diff --git a/base/char.jl b/base/char.jl
index 7a094dec85ce2..05cb6124e1c70 100644
--- a/base/char.jl
+++ b/base/char.jl
@@ -3,6 +3,10 @@ char(x::FloatingPoint) = char(iround(x))
 
 integer(x::Char) = int(x)
 
+convert(::Type{Char}, x::Float16) = char(convert(Uint32, x))
+convert(::Type{Char}, x::Float32) = char(convert(Uint32, x))
+convert(::Type{Char}, x::Float64) = char(convert(Uint32, x))
+
 ## char promotions ##
 
 promote_rule(::Type{Char}, ::Type{Int8})    = Int32
diff --git a/base/float.jl b/base/float.jl
index a43243daf9f08..a4cba309e8c41 100644
--- a/base/float.jl
+++ b/base/float.jl
@@ -1,16 +1,16 @@
 ## conversions to floating-point ##
 
-convert(::Type{Float32}, x::Int128)  = float32(uint128(abs(x)))*(1-2(x<0))
-convert(::Type{Float32}, x::Uint128) = float32(uint64(x)) + ldexp(float32(uint64(x>>>64)),64)
+convert(::Type{Float32}, x::Int128)  = float32(reinterpret(Uint128,abs(x)))*(1-2(x<0))
+convert(::Type{Float32}, x::Uint128) = float32(uint64(x&0xffffffffffffffff)) + ldexp(float32(uint64(x>>>64)),64)
 promote_rule(::Type{Float32}, ::Type{Int128} ) = Float32
 promote_rule(::Type{Float32}, ::Type{Uint128}) = Float32
 
-convert(::Type{Float64}, x::Int128)  = float64(uint128(abs(x)))*(1-2(x<0))
-convert(::Type{Float64}, x::Uint128) = float64(uint64(x)) + ldexp(float64(uint64(x>>>64)),64)
+convert(::Type{Float64}, x::Int128)  = float64(reinterpret(Uint128,abs(x)))*(1-2(x<0))
+convert(::Type{Float64}, x::Uint128) = float64(uint64(x&0xffffffffffffffff)) + ldexp(float64(uint64(x>>>64)),64)
 promote_rule(::Type{Float64}, ::Type{Int128} ) = Float64
 promote_rule(::Type{Float64}, ::Type{Uint128}) = Float64
 
-convert(::Type{Float16}, x::Union(Signed,Unsigned)) = convert(Float16, convert(Float32,x))
+convert(::Type{Float16}, x::Integer) = convert(Float16, convert(Float32,x))
 for t in (Bool,Char,Int8,Int16,Int32,Int64,Uint8,Uint16,Uint32,Uint64)
     @eval promote_rule(::Type{Float16}, ::Type{$t}) = Float32
 end
diff --git a/base/int.jl b/base/int.jl
index bed14be303d9e..a4167ad1a9632 100644
--- a/base/int.jl
+++ b/base/int.jl
@@ -1,13 +1,3 @@
-## type aliases ##
-
-if Int === Int32
-typealias SmallSigned Union(Int8,Int16)
-typealias SmallUnsigned Union(Uint8,Uint16)
-else
-typealias SmallSigned Union(Int8,Int16,Int32)
-typealias SmallUnsigned Union(Uint8,Uint16,Uint32)
-end
-
 ## integer arithmetic ##
 
 const IntTypes = (Int8, Uint8, Int16, Uint16, Int32, Uint32,
@@ -34,11 +24,10 @@ iseven(n::Integer) = !isodd(n)
 signbit(x::Integer) = x < 0
 signbit(x::Unsigned) = false
 
-flipsign(x::Int,    y::Int)    = box(Int,flipsign_int(unbox(Int,x),unbox(Int,y)))
-flipsign(x::Int64,  y::Int64)  = box(Int64,flipsign_int(unbox(Int64,x),unbox(Int64,y)))
-flipsign(x::Int128, y::Int128) = box(Int128,flipsign_int(unbox(Int128,x),unbox(Int128,y)))
+for T in (Int8,Int16,Int32,Int64,Int128)
+    @eval flipsign(x::$T, y::$T) = box($T,flipsign_int(unbox($T,x),unbox($T,y)))
+end
 
-flipsign{T<:Signed}(x::T,y::T)  = flipsign(int(x),int(y))
 flipsign(x::Signed, y::Signed)  = flipsign(promote(x,y)...)
 flipsign(x::Signed, y::Float32) = flipsign(x, reinterpret(Int32,y))
 flipsign(x::Signed, y::Float64) = flipsign(x, reinterpret(Int64,y))
@@ -100,9 +89,13 @@ for T in IntTypes
         ($)(x::$T, y::$T) = box($T,xor_int(unbox($T,x),unbox($T,y)))
 
         <<(x::$T,  y::Int32) = box($T, shl_int(unbox($T,x),unbox(Int32,y)))
-        >>(x::$T,  y::Int32) = box($T,ashr_int(unbox($T,x),unbox(Int32,y)))
         >>>(x::$T, y::Int32) = box($T,lshr_int(unbox($T,x),unbox(Int32,y)))
     end
+    if issubtype(T,Unsigned)
+        @eval >>(x::$T, y::Int32) = box($T,lshr_int(unbox($T,x),unbox(Int32,y)))
+    else
+        @eval >>(x::$T, y::Int32) = box($T,ashr_int(unbox($T,x),unbox(Int32,y)))
+    end
 end
 
 bswap(x::Int8)    = x
@@ -129,29 +122,15 @@ trailing_ones(x::Integer) = trailing_zeros(~x)
 
 ## integer comparisons ##
 
-<(x::Int8,   y::Int8)   = slt_int(unbox(Int8,x),unbox(Int8,y))
-<(x::Int16,  y::Int16)  = slt_int(unbox(Int16,x),unbox(Int16,y))
-<(x::Int32,  y::Int32)  = slt_int(unbox(Int32,x),unbox(Int32,y))
-<(x::Int64,  y::Int64)  = slt_int(unbox(Int64,x),unbox(Int64,y))
-<(x::Int128, y::Int128) = slt_int(unbox(Int128,x),unbox(Int128,y))
-
-<(x::Uint8,   y::Uint8)   = ult_int(unbox(Uint8,x),unbox(Uint8,y))
-<(x::Uint16,  y::Uint16)  = ult_int(unbox(Uint16,x),unbox(Uint16,y))
-<(x::Uint32,  y::Uint32)  = ult_int(unbox(Uint32,x),unbox(Uint32,y))
-<(x::Uint64,  y::Uint64)  = ult_int(unbox(Uint64,x),unbox(Uint64,y))
-<(x::Uint128, y::Uint128) = ult_int(unbox(Uint128,x),unbox(Uint128,y))
-
-<=(x::Int8,   y::Int8)   = sle_int(unbox(Int8,x),unbox(Int8,y))
-<=(x::Int16,  y::Int16)  = sle_int(unbox(Int16,x),unbox(Int16,y))
-<=(x::Int32,  y::Int32)  = sle_int(unbox(Int32,x),unbox(Int32,y))
-<=(x::Int64,  y::Int64)  = sle_int(unbox(Int64,x),unbox(Int64,y))
-<=(x::Int128, y::Int128) = sle_int(unbox(Int128,x),unbox(Int128,y))
-
-<=(x::Uint8,   y::Uint8)   = ule_int(unbox(Uint8,x),unbox(Uint8,y))
-<=(x::Uint16,  y::Uint16)  = ule_int(unbox(Uint16,x),unbox(Uint16,y))
-<=(x::Uint32,  y::Uint32)  = ule_int(unbox(Uint32,x),unbox(Uint32,y))
-<=(x::Uint64,  y::Uint64)  = ule_int(unbox(Uint64,x),unbox(Uint64,y))
-<=(x::Uint128, y::Uint128) = ule_int(unbox(Uint128,x),unbox(Uint128,y))
+for T in IntTypes
+    if issubtype(T,Signed)
+        @eval <( x::$T, y::$T) = slt_int(unbox($T,x),unbox($T,y))
+        @eval <=(x::$T, y::$T) = sle_int(unbox($T,x),unbox($T,y))
+    else
+        @eval <( x::$T, y::$T) = ult_int(unbox($T,x),unbox($T,y))
+        @eval <=(x::$T, y::$T) = ule_int(unbox($T,x),unbox($T,y))
+    end
+end
 
 ==(x::Signed,   y::Unsigned) = (x >= 0) & (unsigned(x) == y)
 ==(x::Unsigned, y::Signed  ) = (y >= 0) & (x == unsigned(y))
@@ -162,11 +141,8 @@ trailing_ones(x::Integer) = trailing_zeros(~x)
 
 ## integer conversions ##
 
-const _inttypes = (Bool, Int8, Uint8, Int16, Uint16, Int32, Uint32, Char,
-                   Int64, Uint64, Int128, Uint128)
-
-for to in _inttypes, from in _inttypes
-    if !(to === from) && !(to === Bool)
+for to in tuple(IntTypes...,Char), from in tuple(IntTypes...,Char,Bool)
+    if !(to === from)
         if to.size < from.size
             if issubtype(to, Signed)
                 @eval convert(::Type{$to}, x::($from)) = box($to,checked_trunc_sint($to,unbox($from,x)))
@@ -218,21 +194,18 @@ function convert(::Type{Uint128}, x::FloatingPoint)
 end
 convert(::Type{Uint128}, x::Float32) = convert(Uint128, float64(x))
 
-convert(::Type{Char}, x::Float32) = char(convert(Int, x))
-convert(::Type{Char}, x::Float64) = char(convert(Int, x))
-
-convert(::Type{Signed}, x::Uint8  ) = convert(Int,x)
-convert(::Type{Signed}, x::Uint16 ) = convert(Int,x)
-convert(::Type{Signed}, x::Uint32 ) = convert(Int,x)
+convert(::Type{Signed}, x::Uint8  ) = convert(Int8,x)
+convert(::Type{Signed}, x::Uint16 ) = convert(Int16,x)
+convert(::Type{Signed}, x::Uint32 ) = convert(Int32,x)
 convert(::Type{Signed}, x::Uint64 ) = convert(Int64,x)
 convert(::Type{Signed}, x::Uint128) = convert(Int128,x)
 convert(::Type{Signed}, x::Float32) = convert(Int,x)
 convert(::Type{Signed}, x::Float64) = convert(Int,x)
 convert(::Type{Signed}, x::Char)    = convert(Int,x)
 
-convert(::Type{Unsigned}, x::Int8   ) = convert(Uint,x)
-convert(::Type{Unsigned}, x::Int16  ) = convert(Uint,x)
-convert(::Type{Unsigned}, x::Int32  ) = convert(Uint,x)
+convert(::Type{Unsigned}, x::Int8   ) = convert(Uint8,x)
+convert(::Type{Unsigned}, x::Int16  ) = convert(Uint16,x)
+convert(::Type{Unsigned}, x::Int32  ) = convert(Uint32,x)
 convert(::Type{Unsigned}, x::Int64  ) = convert(Uint64,x)
 convert(::Type{Unsigned}, x::Int128 ) = convert(Uint128,x)
 convert(::Type{Unsigned}, x::Float32) = convert(Uint,x)
@@ -372,12 +345,12 @@ typemax(::Type{Uint64}) = 0xffffffffffffffff
     typemax(::Type{Int128} ) = $(int128((uint128(-1))>>int32(1)))
 end
 
-widen(::Type{Int8}) = Int
-widen(::Type{Int16}) = Int
+widen(::Type{Int8}) = Int16
+widen(::Type{Int16}) = Int32
 widen(::Type{Int32}) = Int64
 widen(::Type{Int64}) = Int128
-widen(::Type{Uint8}) = Uint
-widen(::Type{Uint16}) = Uint
+widen(::Type{Uint8}) = Uint16
+widen(::Type{Uint16}) = Uint32
 widen(::Type{Uint32}) = Uint64
 widen(::Type{Uint64}) = Uint128
 
@@ -506,10 +479,9 @@ end
 
 for T in (Int8,Uint8)
     @eval function checked_mul(x::$T, y::$T)
-        xy = x*y
-        xy8 = convert($T,xy)
-        xy == xy8 || throw(OverflowError())
-        return xy8
+        xy = widemul(x,y)
+        (typemin($T) <= xy <= typemax($T)) || throw(OverflowError())
+        return itrunc($T,xy)
     end
 end
 
@@ -517,9 +489,8 @@ if WORD_SIZE == 32
 for T in (Int64,Uint64)
     @eval function checked_mul(x::$T, y::$T)
         xy = int128(x)*int128(y)
-        xy64 = convert($T,xy)
-        xy == xy64 || throw(OverflowError())
-        return xy64
+        (typemin($T) <= xy <= typemax($T)) || throw(OverflowError())
+        return itrunc($T,xy)
     end
 end
 else
diff --git a/base/random.jl b/base/random.jl
index 789015dfe4e23..68f69fb834037 100644
--- a/base/random.jl
+++ b/base/random.jl
@@ -104,17 +104,17 @@ rand(r::MersenneTwister) = dsfmt_genrand_close_open(r.state)
 dsfmt_randui32() = dsfmt_gv_genrand_uint32()
 dsfmt_randui64() = uint64(dsfmt_randui32()) | (uint64(dsfmt_randui32())<<32)
 
-rand(::Type{Uint8})   = uint8(rand(Uint32))
-rand(::Type{Uint16})  = uint16(rand(Uint32))
+rand(::Type{Uint8})   = itrunc(Uint8,rand(Uint32))
+rand(::Type{Uint16})  = itrunc(Uint16,rand(Uint32))
 rand(::Type{Uint32})  = dsfmt_randui32()
 rand(::Type{Uint64})  = dsfmt_randui64()
 rand(::Type{Uint128}) = uint128(rand(Uint64))<<64 | rand(Uint64)
 
-rand(::Type{Int8})    = int8(rand(Uint8))
-rand(::Type{Int16})   = int16(rand(Uint16))
-rand(::Type{Int32})   = int32(rand(Uint32))
-rand(::Type{Int64})   = int64(rand(Uint64))
-rand(::Type{Int128})  = int128(rand(Uint128))
+rand(::Type{Int8})    = itrunc(Int8,rand(Uint32))
+rand(::Type{Int16})   = itrunc(Int16,rand(Uint32))
+rand(::Type{Int32})   = reinterpret(Int32,rand(Uint32))
+rand(::Type{Int64})   = reinterpret(Int64,rand(Uint64))
+rand(::Type{Int128})  = reinterpret(Int128,rand(Uint128))
 
 # Arrays of random numbers
 
diff --git a/base/reducedim.jl b/base/reducedim.jl
index 23b0950298174..23d65ab898c47 100644
--- a/base/reducedim.jl
+++ b/base/reducedim.jl
@@ -101,6 +101,14 @@ reducedim_init(f, op::OrFun, A::AbstractArray, region) = reducedim_initarray(A,
 
 # specialize to make initialization more efficient for common cases
 
+if Int === Int32
+typealias SmallSigned Union(Int8,Int16)
+typealias SmallUnsigned Union(Uint8,Uint16)
+else
+typealias SmallSigned Union(Int8,Int16,Int32)
+typealias SmallUnsigned Union(Uint8,Uint16,Uint32)
+end
+
 typealias CommonReduceResult Union(Uint64,Uint128,Int64,Int128,Float32,Float64)
 
 for (IT, RT) in ((CommonReduceResult, :(eltype(A))), (SmallSigned, :Int), (SmallUnsigned, :Uint))
diff --git a/doc/stdlib/base.rst b/doc/stdlib/base.rst
index bfc2ca46c3e65..d4f615077c5c1 100644
--- a/doc/stdlib/base.rst
+++ b/doc/stdlib/base.rst
@@ -3090,9 +3090,9 @@ Mathematical Functions
 
    Returns the nearest integral value of the same type as ``x`` not greater in magnitude than ``x``. ``digits`` and ``base`` work as above.
 
-.. function:: iround(x) -> Integer
+.. function:: iround([T,]x) -> Integer
 
-   Returns the nearest integer to ``x``.
+   Returns the nearest integer to ``x``, converted to an integer type, optionally passed as the first argument.
 
 .. function:: iceil(x) -> Integer
 
@@ -3102,9 +3102,9 @@ Mathematical Functions
 
    Returns the nearest integer not greater than ``x``.
 
-.. function:: itrunc(x) -> Integer
+.. function:: itrunc([T,]x) -> Integer
 
-   Returns the nearest integer not greater in magnitude than ``x``.
+   Returns the nearest integer not greater in magnitude than ``x``, converted to an integer type, optionally passed as the first argument.
 
 .. function:: signif(x, digits, [base])
 
diff --git a/test/numbers.jl b/test/numbers.jl
index 6e8b9408f27fc..0c6473cd3a747 100644
--- a/test/numbers.jl
+++ b/test/numbers.jl
@@ -1459,7 +1459,7 @@ end
 @test -0b000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 ==
     -(0b000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001)
 
-@test isa(-0x00,Uint)
+@test isa(-0x00,Uint8)
 @test isa(-0x0000000000000000,Uint64)
 @test isa(-0x00000000000000000,Uint128)
 @test isa(-0x00000000000000000000000000000000,Uint128)
@@ -1901,9 +1901,9 @@ end
 
 for T = (Uint8,Int8,Uint16,Int16,Uint32,Int32,Uint64,Int64,Uint128,Int128)
     for n = 1:2:1000
-        @test convert(T,n*(n^typemax(T))) == one(T)
+        @test n*(n^typemax(T)) & typemax(T) == 1
         n = rand(T) | one(T)
-        @test convert(T,n*(n^typemax(T))) == one(T)
+        @test n*(n^typemax(T)) == 1
     end
 end
 
@@ -1931,7 +1931,7 @@ end
 # widen
 @test widen(1.5f0) === 1.5
 @test widen(int32(42)) === int64(42)
-@test widen(Int8) === Int
+@test widen(Int8) === Int16
 @test widen(Float32) === Float64
 ## Note: this should change to e.g. Float128 at some point
 @test widen(Float64) === BigFloat