Skip to content

Improve accuracy of rem with Normed types (e.g. ::Float32 % N0f32) #166

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
merged 1 commit into from
Jan 15, 2020
Merged

Improve accuracy of rem with Normed types (e.g. ::Float32 % N0f32) #166

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
22 changes: 18 additions & 4 deletions src/normed.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -101,10 +101,24 @@ function _convert(::Type{N}, x::Tf) where {T, f, N <: Normed{T,f}, Tf <: Union{F
return reinterpret(N, unsafe_trunc(T, yi >> (ex & bits)))
end

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
rem(x::N, ::Type{N}) where {N <: Normed} = x
rem(x::Normed, ::Type{N}) where {T, N <: Normed{T}} = reinterpret(N, _unsafe_trunc(T, round((rawone(N)/rawone(x))*reinterpret(x))))
rem(x::Real, ::Type{N}) where {T, N <: Normed{T}} = reinterpret(N, _unsafe_trunc(T, round(rawone(N)*x)))
rem(x::Float16, ::Type{N}) where {N <: Normed} = rem(Float32(x), N) # avoid overflow
# Float32 and Float64 cannot exactly represent `rawone(N)` with `f` greater than
# the number of their significand bits, resulting in rounding errors (issue #150).
# So, we use another strategy for the large `f`s explained in:
# https://github.com/JuliaMath/FixedPointNumbers.jl/pull/166#issuecomment-574135643
function rem(x::Float32, ::Type{N}) where {f, N <: Normed{UInt32,f}}
f <= 24 && return reinterpret(N, _unsafe_trunc(UInt32, round(rawone(N) * x)))
r = _unsafe_trunc(UInt32, round(x * @f32(0x1p24)))
reinterpret(N, r << UInt8(f - 24) - unsigned(signed(r) >> 0x18))
end
function rem(x::Float64, ::Type{N}) where {f, N <: Normed{UInt64,f}}
f <= 53 && return reinterpret(N, _unsafe_trunc(UInt64, round(rawone(N) * x)))
r = _unsafe_trunc(UInt64, round(x * 0x1p53))
reinterpret(N, r << UInt8(f - 53) - unsigned(signed(r) >> 0x35))
end


function (::Type{T})(x::Normed) where {T <: AbstractFloat}
Expand Down
4 changes: 4 additions & 0 deletions test/normed.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -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
Expand Down