Move arithmetic functions into submodule FixedPointArithmetic

Author: kimikage

src/FixedPointNumbers.jl

@@ -11,9 +11,6 @@ import Base: ==, <, <=, -, +, *, /, ~, isapprox,
 
 import Random: Random, AbstractRNG, SamplerType, rand!
 
-import Base.Checked: checked_neg, checked_abs, checked_add, checked_sub, checked_mul,
-                     checked_div, checked_fld, checked_cld, checked_rem, checked_mod
-
 using Base: @pure
 
 """
@@ -35,14 +32,11 @@ export
 # "special" typealiases
     # Q and N typealiases are exported in separate source files
 # Functions
-    scaledual,
-    wrapping_neg, wrapping_abs, wrapping_add, wrapping_sub, wrapping_mul,
-    wrapping_div, wrapping_fld, wrapping_cld, wrapping_rem, wrapping_mod,
-    saturating_neg, saturating_abs, saturating_add, saturating_sub, saturating_mul,
-    saturating_div, saturating_fld, saturating_cld, saturating_rem, saturating_mod,
-    wrapping_fdiv, saturating_fdiv, checked_fdiv
+    scaledual
 
 include("utilities.jl")
+using .Utilities
+import .Utilities: floattype, rawone, nbitsfrac, rawtype, signbits, nbitsint, scaledual
 
 # reinterpretation
 reinterpret(x::FixedPoint) = x.i
@@ -57,18 +51,6 @@ rawtype(::Type{X}) where {T, X <: FixedPoint{T}} = T
 signbits(::Type{X}) where {T, X <: FixedPoint{T}} = T <: Unsigned ? 0 : 1
 nbitsint(::Type{X}) where {X <: FixedPoint} = bitwidth(X) - nbitsfrac(X) - signbits(X)
 
-# construction using the (approximate) intended value, i.e., N0f8
-*(x::Real, ::Type{X}) where {X <: FixedPoint} = _convert(X, x)
-wrapping_mul(x::Real, ::Type{X}) where {X <: FixedPoint} = x % X
-saturating_mul(x::Real, ::Type{X}) where {X <: FixedPoint} = clamp(x, X)
-checked_mul(x::Real, ::Type{X}) where {X <: FixedPoint} = _convert(X, x)
-
-# type modulus
-rem(x::Real, ::Type{X}) where {X <: FixedPoint} = _rem(x, X)
-wrapping_rem(x::Real, ::Type{X}) where {X <: FixedPoint} = _rem(x, X)
-saturating_rem(x::Real, ::Type{X}) where {X <: FixedPoint} = _rem(x, X)
-checked_rem(x::Real, ::Type{X}) where {X <: FixedPoint} = _rem(x, X)
-
 # constructor-style conversions
 (::Type{X})(x::X) where {X <: FixedPoint}      = x
 (::Type{X})(x::Number) where {X <: FixedPoint} = _convert(X, x)
@@ -139,9 +121,6 @@ zero(::Type{X}) where {X <: FixedPoint} = X(zero(rawtype(X)), 0)
 oneunit(::Type{X}) where {X <: FixedPoint} = X(rawone(X), 0)
 one(::Type{X}) where {X <: FixedPoint} = oneunit(X)
 
-# for Julia v1.0, which does not fold `div_float` before inlining
-inv_rawone(x) = (@generated) ? (y = 1.0 / rawone(x); :($y)) : 1.0 / rawone(x)
-
 # traits
 eps(::Type{X}) where {X <: FixedPoint} = X(oneunit(rawtype(X)), 0)
 typemax(::Type{T}) where {T <: FixedPoint} = T(typemax(rawtype(T)), 0)
@@ -192,164 +171,12 @@ RGB{Float32}
 
 `RGB` itself is not a subtype of `AbstractFloat`, but unlike `RGB{N0f8}` operations with `RGB{Float32}` are not subject to integer overflow.
 """
-floattype(::Type{T}) where {T <: AbstractFloat} = T # fallback (we want a MethodError if no method producing AbstractFloat is defined)
-floattype(::Type{T}) where {T <: Union{ShortInts, Bool}} = Float32
-floattype(::Type{T}) where {T <: Integer} = Float64
-floattype(::Type{T}) where {T <: LongInts} = BigFloat
-floattype(::Type{T}) where {I <: Integer, T <: Rational{I}} = typeof(zero(I)/oneunit(I))
-floattype(::Type{<:AbstractIrrational}) = Float64
 floattype(::Type{X}) where {T <: ShortInts, X <: FixedPoint{T}} = Float32
 floattype(::Type{X}) where {T <: Integer, X <: FixedPoint{T}} = Float64
 floattype(::Type{X}) where {T <: LongInts, X <: FixedPoint{T}} = BigFloat
 
-# Non-Real types
-floattype(::Type{Complex{T}}) where T = Complex{floattype(T)}
-floattype(::Type{Base.TwicePrecision{Float64}}) = Float64    # wider would be nice, but hardware support is paramount
-floattype(::Type{Base.TwicePrecision{T}}) where T<:Union{Float16,Float32} = widen(T)
-
 float(x::FixedPoint) = convert(floattype(x), x)
 
-# wrapping arithmetic
-wrapping_neg(x::X) where {X <: FixedPoint} = X(-x.i, 0)
-wrapping_abs(x::X) where {X <: FixedPoint} = X(abs(x.i), 0)
-wrapping_add(x::X, y::X) where {X <: FixedPoint} = X(x.i + y.i, 0)
-wrapping_sub(x::X, y::X) where {X <: FixedPoint} = X(x.i - y.i, 0)
-wrapping_mul(x::X, y::X) where {X <: FixedPoint} = (float(x) * float(y)) % X
-function wrapping_fdiv(x::X, y::X) where {X <: FixedPoint}
-    z = floattype(X)(x.i) / floattype(X)(y.i)
-    isfinite(z) ? z % X : zero(X)
-end
-function wrapping_div(x::X, y::X, r::RoundingMode = RoundToZero) where {T, X <: FixedPoint{T}}
-    z = round(floattype(X)(x.i) / floattype(X)(y.i), r)
-    isfinite(z) || return zero(T)
-    if T <: Unsigned
-        _unsafe_trunc(T, z)
-    else
-        z > typemax(T) ? typemin(T) : _unsafe_trunc(T, z)
-    end
-end
-wrapping_fld(x::X, y::X) where {X <: FixedPoint} = wrapping_div(x, y, RoundDown)
-wrapping_cld(x::X, y::X) where {X <: FixedPoint} = wrapping_div(x, y, RoundUp)
-wrapping_rem(x::X, y::X, r::RoundingMode = RoundToZero) where {T, X <: FixedPoint{T}} =
-    X(x.i - wrapping_div(x, y, r) * y.i, 0)
-wrapping_mod(x::X, y::X) where {X <: FixedPoint} = wrapping_rem(x, y, RoundDown)
-
-# saturating arithmetic
-saturating_neg(x::X) where {X <: FixedPoint} = X(~min(x.i - true, x.i), 0)
-saturating_neg(x::X) where {X <: FixedPoint{<:Unsigned}} = zero(X)
-
-saturating_abs(x::X) where {X <: FixedPoint} =
-    X(ifelse(signbit(abs(x.i)), typemax(x.i), abs(x.i)), 0)
-
-saturating_add(x::X, y::X) where {X <: FixedPoint} =
-    X(x.i + ifelse(x.i < 0, max(y.i, typemin(x.i) - x.i), min(y.i, typemax(x.i) - x.i)), 0)
-saturating_add(x::X, y::X) where {X <: FixedPoint{<:Unsigned}} = X(x.i + min(~x.i, y.i), 0)
-
-saturating_sub(x::X, y::X) where {X <: FixedPoint} =
-    X(x.i - ifelse(x.i < 0, min(y.i, x.i - typemin(x.i)), max(y.i, x.i - typemax(x.i))), 0)
-saturating_sub(x::X, y::X) where {X <: FixedPoint{<:Unsigned}} = X(x.i - min(x.i, y.i), 0)
-
-saturating_mul(x::X, y::X) where {X <: FixedPoint} = clamp(float(x) * float(y), X)
-
-saturating_fdiv(x::X, y::X) where {X <: FixedPoint} =
-    clamp(floattype(X)(x.i) / floattype(X)(y.i), X)
-
-function saturating_div(x::X, y::X, r::RoundingMode = RoundToZero) where {T, X <: FixedPoint{T}}
-    z = round(floattype(X)(x.i) / floattype(X)(y.i), r)
-    isnan(z) && return zero(T)
-    if T <: Unsigned
-        isfinite(z) ? _unsafe_trunc(T, z) : typemax(T)
-    else
-        _unsafe_trunc(T, clamp(z, typemin(T), typemax(T)))
-    end
-end
-saturating_fld(x::X, y::X) where {X <: FixedPoint} = saturating_div(x, y, RoundDown)
-saturating_cld(x::X, y::X) where {X <: FixedPoint} = saturating_div(x, y, RoundUp)
-function saturating_rem(x::X, y::X, r::RoundingMode = RoundToZero) where {T, X <: FixedPoint{T}}
-    T <: Unsigned && r isa RoundingMode{:Up} && return zero(X)
-    X(x.i - saturating_div(x, y, r) * y.i, 0)
-end
-saturating_mod(x::X, y::X) where {X <: FixedPoint} = saturating_rem(x, y, RoundDown)
-
-# checked arithmetic
-checked_neg(x::X) where {X <: FixedPoint} = checked_sub(zero(X), x)
-function checked_abs(x::X) where {X <: FixedPoint}
-    abs(x.i) >= 0 || throw_overflowerror_abs(x)
-    X(abs(x.i), 0)
-end
-function checked_add(x::X, y::X) where {X <: FixedPoint}
-    r, f = Base.Checked.add_with_overflow(x.i, y.i)
-    z = X(r, 0) # store first
-    f && throw_overflowerror(:+, x, y)
-    z
-end
-function checked_sub(x::X, y::X) where {X <: FixedPoint}
-    r, f = Base.Checked.sub_with_overflow(x.i, y.i)
-    z = X(r, 0) # store first
-    f && throw_overflowerror(:-, x, y)
-    z
-end
-function checked_mul(x::X, y::X) where {X <: FixedPoint}
-    z = float(x) * float(y)
-    typemin(X) - eps(X)/2 <= z < typemax(X) + eps(X)/2 || throw_overflowerror(:*, x, y)
-    z % X
-end
-function checked_fdiv(x::X, y::X) where {T, X <: FixedPoint{T}}
-    y === zero(X) && throw(DivideError())
-    z = floattype(X)(x.i) / floattype(X)(y.i)
-    if T <: Unsigned
-        z < typemax(X) + eps(X)/2 || throw_overflowerror(:/, x, y)
-    else
-        typemin(X) - eps(X)/2 <= z < typemax(X) + eps(X)/2 || throw_overflowerror(:/, x, y)
-    end
-    z % X
-end
-function checked_div(x::X, y::X, r::RoundingMode = RoundToZero) where {T, X <: FixedPoint{T}}
-    y === zero(X) && throw(DivideError())
-    z = round(floattype(X)(x.i) / floattype(X)(y.i), r)
-    if T <: Signed
-        z <= typemax(T) || throw_overflowerror_div(r, x, y)
-    end
-    _unsafe_trunc(T, z)
-end
-checked_fld(x::X, y::X) where {X <: FixedPoint} = checked_div(x, y, RoundDown)
-checked_cld(x::X, y::X) where {X <: FixedPoint} = checked_div(x, y, RoundUp)
-function checked_rem(x::X, y::X, r::RoundingMode = RoundToZero) where {T, X <: FixedPoint{T}}
-    y === zero(X) && throw(DivideError())
-    fx, fy = floattype(X)(x.i), floattype(X)(y.i)
-    z = fx - round(fx / fy, r) * fy
-    if T <: Unsigned && r isa RoundingMode{:Up}
-        z >= zero(z) || throw_overflowerror_rem(r, x, y)
-    end
-    X(_unsafe_trunc(T, z), 0)
-end
-checked_mod(x::X, y::X) where {X <: FixedPoint} = checked_rem(x, y, RoundDown)
-
-# default arithmetic
-const DEFAULT_ARITHMETIC = :wrapping
-
-for (op, name) in ((:-, :neg), (:abs, :abs))
-    f = Symbol(DEFAULT_ARITHMETIC, :_, name)
-    @eval begin
-        $op(x::X) where {X <: FixedPoint} = $f(x)
-    end
-end
-for (op, name) in ((:+, :add), (:-, :sub), (:*, :mul))
-    f = Symbol(DEFAULT_ARITHMETIC, :_, name)
-    @eval begin
-        $op(x::X, y::X) where {X <: FixedPoint} = $f(x, y)
-    end
-end
-# force checked arithmetic
-/(x::X, y::X) where {X <: FixedPoint} = checked_fdiv(x, y)
-div(x::X, y::X, r::RoundingMode = RoundToZero) where {X <: FixedPoint} = checked_div(x, y, r)
-fld(x::X, y::X) where {X <: FixedPoint} = checked_div(x, y, RoundDown)
-cld(x::X, y::X) where {X <: FixedPoint} = checked_div(x, y, RoundUp)
-rem(x::X, y::X) where {X <: FixedPoint} = checked_rem(x, y, RoundToZero)
-rem(x::X, y::X, ::RoundingMode{:Down}) where {X <: FixedPoint} = checked_rem(x, y, RoundDown)
-rem(x::X, y::X, ::RoundingMode{:Up}) where {X <: FixedPoint} = checked_rem(x, y, RoundUp)
-mod(x::X, y::X) where {X <: FixedPoint} = checked_rem(x, y, RoundDown)
-
 function minmax(x::X, y::X) where {X <: FixedPoint}
     a, b = minmax(reinterpret(x), reinterpret(y))
     X(a,0), X(b,0)
@@ -518,6 +345,31 @@ include("normed.jl")
 include("deprecations.jl")
 const UF = (N0f8, N6f10, N4f12, N2f14, N0f16)
 
+include("arithmetic/arithmetic.jl")
+using .FixedPointArithmetic
+# re-export
+for name in names(FixedPointArithmetic.Wrapping)
+    @eval export $name
+end
+for name in names(FixedPointArithmetic.Saturating)
+    @eval export $name
+end
+for name in names(FixedPointArithmetic.Checked)
+    @eval export $name
+end
+
+# construction using the (approximate) intended value, i.e., N0f8
+*(x::Real, ::Type{X}) where {X <: FixedPoint} = _convert(X, x)
+Wrapping.wrapping_mul(x::Real, ::Type{X}) where {X <: FixedPoint} = x % X
+Saturating.saturating_mul(x::Real, ::Type{X}) where {X <: FixedPoint} = clamp(x, X)
+Checked.checked_mul(x::Real, ::Type{X}) where {X <: FixedPoint} = _convert(X, x)
+
+# type modulus
+rem(x::Real, ::Type{X}) where {X <: FixedPoint} = _rem(x, X)
+Wrapping.wrapping_rem(x::Real, ::Type{X}) where {X<:FixedPoint} = _rem(x, X)
+Saturating.saturating_rem(x::Real, ::Type{X}) where {X<:FixedPoint} = _rem(x, X)
+Checked.checked_rem(x::Real, ::Type{X}) where {X<:FixedPoint} = _rem(x, X)
+
 # Promotions
 promote_rule(::Type{X}, ::Type{Tf}) where {X <: FixedPoint, Tf <: AbstractFloat} =
     promote_type(floattype(X), Tf)
@@ -585,29 +437,6 @@ scaledual(::Type{Tdual}, x::AbstractArray{T}) where {Tdual, T <: FixedPoint} =
     throw(ArgumentError(String(take!(io))))
 end
 
-@noinline function throw_overflowerror(op::Symbol, @nospecialize(x), @nospecialize(y))
-    io = IOBuffer()
-    print(io, x, ' ', op, ' ', y, " overflowed for type ")
-    showtype(io, typeof(x))
-    throw(OverflowError(String(take!(io))))
-end
-@noinline function throw_overflowerror_abs(@nospecialize(x))
-    io = IOBuffer()
-    print(io, "abs(", x, ") overflowed for type ")
-    showtype(io, typeof(x))
-    throw(OverflowError(String(take!(io))))
-end
-@noinline function throw_overflowerror_div(r::RoundingMode, @nospecialize(x), @nospecialize(y))
-    io = IOBuffer()
-    op = r === RoundUp ? "cld(" : r === RoundDown ? "fld(" : "div("
-    print(io, op, x, ", ", y, ") overflowed for type ", rawtype(x))
-    throw(OverflowError(String(take!(io))))
-end
-@noinline function throw_overflowerror_rem(r::RoundingMode, @nospecialize(x), @nospecialize(y))
-    io = IOBuffer()
-    print(io, "rem(", x, ", ", y, ", ", r, ") overflowed for type ", typeof(x))
-    throw(OverflowError(String(take!(io))))
-end
 
 function Random.rand(r::AbstractRNG, ::SamplerType{X}) where X <: FixedPoint
     X(rand(r, rawtype(X)), 0)