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Add rounding functions for Fixed
The functions support `Fixed{Int8,8}` and so on, for now.
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‎src/fixed.jl

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Original file line numberDiff line numberDiff line change
@@ -50,6 +50,9 @@ function rawone(::Type{Fixed{T,f}}) where {T, f}
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oneunit(T) << f
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end
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intmask(::Fixed{T,f}) where {T, f} = -oneunit(T) << f # Signed
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fracmask(x::Fixed{T,f}) where {T, f} = ~intmask(x) # Signed
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# unchecked arithmetic
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# with truncation:
@@ -91,6 +94,73 @@ end
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(::Type{TR})(x::Fixed{T,f}) where {TR <: Rational,T,f} =
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TR(x.i>>f + (x.i&(1<<f-1))//(one(widen1(T))<<f))
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function trunc(x::Fixed{T,f}) where {T, f}
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f == 0 && return x
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f == bitwidth(T) && return zero(x) # TODO: remove this line
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f == bitwidth(T) - 1 && return x.i == typemin(T) ? x : zero(x)
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t = x.i & intmask(x)
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r = x.i & fracmask(x)
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_rawone = oneunit(T) << f
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reinterpret(Fixed{T,f}, (x.i < 0) & (r != 0) ? t + _rawone : t)
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end
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function floor(x::Fixed{T,f}) where {T, f}
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f == bitwidth(T) && x.i < 0 && throw_converterror(Fixed{T,f}, -1) # TODO: remove this line
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Fixed{T,f}(x.i & intmask(x), 0)
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end
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function ceil(x::Fixed{T,f}) where {T, f}
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f == 0 && return x
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upper = typemax(T) & intmask(x)
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x.i > upper && throw_converterror(Fixed{T,f}, ceil(float(x)))
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reinterpret(Fixed{T,f}, (x.i + fracmask(x)) & intmask(x))
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end
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function round(x::Fixed{T,f}) where {T, f}
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f == 0 && return x
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f == bitwidth(T) && return zero(x) # TODO: remove this line
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upper = intmask(x) >>> 0x1
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lower = intmask(x) >> 0x1
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if f == bitwidth(T) - 1
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x.i > upper && throw_converterror(Fixed{T,f}, @exp2(bitwidth(T)-f-1))
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return x.i < lower ? typemin(x) : zero(x)
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end
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x.i >= upper && throw_converterror(Fixed{T,f}, @exp2(bitwidth(T)-f-1))
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y = oneunit(T) << UInt8(f - 1) + x.i
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m = oneunit(T) << UInt8(f + 1) - oneunit(T)
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z = y & intmask(x)
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reinterpret(Fixed{T,f}, z - T(y & m == rawone(x)) << f)
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end
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function trunc(::Type{Ti}, x::Fixed{T,f}) where {Ti <: Integer, T, f}
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f == 0 && return convert(Ti, x.i)
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f == bitwidth(T) && return zero(Ti) # TODO: remove this line
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f == bitwidth(T) - 1 && return x.i == typemin(T) ? convert(Ti, -1) : zero(Ti)
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t = x.i >> f
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r = x.i & fracmask(x)
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convert(Ti, (x.i < 0) & (r != 0) ? t + oneunit(T) : t)
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end
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function floor(::Type{Ti}, x::Fixed{T,f}) where {Ti <: Integer, T, f}
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f == bitwidth(T) && return x.i < 0 ? convert(Ti, -1) : zero(Ti) # TODO: remove this line
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convert(Ti, x.i >> f)
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end
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function ceil(::Type{Ti}, x::Fixed{T,f}) where {Ti <: Integer, T, f}
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f == bitwidth(T) && return x.i > 0 ? oneunit(Ti) : zero(Ti) # TODO: remove this line
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y = x.i + fracmask(x)
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convert(Ti, x.i >= 0 ? y >>> f : y >> f)
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end
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function round(::Type{Ti}, x::Fixed{T,f}) where {Ti <: Integer, T, f}
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f == 0 && return convert(Ti, x.i)
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f == bitwidth(T) && return zero(Ti) # TODO: remove this line
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upper = intmask(x) >>> 0x1
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lower = intmask(x) >> 0x1
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if f == bitwidth(T) - 1
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x.i < lower && return convert(Ti, -1)
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return x.i > upper ? oneunit(Ti) : zero(Ti)
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end
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y = oneunit(T) << UInt8(f - 1) + x.i
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m = oneunit(T) << UInt8(f + 1) - oneunit(T)
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z = x.i >= 0 ? y >>> f : y >> f
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convert(Ti, z - Ti(y & m == rawone(x)))
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end
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promote_rule(ft::Type{Fixed{T,f}}, ::Type{TI}) where {T,f,TI <: Integer} = Fixed{T,f}
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promote_rule(::Type{Fixed{T,f}}, ::Type{TF}) where {T,f,TF <: AbstractFloat} = TF
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promote_rule(::Type{Fixed{T,f}}, ::Type{Rational{TR}}) where {T,f,TR} = Rational{TR}

‎test/fixed.jl

Lines changed: 52 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -70,6 +70,18 @@ end
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@test reinterpret(Int8, 0.5Q0f7) === signed(0x40)
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end
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@testset "masks" begin
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@test FixedPointNumbers.intmask(0Q7f0) === signed(0xFF)
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@test FixedPointNumbers.intmask(0Q6f1) === signed(0xFE)
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@test FixedPointNumbers.intmask(0Q1f6) === signed(0xC0)
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@test FixedPointNumbers.intmask(0Q0f7) === signed(0x80)
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@test FixedPointNumbers.fracmask(0Q7f0) === signed(0x00)
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@test FixedPointNumbers.fracmask(0Q6f1) === signed(0x01)
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@test FixedPointNumbers.fracmask(0Q1f6) === signed(0x3F)
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@test FixedPointNumbers.fracmask(0Q0f7) === signed(0x7F)
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end
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@testset "inexactness" begin
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@test_throws InexactError Q0f7(-2)
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# TODO: change back to InexactError when it allows message strings
@@ -96,6 +108,46 @@ end
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end
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end
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@testset "rounding" begin
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for T in (Int8, Int16, Int32, Int64)
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rs = vcat([ oneunit(T) << b - oneunit(T) for b = 0:bitwidth(T)-1],
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[ oneunit(T) << b for b = 1:bitwidth(T)-2],
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[ oneunit(T) << b + oneunit(T) for b = 2:bitwidth(T)-2],
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[-oneunit(T) << b - oneunit(T) for b = 2:bitwidth(T)-2],
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[-oneunit(T) << b for b = 1:bitwidth(T)-1],
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[-oneunit(T) << b + oneunit(T) for b = 1:bitwidth(T)-1])
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@testset "rounding Fixed{$T,$f}" for f = 0:bitwidth(T)-1
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F = Fixed{T,f}
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xs = (reinterpret(F, r) for r in rs)
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@test all(x -> trunc(x) == trunc(float(x)), xs)
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@test all(x -> floor(float(x)) < typemin(F) || floor(x) == floor(float(x)), xs)
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@test all(x -> ceil(float(x)) > typemax(F) || ceil(x) == ceil(float(x)), xs)
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@test all(x -> round(float(x)) > typemax(F) || round(x) == round(float(x)), xs)
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@test all(x -> trunc(Int64, x) === trunc(Int64, float(x)), xs)
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@test all(x -> floor(Int64, x) === floor(Int64, float(x)), xs)
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@test all(x -> ceil(Int64, x) === ceil(Int64, float(x)), xs)
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@test all(x -> round(Int64, x) === round(Int64, float(x)), xs)
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end
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end
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@testset "rounding Fixed{Int16,$f} with overflow" for f = 1:16 # TODO: drop 16
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F = Fixed{Int16,f}
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@test_throws ArgumentError ceil(typemax(F))
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if f == 16
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@test_throws ArgumentError ceil(eps(F))
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elseif f == 15
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@test_throws ArgumentError ceil(eps(F))
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@test_throws ArgumentError round(typemax(F))
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@test_throws ArgumentError round(F(0.5) + eps(F))
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else
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@test_throws ArgumentError ceil(typemin(F) - oneunit(F) + eps(F))
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@test_throws ArgumentError round(typemax(F))
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@test_throws ArgumentError round(typemax(F) - F(0.5) + eps(F))
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end
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end
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@test_throws InexactError trunc(UInt, typemin(Q0f7))
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@test_throws InexactError floor(UInt, -eps(Q0f7))
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end
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@testset "modulus" begin
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T = Fixed{Int8,7}
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for i = -1.0:0.1:typemax(T)

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