replace @pure annotations in Base with effect settings

This commit replaces `@pure`/`@_pure_meta` annotations used in `Base`
with corresponding effect settings (`:total` or `:total_or_throw`).

The concrete evaluation mechanism based on the effect system (#43852)
has the following benefits over the `@pure`-based optimization:
- it can fold cases when consistent exception is thrown
- it can handle constant union-split situation as well
- effects can be propagated inter-procedurally

While revisiting the existing annotations, I removed some unnecessary ones
and also added some more hopefully new annotations (mostly for reflection utilities).
In theory this should give us some performance benefits, e.g. now we
can concrete-evaluate union-spit `typeintersect`:
```julia
@test Base.return_types((Union{Int,Nothing},)) do x
  typeintersect(String, typeof(x))
end |> only === Type{Union{}}
```

Though this commit ends up bigger than I expected -- we should carefully
check a benchmark result so that it doesn't come with any regressions.

base/Base.jl

@@ -183,7 +183,7 @@ include("abstractarraymath.jl")
 include("arraymath.jl")
 
 # SIMD loops
-@pure sizeof(s::String) = Core.sizeof(s)  # needed by gensym as called from simdloop
+sizeof(s::String) = Core.sizeof(s)  # needed by gensym as called from simdloop
 include("simdloop.jl")
 using .SimdLoop
 

base/array.jl

@@ -154,7 +154,7 @@ size(a::Array{<:Any,N}) where {N} = (@inline; ntuple(M -> size(a, M), Val(N))::D
 
 asize_from(a::Array, n) = n > ndims(a) ? () : (arraysize(a,n), asize_from(a, n+1)...)
 
-allocatedinline(T::Type) = (@_pure_meta; ccall(:jl_stored_inline, Cint, (Any,), T) != Cint(0))
+allocatedinline(T::Type) = (@_total_meta; ccall(:jl_stored_inline, Cint, (Any,), T) != Cint(0))
 
 """
     Base.isbitsunion(::Type{T})

base/broadcast.jl

@@ -8,7 +8,7 @@ Module containing the broadcasting implementation.
 module Broadcast
 
 using .Base.Cartesian
-using .Base: Indices, OneTo, tail, to_shape, isoperator, promote_typejoin, promote_typejoin_union, @pure,
+using .Base: Indices, OneTo, tail, to_shape, isoperator, promote_typejoin, promote_typejoin_union,
              _msk_end, unsafe_bitgetindex, bitcache_chunks, bitcache_size, dumpbitcache, unalias, negate
 import .Base: copy, copyto!, axes
 export broadcast, broadcast!, BroadcastStyle, broadcast_axes, broadcastable, dotview, @__dot__, BroadcastFunction
@@ -137,7 +137,7 @@ BroadcastStyle(a::AbstractArrayStyle, ::Style{Tuple})    = a
 BroadcastStyle(::A, ::A) where A<:ArrayStyle             = A()
 BroadcastStyle(::ArrayStyle, ::ArrayStyle)               = Unknown()
 BroadcastStyle(::A, ::A) where A<:AbstractArrayStyle     = A()
-Base.@pure function BroadcastStyle(a::A, b::B) where {A<:AbstractArrayStyle{M},B<:AbstractArrayStyle{N}} where {M,N}
+Base.@assume_effects :total function BroadcastStyle(a::A, b::B) where {A<:AbstractArrayStyle{M},B<:AbstractArrayStyle{N}} where {M,N}
     if Base.typename(A) === Base.typename(B)
         return A(Val(max(M, N)))
     end

base/c.jl

@@ -734,6 +734,6 @@ macro ccall(expr)
     return ccall_macro_lower(:ccall, ccall_macro_parse(expr)...)
 end
 
-macro ccall_effects(effects, expr)
+macro ccall_effects(effects::UInt8, expr)
     return ccall_macro_lower((:ccall, effects), ccall_macro_parse(expr)...)
 end

base/compiler/abstractinterpretation.jl

@@ -1950,7 +1950,7 @@ function abstract_eval_statement(interp::AbstractInterpreter, @nospecialize(e),
         end
         cconv = e.args[5]
         if isa(cconv, QuoteNode) && isa(cconv.value, Tuple{Symbol, UInt8})
-            effects = cconv.value[2]
+            effects = cconv.value[2]::UInt8
             effects = decode_effects_override(effects)
             tristate_merge!(sv, Effects(
                 effects.consistent ? ALWAYS_TRUE : TRISTATE_UNKNOWN,

base/deprecated.jl

@@ -251,11 +251,11 @@ getindex(match::Core.MethodMatch, field::Int) =
 tuple_type_head(T::Type) = fieldtype(T, 1)
 tuple_type_cons(::Type, ::Type{Union{}}) = Union{}
 function tuple_type_cons(::Type{S}, ::Type{T}) where T<:Tuple where S
-    @_pure_meta
+    @_total_but_may_throw_meta
     Tuple{S, T.parameters...}
 end
 function parameter_upper_bound(t::UnionAll, idx)
-    @_pure_meta
+    @_total_but_may_throw_meta
     return rewrap_unionall((unwrap_unionall(t)::DataType).parameters[idx], t)
 end
 

base/essentials.jl

@@ -151,9 +151,37 @@ macro isdefined(s::Symbol)
     return Expr(:escape, Expr(:isdefined, s))
 end
 
+function _is_internal(__module__)
+    if ccall(:jl_base_relative_to, Any, (Any,), __module__)::Module === Core.Compiler ||
+       nameof(__module__) === :Base
+        return true
+    end
+    return false
+end
+
+# can be used in place of `@pure` (supposed to be used for bootstrapping)
 macro _pure_meta()
-    return Expr(:meta, :pure)
+    return _is_internal(__module__) && Expr(:meta, :pure)
+end
+# can be used in place of `@assume_effects :total` (supposed to be used for bootstrapping)
+macro _total_meta()
+    return _is_internal(__module__) && Expr(:meta, Expr(:purity,
+        #=:consistent=#true,
+        #=:effect_free=#true,
+        #=:nothrow=#true,
+        #=:terminates_globally=#true,
+        #=:terminates_locally=#false))
+end
+# can be used in place of `@assume_effects :total_but_may_throw` (supposed to be used for bootstrapping)
+macro _total_but_may_throw_meta()
+    return _is_internal(__module__) && Expr(:meta, Expr(:purity,
+        #=:consistent=#true,
+        #=:effect_free=#true,
+        #=:nothrow=#false,
+        #=:terminates_globally=#true,
+        #=:terminates_locally=#false))
 end
+
 # another version of inlining that propagates an inbounds context
 macro _propagate_inbounds_meta()
     return Expr(:meta, :inline, :propagate_inbounds)

base/intfuncs.jl

@@ -58,11 +58,9 @@ end
 
 # binary GCD (aka Stein's) algorithm
 # about 1.7x (2.1x) faster for random Int64s (Int128s)
-# Unfortunately, we need to manually annotate this as `@pure` to work around #41694. Since
-# this is used in the Rational constructor, constant prop is something we do care about here.
-# This does call generic functions, so it might not be completely sound, but since `_gcd` is
-# restricted to BitIntegers, it is probably fine in practice.
-@pure function _gcd(a::T, b::T) where T<:BitInteger
+# Unfortunately, we need to manually annotate this as `@assume_effects :terminates_locally` to work around #41694.
+# Since this is used in the Rational constructor, constant folding is something we do care about here.
+@assume_effects :terminates_locally function _gcd(a::T, b::T) where T<:BitInteger
     za = trailing_zeros(a)
     zb = trailing_zeros(b)
     k = min(za, zb)

base/irrationals.jl

@@ -48,7 +48,8 @@ AbstractFloat(x::AbstractIrrational) = Float64(x)::Float64
 Float16(x::AbstractIrrational) = Float16(Float32(x)::Float32)
 Complex{T}(x::AbstractIrrational) where {T<:Real} = Complex{T}(T(x))
 
-@pure function Rational{T}(x::AbstractIrrational) where T<:Integer
+# XXX this may change `DEFAULT_PRECISION`, thus not effect free
+@assume_effects :total function Rational{T}(x::AbstractIrrational) where T<:Integer
     o = precision(BigFloat)
     p = 256
     while true
@@ -64,7 +65,7 @@ Complex{T}(x::AbstractIrrational) where {T<:Real} = Complex{T}(T(x))
 end
 Rational{BigInt}(x::AbstractIrrational) = throw(ArgumentError("Cannot convert an AbstractIrrational to a Rational{BigInt}: use rationalize(BigInt, x) instead"))
 
-@pure function (t::Type{T})(x::AbstractIrrational, r::RoundingMode) where T<:Union{Float32,Float64}
+@assume_effects :total function (t::Type{T})(x::AbstractIrrational, r::RoundingMode) where T<:Union{Float32,Float64}
     setprecision(BigFloat, 256) do
         T(BigFloat(x)::BigFloat, r)
     end
@@ -106,11 +107,11 @@ end
 <=(x::AbstractFloat, y::AbstractIrrational) = x < y
 
 # Irrational vs Rational
-@pure function rationalize(::Type{T}, x::AbstractIrrational; tol::Real=0) where T
+@assume_effects :total function rationalize(::Type{T}, x::AbstractIrrational; tol::Real=0) where T
     return rationalize(T, big(x), tol=tol)
 end
-@pure function lessrational(rx::Rational{<:Integer}, x::AbstractIrrational)
-    # an @pure version of `<` for determining if the rationalization of
+@assume_effects :total function lessrational(rx::Rational{<:Integer}, x::AbstractIrrational)
+    # an @assume_effects :total version of `<` for determining if the rationalization of
     # an irrational number required rounding up or down
     return rx < big(x)
 end

base/namedtuple.jl

@@ -218,7 +218,7 @@ function map(f, nt::NamedTuple{names}, nts::NamedTuple...) where names
     NamedTuple{names}(map(f, map(Tuple, (nt, nts...))...))
 end
 
-@pure function merge_names(an::Tuple{Vararg{Symbol}}, bn::Tuple{Vararg{Symbol}})
+@assume_effects :total function merge_names(an::Tuple{Vararg{Symbol}}, bn::Tuple{Vararg{Symbol}})
     @nospecialize an bn
     names = Symbol[an...]
     for n in bn
@@ -229,7 +229,7 @@ end
     (names...,)
 end
 
-@pure function merge_types(names::Tuple{Vararg{Symbol}}, a::Type{<:NamedTuple}, b::Type{<:NamedTuple})
+@assume_effects :total function merge_types(names::Tuple{Vararg{Symbol}}, a::Type{<:NamedTuple}, b::Type{<:NamedTuple})
     @nospecialize names a b
     bn = _nt_names(b)
     return Tuple{Any[ fieldtype(sym_in(names[n], bn) ? b : a, names[n]) for n in 1:length(names) ]...}
@@ -321,7 +321,7 @@ get(f::Callable, nt::NamedTuple, key::Union{Integer, Symbol}) = isdefined(nt, ke
 tail(t::NamedTuple{names}) where names = NamedTuple{tail(names)}(t)
 front(t::NamedTuple{names}) where names = NamedTuple{front(names)}(t)
 
-@pure function diff_names(an::Tuple{Vararg{Symbol}}, bn::Tuple{Vararg{Symbol}})
+@assume_effects :total function diff_names(an::Tuple{Vararg{Symbol}}, bn::Tuple{Vararg{Symbol}})
     @nospecialize an bn
     names = Symbol[]
     for n in an

base/operators.jl

@@ -40,15 +40,8 @@ julia> supertype(Int32)
 Signed
 ```
 """
-function supertype(T::DataType)
-    @_pure_meta
-    T.super
-end
-
-function supertype(T::UnionAll)
-    @_pure_meta
-    UnionAll(T.var, supertype(T.body))
-end
+supertype(T::DataType) = (@_total_meta; T.super)
+supertype(T::UnionAll) = (@_total_meta; UnionAll(T.var, supertype(T.body)))
 
 ## generic comparison ##
 
@@ -247,14 +240,8 @@ isunordered(x) = false
 isunordered(x::AbstractFloat) = isnan(x)
 isunordered(x::Missing) = true
 
-function ==(T::Type, S::Type)
-    @_pure_meta
-    return ccall(:jl_types_equal, Cint, (Any, Any), T, S) != 0
-end
-function !=(T::Type, S::Type)
-    @_pure_meta
-    return !(T == S)
-end
+==(T::Type, S::Type) = (@_total_meta; ccall(:jl_types_equal, Cint, (Any, Any), T, S) != 0)
+!=(T::Type, S::Type) = (@_total_meta; !(T == S))
 ==(T::TypeVar, S::Type) = false
 ==(T::Type, S::TypeVar) = false
 

base/promotion.jl

@@ -10,9 +10,9 @@ they both inherit.
 """
 typejoin() = Bottom
 typejoin(@nospecialize(t)) = t
-typejoin(@nospecialize(t), ts...) = (@_pure_meta; typejoin(t, typejoin(ts...)))
+typejoin(@nospecialize(t), ts...) = (@_total_meta; typejoin(t, typejoin(ts...)))
 function typejoin(@nospecialize(a), @nospecialize(b))
-    @_pure_meta
+    @_total_meta
     if isa(a, TypeVar)
         return typejoin(a.ub, b)
     elseif isa(b, TypeVar)
@@ -128,7 +128,7 @@ end
 # WARNING: this is wrong for some objects for which subtyping is broken
 #          (Core.Compiler.isnotbrokensubtype), use only simple types for `b`
 function typesplit(@nospecialize(a), @nospecialize(b))
-    @_pure_meta
+    @_total_but_may_throw_meta
     if a <: b
         return Bottom
     end
@@ -180,7 +180,7 @@ function promote_typejoin_union(::Type{T}) where T
 end
 
 function typejoin_union_tuple(T::DataType)
-    @_pure_meta
+    @_total_but_may_throw_meta
     u = Base.unwrap_unionall(T)
     p = (u::DataType).parameters
     lr = length(p)::Int