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promotion.jl
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promotion.jl
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# This file is a part of Julia. License is MIT: http://julialang.org/license
## type join (closest common ancestor, or least upper bound) ##
typejoin() = (@_pure_meta; Bottom)
typejoin(t::ANY) = (@_pure_meta; t)
typejoin(t::ANY, ts...) = (@_pure_meta; typejoin(t, typejoin(ts...)))
function typejoin(a::ANY, b::ANY)
@_pure_meta
if a <: b
return b
elseif b <: a
return a
elseif isa(a,UnionAll)
return UnionAll(a.var, typejoin(a.body, b))
elseif isa(b,UnionAll)
return UnionAll(b.var, typejoin(a, b.body))
elseif isa(a,TypeVar)
return typejoin(a.ub, b)
elseif isa(b,TypeVar)
return typejoin(a, b.ub)
elseif isa(a,Union)
return typejoin(typejoin(a.a,a.b), b)
elseif isa(b,Union)
return typejoin(a, typejoin(b.a,b.b))
elseif a <: Tuple
if !(b <: Tuple)
return Any
end
ap, bp = a.parameters, b.parameters
lar = length(ap)::Int; lbr = length(bp)::Int
laf, afixed = full_va_len(ap)
lbf, bfixed = full_va_len(bp)
if lar==0 || lbr==0
return Tuple
end
if laf < lbf
if isvarargtype(ap[lar]) && !afixed
c = Vector{Any}(laf)
c[laf] = Vararg{typejoin(unwrapva(ap[lar]), tailjoin(bp,laf))}
n = laf-1
else
c = Vector{Any}(laf+1)
c[laf+1] = Vararg{tailjoin(bp,laf+1)}
n = laf
end
elseif lbf < laf
if isvarargtype(bp[lbr]) && !bfixed
c = Vector{Any}(lbf)
c[lbf] = Vararg{typejoin(unwrapva(bp[lbr]), tailjoin(ap,lbf))}
n = lbf-1
else
c = Vector{Any}(lbf+1)
c[lbf+1] = Vararg{tailjoin(ap,lbf+1)}
n = lbf
end
else
c = Vector{Any}(laf)
n = laf
end
for i = 1:n
ai = ap[min(i,lar)]; bi = bp[min(i,lbr)]
ci = typejoin(unwrapva(ai),unwrapva(bi))
c[i] = i == length(c) && (isvarargtype(ai) || isvarargtype(bi)) ? Vararg{ci} : ci
end
return Tuple{c...}
elseif b <: Tuple
return Any
end
while b !== Any
if a <: b.name.wrapper
while a.name !== b.name
a = supertype(a)
end
aprimary = unwrap_unionall(a.name.wrapper)
# join on parameters
n = length(a.parameters)
if n == 0
return aprimary
end
p = Vector{Any}(n)
for i = 1:n
ai, bi = a.parameters[i], b.parameters[i]
if ai === bi || (isa(ai,Type) && isa(bi,Type) && typeseq(ai,bi))
p[i] = ai
else
p[i] = aprimary.parameters[i]
end
end
return rewrap_unionall(a.name.wrapper{p...}, a.name.wrapper)
end
b = supertype(b)
end
return Any
end
# Returns length, isfixed
function full_va_len(p)
isempty(p) && return 0, true
last = p[end]
if isvarargtype(last)
N = unwrap_unionall(last).parameters[2]
if isa(N, Integer)
return (length(p) + N - 1)::Int, true
end
return length(p)::Int, false
end
return length(p)::Int, true
end
# reduce typejoin over A[i:end]
function tailjoin(A, i)
if i > length(A)
return unwrapva(A[end])
end
t = Bottom
for j = i:length(A)
t = typejoin(t, unwrapva(A[j]))
end
return t
end
## promotion mechanism ##
promote_type() = (@_pure_meta; Bottom)
promote_type(T) = (@_pure_meta; T)
promote_type(T, S, U, V...) = (@_pure_meta; promote_type(T, promote_type(S, U, V...)))
promote_type(::Type{Bottom}, ::Type{Bottom}) = (@_pure_meta; Bottom)
promote_type{T}(::Type{T}, ::Type{T}) = (@_pure_meta; T)
promote_type{T}(::Type{T}, ::Type{Bottom}) = (@_pure_meta; T)
promote_type{T}(::Type{Bottom}, ::Type{T}) = (@_pure_meta; T)
"""
promote_type(type1, type2)
Determine a type big enough to hold values of each argument type without loss, whenever
possible. In some cases, where no type exists to which both types can be promoted
losslessly, some loss is tolerated; for example, `promote_type(Int64,Float64)` returns
`Float64` even though strictly, not all `Int64` values can be represented exactly as
`Float64` values.
"""
function promote_type{T,S}(::Type{T}, ::Type{S})
@_pure_meta
# 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_result(T, S, promote_rule(T,S), promote_rule(S,T))
end
promote_rule(T, S) = (@_pure_meta; Bottom)
promote_result(t,s,T,S) = (@_pure_meta; 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}) = (@_pure_meta; 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) = (@_pure_meta; typeof(x))
promote_typeof(x, xs...) = (@_pure_meta; 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...)
(convert(promote_typeof(x,y,zs...), x),
convert(promote_typeof(x,y,zs...), y),
convert(Tuple{Vararg{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.
function promote_result{T<:Number,S<:Number}(::Type{T},::Type{S},::Type{Bottom},::Type{Bottom})
@_pure_meta
promote_to_supertype(T, S, typejoin(T,S))
end
# 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_supertype{T<:Number }(::Type{T}, ::Type{T}, ::Type{T}) = (@_pure_meta; T)
promote_to_supertype{T<:Number,S<:Number}(::Type{T}, ::Type{S}, ::Type{T}) = (@_pure_meta; T)
promote_to_supertype{T<:Number,S<:Number}(::Type{T}, ::Type{S}, ::Type{S}) = (@_pure_meta; S)
promote_to_supertype{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, y)
Exponentiation operator.
"""
^(x::Number, y::Number) = ^(promote(x,y)...)
fma(x::Number, y::Number, z::Number) = fma(promote(x,y,z)...)
muladd(x::Number, y::Number, z::Number) = muladd(promote(x,y,z)...)
(&)(x::Integer, y::Integer) = (&)(promote(x,y)...)
(|)(x::Integer, y::Integer) = (|)(promote(x,y)...)
xor(x::Integer, y::Integer) = xor(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)...)
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)...)
# "Promotion" that takes a function into account and tries to preserve
# non-concrete types. These are meant to be used mainly by elementwise
# operations, so it is advised against overriding them
_default_type(T::Type) = (@_pure_meta; T)
if isdefined(Core, :Inference)
_return_type(f::ANY, t::ANY) = Core.Inference.return_type(f, t)
else
_return_type(f::ANY, t::ANY) = Any
end
promote_op(::Any...) = (@_pure_meta; Any)
function promote_op{S}(f, ::Type{S})
@_inline_meta
T = _return_type(f, Tuple{_default_type(S)})
isleaftype(S) && return isleaftype(T) ? T : Any
return typejoin(S, T)
end
function promote_op{R,S}(f, ::Type{R}, ::Type{S})
@_inline_meta
T = _return_type(f, Tuple{_default_type(R), _default_type(S)})
isleaftype(R) && isleaftype(S) && return isleaftype(T) ? T : Any
return typejoin(R, S, T)
end
## 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)
fma{T<:Number}(x::T, y::T, z::T) = no_op_err("fma", T)
fma(x::Integer, y::Integer, z::Integer) = x*y+z
muladd{T<:Number}(x::T, y::T, z::T) = x*y+z
(&){T<:Integer}(x::T, y::T) = no_op_err("&", T)
(|){T<:Integer}(x::T, y::T) = no_op_err("|", T)
xor{T<:Integer}(x::T, y::T) = no_op_err("xor", T)
=={T<:Number}(x::T, y::T) = x === y
<{T<:Real}(x::T, y::T) = no_op_err("<" , T)
<={T<:Real}(x::T, y::T) = no_op_err("<=", T)
rem{T<:Real}(x::T, y::T) = no_op_err("rem", T)
mod{T<:Real}(x::T, y::T) = no_op_err("mod", T)
min(x::Real) = x
max(x::Real) = x
minmax(x::Real) = (x, x)
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)