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Merged
merged 6 commits into from
Sep 24, 2016
Merged

Implement promotion among UFixed, make convert errors more informative #53

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0131751
Add a missing rem method
timholy Sep 22, 2016
88cd163
Support promotion among UFixed types
timholy Sep 22, 2016
49934cd
Fix typo in <=
timholy Sep 23, 2016
e958121
Make `convert` errors more informative
timholy Sep 23, 2016
77d1585
Fix test failure on 32-bit
timholy Sep 23, 2016
526a7b9
Fix issues with UInt128 and high-precision UFixed types
timholy Sep 24, 2016
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9 changes: 9 additions & 0 deletions src/FixedPointNumbers.jl
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Expand Up @@ -109,4 +109,13 @@ end
const _log2_10 = 3.321928094887362
showcompact{T,f}(io::IO, x::FixedPoint{T,f}) = show(io, round(convert(Float64,x), ceil(Int,f/_log2_10)))

@noinline function throw_converterror{T<:FixedPoint}(::Type{T}, x)
n = 2^(8*sizeof(T))
bitstring = sizeof(T) == 1 ? "an 8-bit" : "a $(8*sizeof(T))-bit"
io = IOBuffer()
showcompact(io, typemin(T)); Tmin = takebuf_string(io)
showcompact(io, typemax(T)); Tmax = takebuf_string(io)
throw(ArgumentError("$T is $bitstring type representing $n values from $Tmin to $Tmax; cannot represent $x"))
end

end # module
56 changes: 44 additions & 12 deletions src/ufixed.jl
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Expand Up @@ -9,7 +9,9 @@ immutable UFixed{T<:Unsigned,f} <: FixedPoint{T,f}
end

rawtype{T,f}(::Type{UFixed{T,f}}) = T
rawtype(x::Number) = rawtype(typeof(x))
nbitsfrac{T,f}(::Type{UFixed{T,f}}) = f
nbitsfrac(x::Number) = nbitsfract(typeof(x))

typealias UFixed8 UFixed{UInt8,8}
typealias UFixed10 UFixed{UInt16,10}
Expand All @@ -31,29 +33,40 @@ const uf14 = UFixedConstructor{UInt16,14}()
const uf16 = UFixedConstructor{UInt16,16}()

zero{T,f}(::Type{UFixed{T,f}}) = UFixed{T,f}(zero(T),0)
@generated function one{T<:UFixed}(::Type{T})
f = 2^nbitsfrac(T)-1
:( T($f,0) )
function one{T<:UFixed}(::Type{T})
T(typemax(rawtype(T)) >> (8*sizeof(T)-nbitsfrac(T)), 0)
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the generated version might be faster. see #44 (comment). or does the use of >> instead of ^ close the gap?

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LLVM inlines this new version to a constant:

julia> @code_llvm one(UFixed{UInt64, 51})

define %UFixed @julia_one_70810(%jl_value_t*) #0 {
top:
  ret %UFixed { i64 2251799813685247 }
}

The bigger issue was that for UInt128 (or even for UInt64 on 32-bit machines), 2^f was returning 0 for f bigger than the WORD_SIZE. This version is guaranteed to be safe no matter what kind of machine or what kind of precision we're using.

end
zero(x::UFixed) = zero(typeof(x))
one(x::UFixed) = one(typeof(x))
rawone(v) = reinterpret(one(v))

# Conversions
convert{T<:UFixed}(::Type{T}, x::T) = x
convert{T1<:UFixed}(::Type{T1}, x::UFixed) = reinterpret(T1, round(rawtype(T1), (rawone(T1)/rawone(x))*reinterpret(x)))
function convert{T<:UFixed}(::Type{T}, x::UFixed)
y = round((rawone(T)/rawone(x))*reinterpret(x))
(0 <= y) & (y <= typemax(rawtype(T))) || throw_converterror(T, x)
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why not just say (0 <= y <= typemax(rawtype(T))) || ... ?

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Performance. Currently a <= x <= b gets lowered to (a <= x) && (x <= b) rather than (a <= x) & (x <= b), which means there are two branches rather than one.

This is something that should probably be changed in Julia, but neither I nor anyone else has gotten to it yet.

reinterpret(T, _unsafe_trunc(rawtype(T), y))
end
convert(::Type{UFixed16}, x::UFixed8) = reinterpret(UFixed16, convert(UInt16, 0x0101*reinterpret(x)))
convert{U<:UFixed}(::Type{U}, x::Real) = _convert(U, rawtype(U), x)
_convert{U<:UFixed,T}(::Type{U}, ::Type{T}, x) = U(round(T, widen1(rawone(U))*x), 0)
_convert{U<:UFixed }(::Type{U}, ::Type{UInt128}, x) = U(round(UInt128, rawone(U)*x), 0)
function _convert{U<:UFixed,T}(::Type{U}, ::Type{T}, x)
y = round(widen1(rawone(U))*x)
(0 <= y) & (y <= typemax(T)) || throw_converterror(U, x)
U(_unsafe_trunc(T, y), 0)
end
function _convert{U<:UFixed}(::Type{U}, ::Type{UInt128}, x)
y = round(rawone(U)*x) # for UInt128, we can't widen
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@vchuravy vchuravy Sep 23, 2016 •
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If we definedwiden1(::Type{UInt128}) = UInt128 we wouldn't need to duplicate the code path and we would be forward compatible for the glorious day when we have UInt256.

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I thought about that. The flip side is that if one is counting on widen1 to actually protect you, then you'll be mistaken.

But perhaps that's at too low of a level to matter, and that the only issue that matters is whether convert successfully catches the problem. Which refusing to defining widen1 doesn't actually help with. I will change it.

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OK, we had a number of problems with high-precision UFixed types.

(0 <= y) & (y <= typemax(UInt128)) & (x <= Float64(typemax(U))) || throw_converterror(U, x)
U(_unsafe_trunc(UInt128, y), 0)
end

rem{T<:UFixed}(x::T, ::Type{T}) = x
rem{T<:UFixed}(x::UFixed, ::Type{T}) = reinterpret(T, unsafe_trunc(rawtype(T), round((rawone(T)/rawone(x))*reinterpret(x))))
rem{T<:UFixed}(x::Real, ::Type{T}) = reinterpret(T, unsafe_trunc(rawtype(T), round(rawone(T)*x)))
rem{T<:UFixed}(x::UFixed, ::Type{T}) = reinterpret(T, _unsafe_trunc(rawtype(T), round((rawone(T)/rawone(x))*reinterpret(x))))
rem{T<:UFixed}(x::Real, ::Type{T}) = reinterpret(T, _unsafe_trunc(rawtype(T), round(rawone(T)*x)))

convert(::Type{BigFloat}, x::UFixed) = reinterpret(x)*(1/BigFloat(rawone(x)))
function convert{T<:AbstractFloat}(::Type{T}, x::UFixed)
y = reinterpret(x)*(1/convert(T, rawone(x)))
y = reinterpret(x)*(one(rawtype(x))/convert(T, rawone(x)))
convert(T, y) # needed for types like Float16 which promote arithmetic to Float32
end
convert(::Type{Bool}, x::UFixed) = x == zero(x) ? false : true
Expand All @@ -68,17 +81,21 @@ sizeof{T<:UFixed}(::Type{T}) = sizeof(rawtype(T))
abs(x::UFixed) = x

# Arithmetic
@generated function floattype{U<:UFixed}(::Type{U})
eps(U) < eps(Float32) ? :(Float64) : :(Float32)
end

(-){T<:UFixed}(x::T) = T(-reinterpret(x), 0)
(~){T<:UFixed}(x::T) = T(~reinterpret(x), 0)

+{T,f}(x::UFixed{T,f}, y::UFixed{T,f}) = UFixed{T,f}(convert(T, x.i+y.i),0)
-{T,f}(x::UFixed{T,f}, y::UFixed{T,f}) = UFixed{T,f}(convert(T, x.i-y.i),0)
*{T<:UFixed}(x::T, y::T) = convert(T,convert(Float32, x)*convert(Float32, y))
/{T<:UFixed}(x::T, y::T) = convert(T,convert(Float32, x)/convert(Float32, y))
*{T<:UFixed}(x::T, y::T) = convert(T,convert(floattype(T), x)*convert(floattype(T), y))
/{T<:UFixed}(x::T, y::T) = convert(T,convert(floattype(T), x)/convert(floattype(T), y))

# Comparisons
<{T<:UFixed}(x::T, y::T) = reinterpret(x) < reinterpret(y)
<={T<:UFixed}(x::T, y::T) = reinterpret(x) < reinterpret(y)
<={T<:UFixed}(x::T, y::T) = reinterpret(x) <= reinterpret(y)

# Functions
trunc{T<:UFixed}(x::T) = T(div(reinterpret(x), rawone(T))*rawone(T),0)
Expand Down Expand Up @@ -150,3 +167,18 @@ promote_rule{T<:UFixed, R<:Rational}(::Type{T}, ::Type{R}) = R
Tp = eps(convert(Float32, typemax(Ti))) > eps(T) ? Float64 : Float32
:( $Tp )
end
@generated function promote_rule{T1,T2,f1,f2}(::Type{UFixed{T1,f1}}, ::Type{UFixed{T2,f2}})
f = max(f1, f2) # ensure we have enough precision
T = promote_type(T1, T2)
# make sure we have enough integer bits
i1, i2 = 8*sizeof(T1)-f1, 8*sizeof(T2)-f2 # number of integer bits for each
i = 8*sizeof(T)-f
while i < max(i1, i2)
T = widen1(T)
i = 8*sizeof(T)-f
end
:(UFixed{$T,$f})
end

_unsafe_trunc{T}(::Type{T}, x::Integer) = x % T
_unsafe_trunc{T}(::Type{T}, x) = unsafe_trunc(T, x)
44 changes: 31 additions & 13 deletions test/ufixed.jl
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Expand Up @@ -21,7 +21,7 @@ v = @compat UFixed12.([2])
@test v == UFixed12[0x1ffeuf12]
@test isa(v, Vector{UFixed12})

UF2 = (UFixed{UInt32,16}, UFixed{UInt64,3}, UFixed{UInt128,7})
UF2 = (UFixed{UInt32,16}, UFixed{UInt64,3}, UFixed{UInt64,51}, UFixed{UInt128,7}, UFixed{UInt128,51})

for T in (FixedPointNumbers.UF..., UF2...)
@test zero(T) == 0
Expand All @@ -43,15 +43,19 @@ end
@test typemax(UFixed{UInt32,16}) == typemax(UInt32) // (2^16-1)
@test typemax(UFixed{UInt64,3}) == typemax(UInt64) // (2^3-1)
@test typemax(UFixed{UInt128,7}) == typemax(UInt128) // (2^7-1)

@test_throws InexactError UFixed8(2)
@test_throws InexactError UFixed8(255)
@test_throws InexactError UFixed8(0xff)
@test_throws InexactError UFixed16(2)
@test_throws InexactError UFixed16(0xff)
@test_throws InexactError UFixed16(0xffff)
@test_throws InexactError convert(UFixed8, typemax(UFixed10))
@test_throws InexactError convert(UFixed16, typemax(UFixed10))
@test typemax(UFixed{UInt128,100}) == typemax(UInt128) // (UInt128(2)^100-1)

# TODO: change back to InexactError when it allows message strings
@test_throws ArgumentError UFixed8(2)
@test_throws ArgumentError UFixed8(255)
@test_throws ArgumentError UFixed8(0xff)
@test_throws ArgumentError UFixed16(2)
@test_throws ArgumentError UFixed16(0xff)
@test_throws ArgumentError UFixed16(0xffff)
@test_throws ArgumentError convert(UFixed8, typemax(UFixed10))
@test_throws ArgumentError convert(UFixed16, typemax(UFixed10))
@test_throws ArgumentError convert(UFixed{UInt128,100}, 10^9)
@test_throws ArgumentError convert(UFixed{UInt128,100}, 10.0^9)

x = UFixed8(0.5)
@test isfinite(x) == true
Expand All @@ -64,7 +68,7 @@ x = UFixed8(0.5)
@test convert(UFixed14, 1.1/typemax(UInt16)*4) == eps(UFixed14)
@test convert(UFixed16, 1.1/typemax(UInt16)) == eps(UFixed16)
@test convert(UFixed{UInt32,16}, 1.1/typemax(UInt32)*2^16) == eps(UFixed{UInt32,16})
@test convert(UFixed{UInt64,3}, 1.1/typemax(UInt64)*2^61) == eps(UFixed{UInt64,3})
@test convert(UFixed{UInt64,3}, 1.1/typemax(UInt64)*UInt64(2)^61) == eps(UFixed{UInt64,3})
@test convert(UFixed{UInt128,7}, 1.1/typemax(UInt128)*UInt128(2)^121) == eps(UFixed{UInt128,7})

@test convert(UFixed8, 1.1f0/typemax(UInt8)) == eps(UFixed8)
Expand Down Expand Up @@ -93,15 +97,18 @@ end
@test (65.2 % UFixed10).i == round(Int, 65.2*1023) % UInt16
@test (-0.3 % UFixed10).i == round(Int, -0.3*1023) % UInt16

@test 1 % UFixed8 == 1
@test 2 % UFixed8 == UFixed8(0.996)

x = UFixed8(0b01010001, 0)
@test ~x == UFixed8(0b10101110, 0)
@test -x == 0xafuf8

for T in (FixedPointNumbers.UF..., UF2...)
x = T(0x10,0)
y = T(0x25,0)
fx = convert(Float32, x)
fy = convert(Float32, y)
fx = convert(FixedPointNumbers.floattype(T), x)
fy = convert(FixedPointNumbers.floattype(T), y)
@test y > x
@test y != x
@test typeof(x+y) == T
Expand Down Expand Up @@ -154,6 +161,9 @@ for T in (FixedPointNumbers.UF..., UF2...)
testtrunc(eps(T))
end

@test !(UFixed8(0.5) < UFixed8(0.5))
@test UFixed8(0.5) <= UFixed8(0.5)

@test div(0x10uf8, 0x02uf8) == fld(0x10uf8, 0x02uf8) == 8
@test div(0x0fuf8, 0x02uf8) == fld(0x0fuf8, 0x02uf8) == 7
@test Base.fld1(0x10uf8, 0x02uf8) == 8
Expand All @@ -166,6 +176,14 @@ end
r = 1uf8:1uf8:48uf8
@test length(r) == 48

# Promotion within UFixed
@test @inferred(promote(UFixed8(0.2), UFixed8(0.8))) ===
(UFixed8(0.2), UFixed8(0.8))
@test @inferred(promote(UFixed{UInt16,3}(0.2), UFixed{UInt8,3}(0.86))) ===
(UFixed{UInt16,3}(0.2), UFixed{UInt16,3}(0.86))
@test @inferred(promote(UFixed{UInt8,7}(0.197), UFixed{UInt8,4}(0.8))) ===
(UFixed{UInt16,7}(0.197), UFixed{UInt16,7}(0.8))

# Show
x = 0xaauf8
iob = IOBuffer()
Expand Down