promotion.jl

# 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 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,Union) || isa(b,Union)
        u = Union{a, b}
        if !isa(u,Union)
            return u
        end
        return reduce(typejoin, Bottom, u.types)
    end
    if 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(ap[lar].parameters[1], 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(bp[lbr].parameters[1], 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.primary
            while a.name !== b.name
                a = supertype(a)
            end
            # join on parameters
            n = length(a.parameters)
            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] = a.name.primary.parameters[i]
                end
            end
            return a.name.primary{p...}
        end
        b = supertype(b)
    end
    return Any
end

# Returns length, isfixed
function full_va_len(p)
    isempty(p) && return 0, true
    if isvarargtype(p[end])
        N = p[end].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)

# 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
function promote_type{T,S}(::Type{T}, ::Type{S})
    @_pure_meta
    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::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)

promote_op(::Any...) = (@_pure_meta; Any)
function promote_op{S}(f, ::Type{S})
    @_inline_meta
    Z = Tuple{_default_type(S)}
    T = _default_eltype(Generator{Z, typeof(f)})
    isleaftype(S) && return isleaftype(T) ? T : Any
    return typejoin(S, T)
end
function promote_op{R,S}(f, ::Type{R}, ::Type{S})
    @_inline_meta
    Z = Iterators.Zip2{Tuple{_default_type(R)}, Tuple{_default_type(S)}}
    T = _default_eltype(Generator{Z, typeof(a -> f(a...))})
    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)