Improve accuracy of rem with Normed types (e.g. ::Float32 % N0f32)

Author: kimikage

src/normed.jl

@@ -105,6 +105,16 @@ rem(x::T, ::Type{T}) where {T <: Normed} = x
 rem(x::Normed, ::Type{T}) where {T <: Normed} = reinterpret(T, _unsafe_trunc(rawtype(T), round((rawone(T)/rawone(x))*reinterpret(x))))
 rem(x::Real, ::Type{T}) where {T <: Normed} = reinterpret(T, _unsafe_trunc(rawtype(T), round(rawone(T)*x)))
 rem(x::Float16, ::Type{T}) where {T <: Normed} = rem(Float32(x), T)  # avoid overflow
+function rem(x::Float32, ::Type{T}) where {f, T <: Normed{UInt32,f}}
+    f <= 24 && return reinterpret(T, _unsafe_trunc(UInt32, round(rawone(T) * x)))
+    r = _unsafe_trunc(UInt32, round(x * @f32(0x1p24)))
+    reinterpret(T, r << UInt8(f - 24) - unsigned(signed(r) >> 0x18))
+end
+function rem(x::Float64, ::Type{T}) where {f, T <: Normed{UInt64,f}}
+    f <= 53 && return reinterpret(T, _unsafe_trunc(UInt64, round(rawone(T) * x)))
+    r = _unsafe_trunc(UInt64, round(x * 0x1p53))
+    reinterpret(T, r << UInt8(f - 53) - unsigned(signed(r) >> 0x35))
+end
 
 
 function (::Type{T})(x::Normed) where {T <: AbstractFloat}

test/normed.jl

@@ -200,6 +200,10 @@ end
 
     @test 1 % N0f8 == 1
     @test 2 % N0f8 == N0f8(0.996)
+
+    # issue #150
+    @test all(f -> 1.0f0 % Normed{UInt32,f} == oneunit(Normed{UInt32,f}), 1:32)
+    @test all(f -> 1.0e0 % Normed{UInt64,f} == oneunit(Normed{UInt64,f}), 1:64)
 end
 
 @testset "bitwise" begin