627370497
@@ -1579,3 +1579,14 @@ end
 
 @test nextprod([2,3,5],30) == 30
 @test nextprod([2,3,5],33) == 36
+
+@test nextfloat(0.0) == 5.0e-324
+@test prevfloat(0.0) == -5.0e-324
+@test nextfloat(-0.0) == 5.0e-324
+@test prevfloat(-0.0) == -5.0e-324
+@test nextfloat(-5.0e-324) == 0.0
+@test prevfloat(5.0e-324) == 0.0
+@test nextfloat(-1.0) > -1.0
+@test prevfloat(-1.0) < -1.0
+@test nextfloat(nextfloat(0.0),-2) == -5.0e-324
+@test nextfloat(prevfloat(0.0), 2) ==  5.0e-324