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promotion.jl
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promotion.jl
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## type join (closest common ancestor, or least upper bound) ##
typejoin() = Bottom
typejoin(t::ANY) = t
typejoin(t::ANY, ts...) = typejoin(t, typejoin(ts...))
function typejoin(a::ANY, b::ANY)
if isa(a,TypeConstructor); a = a.body; end
if isa(b,TypeConstructor); b = b.body; end
if a <: b
return b
elseif b <: a
return a
end
if isa(a,TypeVar)
return typejoin(a.ub, b)
end
if isa(b,TypeVar)
return typejoin(a, b.ub)
end
if isa(a,UnionType) || isa(b,UnionType)
u = Union(a, b)
if !isa(u,UnionType)
return u
end
return reduce(typejoin, Bottom, u.types)
end
if isa(a,Tuple)
if !isa(b,Tuple)
return Any
end
la = length(a)::Int; lb = length(b)::Int
if la==0 || lb==0
return Tuple
end
if la < lb
if isvarargtype(a[la])
c = cell(la)
c[la] = Vararg{typejoin(a[la].parameters[1], tailjoin(b,la))}
n = la-1
else
c = cell(la+1)
c[la+1] = Vararg{tailjoin(b,la+1)}
n = la
end
elseif lb < la
if isvarargtype(b[lb])
c = cell(lb)
c[lb] = Vararg{typejoin(b[lb].parameters[1], tailjoin(a,lb))}
n = lb-1
else
c = cell(lb+1)
c[lb+1] = Vararg{tailjoin(a,lb+1)}
n = lb
end
else
c = cell(la)
n = la
end
for i=1:n
ai = a[i]; bi = b[i]
va = false
if isvarargtype(ai); va=true; ai = ai.parameters[1]; end
if isvarargtype(bi); va=true; bi = bi.parameters[1]; end
t = typejoin(ai,bi)
c[i] = va ? Vararg{t} : t
end
return tuple(c...)
elseif isa(b,Tuple)
return Any
end
while !is(b,Any)
if a <: b
return b
end
if a <: b.name.primary
return b.name.primary
end
b = super(b)
end
return Any
end
# reduce typejoin over tup[i:end]
function tailjoin(tup, i)
t = Bottom
for j = i:length(tup)
tj = tup[j]
t = typejoin(t, isvarargtype(tj)?tj.parameters[1]:tj)
end
return t
end
## promotion mechanism ##
promote_type() = Bottom
promote_type(T) = T
promote_type(T, S, U, V...) = promote_type(T, promote_type(S, U, V...))
promote_type(::Type{Bottom}, ::Type{Bottom}) = Bottom
promote_type{T}(::Type{T}, ::Type{T}) = T
promote_type{T}(::Type{T}, ::Type{Bottom}) = T
promote_type{T}(::Type{Bottom}, ::Type{T}) = T
# Try promote_rule in both orders. Typically only one is defined,
# and there is a fallback returning Bottom below, so the common case is
# promote_type(T, S) =>
# promote_result(T, S, result, Bottom) =>
# typejoin(result, Bottom) => result
promote_type{T,S}(::Type{T}, ::Type{S}) =
promote_result(T, S, promote_rule(T,S), promote_rule(S,T))
promote_rule(T, S) = Bottom
promote_result(t,s,T,S) = promote_type(T,S)
# If no promote_rule is defined, both directions give Bottom. In that
# case use typejoin on the original types instead.
promote_result{T,S}(::Type{T},::Type{S},::Type{Bottom},::Type{Bottom}) = typejoin(T, S)
promote() = ()
promote(x) = (x,)
function promote{T,S}(x::T, y::S)
(convert(promote_type(T,S),x), convert(promote_type(T,S),y))
end
promote_typeof(x) = typeof(x)
promote_typeof(x, xs...) = promote_type(typeof(x), promote_typeof(xs...))
function promote(x, y, z)
(convert(promote_typeof(x,y,z), x),
convert(promote_typeof(x,y,z), y),
convert(promote_typeof(x,y,z), z))
end
function promote(x, y, zs...)
tuple(convert(promote_typeof(x,y,zs...), x),
convert(promote_typeof(x,y,zs...), y),
convert((promote_typeof(x,y,zs...)...), zs)...)
end
# TODO: promote{T}(x::T, ys::T...) here to catch all circularities?
## promotions in arithmetic, etc. ##
# Because of the promoting fallback definitions for Number, we need
# a special case for undefined promote_rule on numeric types.
# Otherwise, typejoin(T,S) is called (returning Number) so no conversion
# happens, and +(promote(x,y)...) is called again, causing a stack
# overflow.
promote_result{T<:Number,S<:Number}(::Type{T},::Type{S},::Type{Bottom},::Type{Bottom}) =
promote_to_super(T, S, typejoin(T,S))
# promote numeric types T and S to typejoin(T,S) if T<:S or S<:T
# for example this makes promote_type(Integer,Real) == Real without
# promoting arbitrary pairs of numeric types to Number.
promote_to_super{T<:Number }(::Type{T}, ::Type{T}, ::Type{T}) = T
promote_to_super{T<:Number,S<:Number}(::Type{T}, ::Type{S}, ::Type{T}) = T
promote_to_super{T<:Number,S<:Number}(::Type{T}, ::Type{S}, ::Type{S}) = S
promote_to_super{T<:Number,S<:Number}(::Type{T}, ::Type{S}, ::Type) =
error("no promotion exists for ", T, " and ", S)
+(x::Number, y::Number) = +(promote(x,y)...)
*(x::Number, y::Number) = *(promote(x,y)...)
-(x::Number, y::Number) = -(promote(x,y)...)
/(x::Number, y::Number) = /(promote(x,y)...)
^(x::Number, y::Number) = ^(promote(x,y)...)
(&)(x::Integer, y::Integer) = (&)(promote(x,y)...)
(|)(x::Integer, y::Integer) = (|)(promote(x,y)...)
($)(x::Integer, y::Integer) = ($)(promote(x,y)...)
==(x::Number, y::Number) = (==)(promote(x,y)...)
< (x::Real, y::Real) = (< )(promote(x,y)...)
<=(x::Real, y::Real) = (<=)(promote(x,y)...)
div(x::Real, y::Real) = div(promote(x,y)...)
fld(x::Real, y::Real) = fld(promote(x,y)...)
cld(x::Real, y::Real) = cld(promote(x,y)...)
rem(x::Real, y::Real) = rem(promote(x,y)...)
mod(x::Real, y::Real) = mod(promote(x,y)...)
mod1(x::Real, y::Real) = mod1(promote(x,y)...)
rem1(x::Real, y::Real) = rem1(promote(x,y)...)
fld1(x::Real, y::Real) = fld1(promote(x,y)...)
max(x::Real, y::Real) = max(promote(x,y)...)
min(x::Real, y::Real) = min(promote(x,y)...)
minmax(x::Real, y::Real) = minmax(promote(x, y)...)
## catch-alls to prevent infinite recursion when definitions are missing ##
no_op_err(name, T) = error(name," not defined for ",T)
+{T<:Number}(x::T, y::T) = no_op_err("+", T)
*{T<:Number}(x::T, y::T) = no_op_err("*", T)
-{T<:Number}(x::T, y::T) = no_op_err("-", T)
/{T<:Number}(x::T, y::T) = no_op_err("/", T)
^{T<:Number}(x::T, y::T) = no_op_err("^", T)
(&){T<:Integer}(x::T, y::T) = no_op_err("&", T)
(|){T<:Integer}(x::T, y::T) = no_op_err("|", T)
($){T<:Integer}(x::T, y::T) = no_op_err("\$", T)
=={T<:Number}(x::T, y::T) = x === y
<{T<:Real}(x::T, y::T) = no_op_err("<", T)
max{T<:Real}(x::T, y::T) = ifelse(y < x, x, y)
min{T<:Real}(x::T, y::T) = ifelse(y < x, y, x)
minmax{T<:Real}(x::T, y::T) = y < x ? (y, x) : (x, y)