Integrate lazy broadcast representation into new broadcast machinery

Among other things, this supports returning AbstractRanges for appropriate inputs.

Fixes #21094, fixes #22053

base/mpfr.jl

@@ -267,6 +267,9 @@ promote_rule(::Type{BigFloat}, ::Type{<:AbstractFloat}) = BigFloat
 
 big(::Type{<:AbstractFloat}) = BigFloat
 
+# Support conversion of AbstractRanges to high precision
+Base.Broadcast.maybe_range_safe_f(::typeof(big)) = true
+
 function (::Type{Rational{BigInt}})(x::AbstractFloat)
     isnan(x) && return zero(BigInt) // zero(BigInt)
     isinf(x) && return copysign(one(BigInt),x) // zero(BigInt)

base/show.jl

@@ -524,6 +524,7 @@ end
 show_comma_array(io::IO, itr, o, c) = show_delim_array(io, itr, o, ',', c, false)
 show(io::IO, t::Tuple) = show_delim_array(io, t, '(', ',', ')', true)
 show(io::IO, v::SimpleVector) = show_delim_array(io, v, "svec(", ',', ')', false)
+show(io::IO, t::TupleLL) = show_delim_array(io, t, '{', ',', '}', true)
 
 show(io::IO, s::Symbol) = show_unquoted_quote_expr(io, s, 0, 0)
 

base/sparse/higherorderfns.jl

@@ -4,14 +4,15 @@ module HigherOrderFns
 
 # This module provides higher order functions specialized for sparse arrays,
 # particularly map[!]/broadcast[!] for SparseVectors and SparseMatrixCSCs at present.
-import Base: map, map!, broadcast, broadcast!
+import Base: map, map!, broadcast, copy, copyto!
 
-using Base: front, tail, to_shape
+using Base: TupleLL, front, tail, to_shape
 using ..SparseArrays: SparseVector, SparseMatrixCSC, AbstractSparseVector,
                       AbstractSparseMatrix, AbstractSparseArray, indtype, nnz, nzrange
-using Base.Broadcast: BroadcastStyle
+using Base.Broadcast: BroadcastStyle, Broadcasted, flatten
 
 # This module is organized as follows:
+# (0) Define BroadcastStyle rules and convenience types for dispatch
 # (1) Define a common interface to SparseVectors and SparseMatrixCSCs sufficient for
 #       map[!]/broadcast[!]'s purposes. The methods below are written against this interface.
 # (2) Define entry points for map[!] (short children of _map_[not]zeropres!).
@@ -28,11 +29,70 @@ using Base.Broadcast: BroadcastStyle
 # (12) Define map[!] methods handling combinations of sparse and structured matrices.
 
 
+# (0) BroadcastStyle rules and convenience types for dispatch
+
+SparseVecOrMat = Union{SparseVector,SparseMatrixCSC}
+
+# broadcast container type promotion for combinations of sparse arrays and other types
+struct SparseVecStyle <: Broadcast.AbstractArrayStyle{1} end
+struct SparseMatStyle <: Broadcast.AbstractArrayStyle{2} end
+Broadcast.BroadcastStyle(::Type{<:SparseVector}) = SparseVecStyle()
+Broadcast.BroadcastStyle(::Type{<:SparseMatrixCSC}) = SparseMatStyle()
+const SPVM = Union{SparseVecStyle,SparseMatStyle}
+
+# SparseVecStyle handles 0-1 dimensions, SparseMatStyle 0-2 dimensions.
+# SparseVecStyle promotes to SparseMatStyle for 2 dimensions.
+# Fall back to DefaultArrayStyle for higher dimensionality.
+SparseVecStyle(::Val{0}) = SparseVecStyle()
+SparseVecStyle(::Val{1}) = SparseVecStyle()
+SparseVecStyle(::Val{2}) = SparseMatStyle()
+SparseVecStyle(::Val{N}) where N = Broadcast.DefaultArrayStyle{N}()
+SparseMatStyle(::Val{0}) = SparseMatStyle()
+SparseMatStyle(::Val{1}) = SparseMatStyle()
+SparseMatStyle(::Val{2}) = SparseMatStyle()
+SparseMatStyle(::Val{N}) where N = Broadcast.DefaultArrayStyle{N}()
+
+Broadcast.BroadcastStyle(::SparseMatStyle, ::SparseVecStyle) = SparseMatStyle()
+
+struct PromoteToSparse <: Broadcast.AbstractArrayStyle{2} end
+StructuredMatrix = Union{Diagonal,Bidiagonal,Tridiagonal,SymTridiagonal}
+Broadcast.BroadcastStyle(::Type{<:StructuredMatrix}) = PromoteToSparse()
+
+PromoteToSparse(::Val{0}) = PromoteToSparse()
+PromoteToSparse(::Val{1}) = PromoteToSparse()
+PromoteToSparse(::Val{2}) = PromoteToSparse()
+PromoteToSparse(::Val{N}) where N = Broadcast.DefaultArrayStyle{N}()
+
+Broadcast.BroadcastStyle(::PromoteToSparse, ::SPVM) = PromoteToSparse()
+
+# FIXME: switch to DefaultArrayStyle once we can delete VectorStyle and MatrixStyle
+BroadcastStyle(::Type{<:Base.Adjoint{T,<:Vector}}) where T = Broadcast.MatrixStyle() # Adjoint not yet defined when broadcast.jl loaded
+BroadcastStyle(::Type{<:Base.Transpose{T,<:Vector}}) where T = Broadcast.MatrixStyle() # Transpose not yet defined when broadcast.jl loaded
+Broadcast.BroadcastStyle(::SPVM, ::Broadcast.VectorStyle) = PromoteToSparse()
+Broadcast.BroadcastStyle(::SPVM, ::Broadcast.MatrixStyle) = PromoteToSparse()
+Broadcast.BroadcastStyle(::SparseVecStyle, ::Broadcast.DefaultArrayStyle{N}) where N =
+    Broadcast.DefaultArrayStyle(Broadcast._max(Val(N), Val(1)))
+Broadcast.BroadcastStyle(::SparseMatStyle, ::Broadcast.DefaultArrayStyle{N}) where N =
+    Broadcast.DefaultArrayStyle(Broadcast._max(Val(N), Val(2)))
+# end FIXME
+
+# Tuples promote to dense
+Broadcast.BroadcastStyle(::SparseVecStyle, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{1}()
+Broadcast.BroadcastStyle(::SparseMatStyle, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{2}()
+Broadcast.BroadcastStyle(::PromoteToSparse, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{2}()
+
+# Dispatch on broadcast operations by number of arguments
+const Broadcasted0{Style<:Union{Nothing,BroadcastStyle},ElType,Axes,Indexing<:Union{Nothing,TupleLL{Nothing,Nothing}},F} =
+    Broadcasted{Style,ElType,Axes,Indexing,F,TupleLL{Nothing,Nothing}}
+const SpBroadcasted1{Style<:SPVM,ElType,Axes,Indexing<:Union{Nothing,TupleLL},F,Args<:TupleLL{<:SparseVecOrMat,Nothing}} =
+    Broadcasted{Style,ElType,Axes,Indexing,F,Args}
+const SpBroadcasted2{Style<:SPVM,ElType,Axes,Indexing<:Union{Nothing,TupleLL},F,Args<:TupleLL{<:SparseVecOrMat,TupleLL{<:SparseVecOrMat,Nothing}}} =
+    Broadcasted{Style,ElType,Axes,Indexing,F,Args}
+
 # (1) The definitions below provide a common interface to sparse vectors and matrices
 # sufficient for the purposes of map[!]/broadcast[!]. This interface treats sparse vectors
 # as n-by-one sparse matrices which, though technically incorrect, is how broacast[!] views
 # sparse vectors in practice.
-SparseVecOrMat = Union{SparseVector,SparseMatrixCSC}
 @inline numrows(A::SparseVector) = A.n
 @inline numrows(A::SparseMatrixCSC) = A.m
 @inline numcols(A::SparseVector) = 1
@@ -91,11 +151,11 @@ function _noshapecheck_map(f::Tf, A::SparseVecOrMat, Bs::Vararg{SparseVecOrMat,N
                         _map_notzeropres!(f, fofzeros, C, A, Bs...)
 end
 # (3) broadcast[!] entry points
-broadcast(f::Tf, A::SparseVector) where {Tf} = _noshapecheck_map(f, A)
-broadcast(f::Tf, A::SparseMatrixCSC) where {Tf} = _noshapecheck_map(f, A)
+copy(bc::SpBroadcasted1) = _noshapecheck_map(bc.f, bc.args.head)
 
-@inline function broadcast!(f::Tf, C::SparseVecOrMat, ::Nothing) where Tf
+@inline function copyto!(C::SparseVecOrMat, bc::Broadcasted0{Nothing})
     isempty(C) && return _finishempty!(C)
+    f = bc.f
     fofnoargs = f()
     if _iszero(fofnoargs) # f() is zero, so empty C
         trimstorage!(C, 0)
@@ -108,13 +168,6 @@ broadcast(f::Tf, A::SparseMatrixCSC) where {Tf} = _noshapecheck_map(f, A)
     return C
 end
 
-# the following three similar defs are necessary for type stability in the mixed vector/matrix case
-broadcast(f::Tf, A::SparseVector, Bs::Vararg{SparseVector,N}) where {Tf,N} =
-    _aresameshape(A, Bs...) ? _noshapecheck_map(f, A, Bs...) : _diffshape_broadcast(f, A, Bs...)
-broadcast(f::Tf, A::SparseMatrixCSC, Bs::Vararg{SparseMatrixCSC,N}) where {Tf,N} =
-    _aresameshape(A, Bs...) ? _noshapecheck_map(f, A, Bs...) : _diffshape_broadcast(f, A, Bs...)
-broadcast(f::Tf, A::SparseVecOrMat, Bs::Vararg{SparseVecOrMat,N}) where {Tf,N} =
-    _diffshape_broadcast(f, A, Bs...)
 function _diffshape_broadcast(f::Tf, A::SparseVecOrMat, Bs::Vararg{SparseVecOrMat,N}) where {Tf,N}
     fofzeros = f(_zeros_eltypes(A, Bs...)...)
     fpreszeros = _iszero(fofzeros)
@@ -139,7 +192,14 @@ end
 @inline _aresameshape(A) = true
 @inline _aresameshape(A, B) = size(A) == size(B)
 @inline _aresameshape(A, B, Cs...) = _aresameshape(A, B) ? _aresameshape(B, Cs...) : false
+@inline _aresameshape(t::TupleLL{<:Any,Nothing}) = true
+@inline _aresameshape(t::TupleLL{<:Any,<:TupleLL}) =
+    _aresameshape(t.head, t.rest.head) ? _aresameshape(t.rest) : false
 @inline _checksameshape(As...) = _aresameshape(As...) || throw(DimensionMismatch("argument shapes must match"))
+@inline _all_args_isa(t::TupleLL{<:Any,Nothing}, ::Type{T}) where T = isa(t.head, T)
+@inline _all_args_isa(t::TupleLL, ::Type{T}) where T = isa(t.head, T) & _all_args_isa(t.rest, T)
+@inline _all_args_isa(t::TupleLL{<:Broadcasted,Nothing}, ::Type{T}) where T = _all_args_isa(t.head.args, T)
+@inline _all_args_isa(t::TupleLL{<:Broadcasted}, ::Type{T}) where T = _all_args_isa(t.head.args, T) & _all_args_isa(t.rest, T)
 @inline _densennz(shape::NTuple{1}) = shape[1]
 @inline _densennz(shape::NTuple{2}) = shape[1] * shape[2]
 _maxnnzfrom(shape::NTuple{1}, A) = nnz(A) * div(shape[1], A.n)
@@ -892,37 +952,42 @@ end
 
 # (10) broadcast over combinations of broadcast scalars and sparse vectors/matrices
 
-# broadcast container type promotion for combinations of sparse arrays and other types
-struct SparseVecStyle <: Broadcast.AbstractArrayStyle{1} end
-struct SparseMatStyle <: Broadcast.AbstractArrayStyle{2} end
-Broadcast.BroadcastStyle(::Type{<:SparseVector}) = SparseVecStyle()
-Broadcast.BroadcastStyle(::Type{<:SparseMatrixCSC}) = SparseMatStyle()
-const SPVM = Union{SparseVecStyle,SparseMatStyle}
-
-# SparseVecStyle handles 0-1 dimensions, SparseMatStyle 0-2 dimensions.
-# SparseVecStyle promotes to SparseMatStyle for 2 dimensions.
-# Fall back to DefaultArrayStyle for higher dimensionality.
-SparseVecStyle(::Val{0}) = SparseVecStyle()
-SparseVecStyle(::Val{1}) = SparseVecStyle()
-SparseVecStyle(::Val{2}) = SparseMatStyle()
-SparseVecStyle(::Val{N}) where N = Broadcast.DefaultArrayStyle{N}()
-SparseMatStyle(::Val{0}) = SparseMatStyle()
-SparseMatStyle(::Val{1}) = SparseMatStyle()
-SparseMatStyle(::Val{2}) = SparseMatStyle()
-SparseMatStyle(::Val{N}) where N = Broadcast.DefaultArrayStyle{N}()
-
-Broadcast.BroadcastStyle(::SparseMatStyle, ::SparseVecStyle) = SparseMatStyle()
-
-# Tuples promote to dense
-Broadcast.BroadcastStyle(::SparseVecStyle, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{1}()
-Broadcast.BroadcastStyle(::SparseMatStyle, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{2}()
-
 # broadcast entry points for combinations of sparse arrays and other (scalar) types
-function broadcast(f, ::SPVM, ::Nothing, ::Nothing, mixedargs::Vararg{Any,N}) where N
-    parevalf, passedargstup = capturescalars(f, mixedargs)
+function copy(bc::Broadcasted{<:SPVM})
+    bcf = flatten(bc)
+    _all_args_isa(bcf.args, SparseVector) && return _shapecheckbc(bcf)
+    _all_args_isa(bcf.args, SparseMatrixCSC) && return _shapecheckbc(bcf)
+    args = Tuple(bcf.args)
+    _all_args_isa(bcf.args, SparseVecOrMat) && return _diffshape_broadcast(bcf.f, args...)
+    parevalf, passedargstup = capturescalars(bcf.f, args)
     return broadcast(parevalf, passedargstup...)
 end
-# for broadcast! see (11)
+function _shapecheckbc(bc::Broadcasted)
+    args = Tuple(bc.args)
+    _aresameshape(bc.args) ? _noshapecheck_map(bc.f, args...) : _diffshape_broadcast(bc.f, args...)
+end
+
+function copyto!(dest::SparseVecOrMat, bc::Broadcasted{<:SPVM})
+    if bc.f === identity && bc isa SpBroadcasted1 && Base.axes(dest) == (A = bc.args.head; Base.axes(A))
+        return copyto!(dest, A)
+    end
+    bcf = flatten(bc)
+    As = Tuple(bcf.args)
+    if _all_args_isa(bcf.args, SparseVecOrMat)
+        _aresameshape(dest, As...) && return _noshapecheck_map!(bcf.f, dest, As...)
+        Base.Broadcast.check_broadcast_indices(axes(dest), As...)
+        fofzeros = bcf.f(_zeros_eltypes(As...)...)
+        fpreszeros = _iszero(fofzeros)
+        fpreszeros ? _broadcast_zeropres!(bcf.f, dest, As...) :
+                     _broadcast_notzeropres!(bcf.f, fofzeros, dest, As...)
+    else
+        # As contains nothing but SparseVecOrMat and scalars
+        # See below for capturescalars
+        parevalf, passedsrcargstup = capturescalars(bcf.f, As)
+        broadcast!(parevalf, dest, passedsrcargstup...)
+    end
+    return dest
+end
 
 # capturescalars takes a function (f) and a tuple of mixed sparse vectors/matrices and
 # broadcast scalar arguments (mixedargs), and returns a function (parevalf, i.e. partially
@@ -971,59 +1036,16 @@ broadcast(f::Tf, A::SparseMatrixCSC, ::Type{T}) where {Tf,T} = broadcast(x -> f(
 # vectors/matrices, promote all structured matrices and dense vectors/matrices to sparse
 # and rebroadcast. otherwise, divert to generic AbstractArray broadcast code.
 
-struct PromoteToSparse <: Broadcast.AbstractArrayStyle{2} end
-StructuredMatrix = Union{Diagonal,Bidiagonal,Tridiagonal,SymTridiagonal}
-Broadcast.BroadcastStyle(::Type{<:StructuredMatrix}) = PromoteToSparse()
-
-PromoteToSparse(::Val{0}) = PromoteToSparse()
-PromoteToSparse(::Val{1}) = PromoteToSparse()
-PromoteToSparse(::Val{2}) = PromoteToSparse()
-PromoteToSparse(::Val{N}) where N = Broadcast.DefaultArrayStyle{N}()
-
-Broadcast.BroadcastStyle(::PromoteToSparse, ::SPVM) = PromoteToSparse()
-Broadcast.BroadcastStyle(::PromoteToSparse, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{2}()
-
-# FIXME: switch to DefaultArrayStyle once we can delete VectorStyle and MatrixStyle
-# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{0}) = PromoteToSparse()
-# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{1}) = PromoteToSparse()
-# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{2}) = PromoteToSparse()
-BroadcastStyle(::Type{<:Base.Adjoint{T,<:Vector}}) where T = Broadcast.MatrixStyle() # Adjoint not yet defined when broadcast.jl loaded
-BroadcastStyle(::Type{<:Base.Transpose{T,<:Vector}}) where T = Broadcast.MatrixStyle() # Transpose not yet defined when broadcast.jl loaded
-Broadcast.BroadcastStyle(::SPVM, ::Broadcast.VectorStyle) = PromoteToSparse()
-Broadcast.BroadcastStyle(::SPVM, ::Broadcast.MatrixStyle) = PromoteToSparse()
-Broadcast.BroadcastStyle(::SparseVecStyle, ::Broadcast.DefaultArrayStyle{N}) where N =
-    Broadcast.DefaultArrayStyle(Broadcast._max(Val(N), Val(1)))
-Broadcast.BroadcastStyle(::SparseMatStyle, ::Broadcast.DefaultArrayStyle{N}) where N =
-    Broadcast.DefaultArrayStyle(Broadcast._max(Val(N), Val(2)))
-# end FIXME
-
-broadcast(f, ::PromoteToSparse, ::Nothing, ::Nothing, As::Vararg{Any,N}) where {N} =
-    broadcast(f, map(_sparsifystructured, As)...)
-
-# For broadcast! with ::Any inputs, we need a layer of indirection to determine whether
-# the inputs can be promoted to SparseVecOrMat. If it's just SparseVecOrMat and scalars,
-# we can handle it here, otherwise see below for the promotion machinery.
-function broadcast!(f::Tf, dest::SparseVecOrMat, ::SPVM, A::SparseVecOrMat, Bs::Vararg{SparseVecOrMat,N}) where {Tf,N}
-    if f isa typeof(identity) && N == 0 && Base.axes(dest) == Base.axes(A)
-        return copyto!(dest, A)
-    end
-    _aresameshape(dest, A, Bs...) && return _noshapecheck_map!(f, dest, A, Bs...)
-    Base.Broadcast.check_broadcast_indices(axes(dest), A, Bs...)
-    fofzeros = f(_zeros_eltypes(A, Bs...)...)
-    fpreszeros = _iszero(fofzeros)
-    fpreszeros ? _broadcast_zeropres!(f, dest, A, Bs...) :
-                        _broadcast_notzeropres!(f, fofzeros, dest, A, Bs...)
-    return dest
+function copy(bc::Broadcasted{PromoteToSparse})
+    bcf = flatten(bc)
+    As = Tuple(bcf.args)
+    broadcast(bcf.f, map(_sparsifystructured, As)...)
 end
-function broadcast!(f::Tf, dest::SparseVecOrMat, ::SPVM, mixedsrcargs::Vararg{Any,N}) where {Tf,N}
-    # mixedsrcargs contains nothing but SparseVecOrMat and scalars
-    parevalf, passedsrcargstup = capturescalars(f, mixedsrcargs)
-    broadcast!(parevalf, dest, passedsrcargstup...)
-    return dest
-end
-function broadcast!(f::Tf, dest::SparseVecOrMat, ::PromoteToSparse, mixedsrcargs::Vararg{Any,N}) where {Tf,N}
-    broadcast!(f, dest, map(_sparsifystructured, mixedsrcargs)...)
-    return dest
+
+function copyto!(dest::SparseVecOrMat, bc::Broadcasted{PromoteToSparse})
+    bcf = flatten(bc)
+    As = Tuple(bcf.args)
+    broadcast!(bcf.f, dest, map(_sparsifystructured, As)...)
 end
 
 _sparsifystructured(M::AbstractMatrix) = SparseMatrixCSC(M)

base/tuple.jl

@@ -352,3 +352,53 @@ any(x::Tuple{Bool, Bool, Bool}) = x[1]|x[2]|x[3]
 Returns an empty tuple, `()`.
 """
 empty(x::Tuple) = ()
+
+## Linked-list representation of a tuple. Inferrable even for Type elements.
+
+struct TupleLL{T, Rest}
+    head::T    # car
+    rest::Rest # cdr
+    TupleLL(x, rest::TupleLL) where {} = new{Core.Typeof(x), typeof(rest)}(x, rest) # (cons x rest)
+    TupleLL(x, rest::Nothing) where {} = new{Core.Typeof(x), typeof(rest)}(x, rest) # (cons x nil)
+    TupleLL(x) where {} = new{Core.Typeof(x), Nothing}(x, nothing) # (list x)
+    TupleLL() where {} = new{Nothing, Nothing}(nothing, nothing)
+end
+# (apply list a)
+make_TupleLL() = TupleLL()
+make_TupleLL(a) = TupleLL(a)
+make_TupleLL(a, args...) = TupleLL(a, make_TupleLL(args...))
+
+# (map f tt)
+map(f, tt::TupleLL{Nothing, Nothing}) = ()
+map(f, tt::TupleLL{<:Any, Nothing}) = (f(tt.head),)
+function map(f, tt::TupleLL)
+    return (f(tt.head), map(f, tt.rest)...)
+end
+
+mapTupleLL(f, tt::TupleLL{Nothing, Nothing}) = TupleLL()
+mapTupleLL(f, tt::TupleLL{<:Any, Nothing}) = TupleLL(f(tt.head),)
+function mapTupleLL(f, tt::TupleLL)
+    return TupleLL(f(tt.head), mapTupleLL(f, tt.rest))
+end
+
+convert(::Type{Tuple}, tt::TupleLL) = map(identity, tt)
+(::Type{Tuple})(tt::TupleLL) = convert(Tuple, tt)
+
+any(f::Function, tt::TupleLL{Nothing, Nothing}) = false
+any(f::Function, tt::TupleLL{<:Any, Nothing}) = f(tt.head)
+any(f::Function, tt::TupleLL) = f(tt.head) || any(f, tt.rest)
+
+all(f::Function, tt::TupleLL{Nothing, Nothing}) = true
+all(f::Function, tt::TupleLL{<:Any, Nothing}) = f(tt.head)
+all(f::Function, tt::TupleLL) = f(tt.head) && all(f, tt.rest)
+
+start(tt::TupleLL) = tt
+next(::TupleLL, tt::TupleLL) = (tt.head, tt.rest)
+done(::TupleLL{Nothing, Nothing}, tt::TupleLL{Nothing, Nothing}) = true
+done(::TupleLL, tt::Nothing) = true
+done(::TupleLL, tt::TupleLL) = false
+
+length(tt::TupleLL{Nothing, Nothing}) = 0
+length(tt::TupleLL) = _length(1, tt.rest)
+_length(l::Int, tt::TupleLL) = _length(l+1, tt.rest)
+_length(l::Int, ::Nothing) = l