fusion of nested f.(args) calls into a single broadcast call

NEWS.md

@@ -10,7 +10,8 @@ New language features
   * Generators and comprehensions support filtering using `if` ([#550]) and nested
     iteration using multiple `for` keywords ([#4867]).
 
-  * Broadcasting syntax: ``f.(args...)`` is equivalent to ``broadcast(f, args...)`` ([#15032]).
+  * Broadcasting syntax: ``f.(args...)`` is equivalent to ``broadcast(f, args...)`` ([#15032]),
+    and nested `f.(g.(args...))` calls are fused into a single `broadcast` loop ([#17300]).
 
   * Macro expander functions are now generic, so macros can have multiple definitions
     (e.g. for different numbers of arguments, or optional arguments) ([#8846], [#9627]).
@@ -316,4 +317,5 @@ Deprecated or removed
 [#17037]: https://github.com/JuliaLang/julia/issues/17037
 [#17075]: https://github.com/JuliaLang/julia/issues/17075
 [#17266]: https://github.com/JuliaLang/julia/issues/17266
+[#17300]: https://github.com/JuliaLang/julia/issues/17300
 [#17374]: https://github.com/JuliaLang/julia/issues/17374

doc/manual/functions.rst

@@ -640,6 +640,22 @@ then ``f.(pi,A)`` will return a new array consisting of ``f(pi,a)`` for each
 consisting of ``f(vector1[i],vector2[i])`` for each index ``i``
 (throwing an exception if the vectors have different length).
 
+Moreover, *nested* ``f.(args...)`` calls are *fused* into a single ``broadcast``
+loop.  For example, ``sin.(cos.(X))`` is equivalent to ``broadcast(x -> sin(cos(x)), X)``,
+similar to ``[sin(cos(x)) for x in X]``: there is only a single loop over ``X``,
+and a single array is allocated for the result.   [In contrast, ``sin(cos(X))``
+in a typical "vectorized" language would first allocate one temporary array for ``tmp=cos(X)``,
+and then compute ``sin(tmp)`` in a separate loop, allocating a second array.]
+This loop fusion is not a compiler optimization that may or may not occur, it
+is a *syntactic guarantee* whenever nested ``f.(args...)`` calls are encountered.  Technically,
+the fusion stops as soon as a "non-dot" function is encountered; for example,
+in ``sin.(sort(cos.(X)))`` the ``sin`` and ``cos`` loops cannot be merged
+because of the intervening ``sort`` function.
+
+(In future versions of Julia, operators like ``.*`` will also be handled with
+the same mechanism: they will be equivalent to ``broadcast`` calls and
+will be fused with other nested "dot" calls.)
+
 Further Reading
 ---------------
 

src/julia-syntax.scm

@@ -1546,6 +1546,121 @@
         (cadr expr)  ;; eta reduce `x->f(x)` => `f`
         `(-> ,argname (block ,@splat ,expr)))))
 
+(define (getfield-field? x) ; whether x from (|.| f x) is a getfield call
+  (or (eq? (car x) 'quote) (eq? (car x) 'inert) (eq? (car x) '$)))
+
+;; fuse nested calls to f.(args...) into a single broadcast call
+(define (expand-fuse-broadcast f args)
+  (define (fuse? e) (and (pair? e) (eq? (car e) 'fuse)))
+  (define (anyfuse? exprs)
+    (if (null? exprs) #f (if (fuse? (car exprs)) #t (anyfuse? (cdr exprs)))))
+  (define (to-lambda f args kwargs) ; convert f to anonymous function with hygienic tuple args
+    (define (genarg arg) (if (vararg? arg) (list '... (gensy)) (gensy)))
+    ; (To do: optimize the case where f is already an anonymous function, in which
+    ;  case we only need to hygienicize the arguments?   But it is quite tricky
+    ;  to fully handle splatted args, typed args, keywords, etcetera.  And probably
+    ;  the extra function call is harmless because it will get inlined anyway.)
+    (let ((genargs (map genarg args))) ; hygienic formal parameters
+      (if (null? kwargs)
+          `(-> ,(cons 'tuple genargs) (call ,f ,@genargs)) ; no keyword args
+          `(-> ,(cons 'tuple genargs) (call ,f (parameters ,@kwargs) ,@genargs)))))
+  (define (from-lambda f) ; convert (-> (tuple args...) (call func args...)) back to func
+    (if (and (pair? f) (eq? (car f) '->) (pair? (cadr f)) (eq? (caadr f) 'tuple)
+             (pair? (caddr f)) (eq? (caaddr f) 'call) (equal? (cdadr f) (cdr (cdaddr f))))
+        (car (cdaddr f))
+        f))
+  (define (fuse-args oldargs) ; replace (fuse f args) with args in oldargs list
+    (define (fargs newargs oldargs)
+      (if (null? oldargs)
+          newargs
+          (fargs (if (fuse? (car oldargs))
+                     (append (reverse (caddar oldargs)) newargs)
+                     (cons (car oldargs) newargs))
+                 (cdr oldargs))))
+    (reverse (fargs '() oldargs)))
+  (define (fuse-funcs f args) ; for (fuse g a) in args, merge/inline g into f
+    ; any argument A of f that is (fuse g a) gets replaced by let A=(body of g):
+    (define (fuse-lets fargs args lets)
+      (if (null? args)
+          lets
+          (if (fuse? (car args))
+              (fuse-lets (cdr fargs) (cdr args) (cons (list '= (car fargs) (caddr (cadar args))) lets))
+              (fuse-lets (cdr fargs) (cdr args) lets))))
+    (let ((fargs (cdadr f))
+          (fbody (caddr f)))
+      `(->
+        (tuple ,@(fuse-args (map (lambda (oldarg arg) (if (fuse? arg)
+                                                 `(fuse _ ,(cdadr (cadr arg)))
+                                                 oldarg))
+                                 fargs args)))
+        (let ,fbody ,@(reverse (fuse-lets fargs args '()))))))
+  (define (make-fuse f args) ; check for nested (fuse f args) exprs and combine
+    (define (split-kwargs args) ; return (cons keyword-args positional-args) extracted from args
+      (define (sk args kwargs pargs)
+        (if (null? args)
+            (cons kwargs pargs)
+            (if (kwarg? (car args))
+                (sk (cdr args) (cons (car args) kwargs) pargs)
+                (sk (cdr args) kwargs (cons (car args) pargs)))))
+      (if (has-parameters? args)
+          (sk (reverse (cdr args)) (cdar args) '())
+          (sk (reverse args) '() '())))
+    (define (dot-to-fuse e) ; convert e == (. f (tuple args)) to (fuse f args)
+      (if (and (pair? e) (eq? (car e) '|.|) (not (getfield-field? (caddr e))))
+          (make-fuse (cadr e) (cdaddr e))
+          e))
+    (let* ((kws.args (split-kwargs args))
+           (kws (car kws.args))
+           (args (cdr kws.args)) ; fusing occurs on positional args only
+           (args_ (map dot-to-fuse args)))
+      (if (anyfuse? args_)
+          `(fuse ,(fuse-funcs (to-lambda f args kws) args_) ,(fuse-args args_))
+          `(fuse ,(to-lambda f args kws) ,args_))))
+  ; given e == (fuse lambda args), compress the argument list by removing (pure)
+  ; duplicates in args, inlining literals, and moving any varargs to the end:
+  (define (compress-fuse e)
+    (define (findfarg arg args fargs) ; for arg in args, return corresponding farg
+      (if (eq? arg (car args))
+          (car fargs)
+          (findfarg arg (cdr args) (cdr fargs))))
+    (let ((f (cadr e))
+          (args (caddr e)))
+      (define (cf old-fargs old-args new-fargs new-args renames varfarg vararg)
+        (if (null? old-args)
+            (let ((nfargs (if (null? varfarg) new-fargs (cons varfarg new-fargs)))
+                  (nargs (if (null? vararg) new-args (cons vararg new-args))))
+              `(fuse (-> (tuple ,@(reverse nfargs)) ,(replace-vars (caddr f) renames))
+                     ,(reverse nargs)))
+            (let ((farg (car old-fargs)) (arg (car old-args)))
+              (cond
+               ((and (vararg? farg) (vararg? arg)) ; arg... must be the last argument
+                (if (null? varfarg)
+                    (cf (cdr old-fargs) (cdr old-args)
+                        new-fargs new-args renames farg arg)
+                    (if (eq? (cadr vararg) (cadr arg))
+                        (cf (cdr old-fargs) (cdr old-args)
+                            new-fargs new-args (cons (cons (cadr farg) (cadr varfarg)) renames)
+                            varfarg vararg)
+                        (error "multiple splatted args cannot be fused into a single broadcast"))))
+               ((number? arg) ; inline numeric literals
+                (cf (cdr old-fargs) (cdr old-args)
+                    new-fargs new-args
+                    (cons (cons farg arg) renames)
+                    varfarg vararg))
+               ((and (symbol? arg) (memq arg new-args)) ; combine duplicate args
+                ; (note: calling memq for every arg is O(length(args)^2) ...
+                ;  ... would be better to replace with a hash table if args is long)
+                (cf (cdr old-fargs) (cdr old-args)
+                    new-fargs new-args
+                    (cons (cons farg (findfarg arg new-args new-fargs)) renames)
+                    varfarg vararg))
+               (else
+                (cf (cdr old-fargs) (cdr old-args)
+                    (cons farg new-fargs) (cons arg new-args) renames varfarg vararg))))))
+      (cf (cdadr f) args '() '() '() '() '())))
+  (let ((e (compress-fuse (make-fuse f args)))) ; an expression '(fuse func args)
+    (expand-forms `(call broadcast ,(from-lambda (cadr e)) ,@(caddr e)))))
+
 ;; table mapping expression head to a function expanding that form
 (define expand-table
   (table
@@ -1584,11 +1699,11 @@
    (lambda (e) ; e = (|.| f x)
      (let ((f (cadr e))
            (x (caddr e)))
-       (if (or (eq? (car x) 'quote) (eq? (car x) 'inert) (eq? (car x) '$))
-         `(call (core getfield) ,(expand-forms f) ,(expand-forms x))
-         ; otherwise, came from f.(args...) --> broadcast(f, args...),
-         ; where x = (tuple args...) at this point:
-         (expand-forms `(call broadcast ,f ,@(cdr x))))))
+       (if (getfield-field? x)
+           `(call (core getfield) ,(expand-forms f) ,(expand-forms x))
+          ; otherwise, came from f.(args...) --> broadcast(f, args...),
+          ; where we want to fuse with any nested broadcast calls.
+          (expand-fuse-broadcast f (cdr x)))))
 
    '|<:| syntactic-op-to-call
    '|>:| syntactic-op-to-call

test/broadcast.jl

@@ -212,6 +212,41 @@ let a = sin.([1, 2])
     @test a ≈ [0.8414709848078965, 0.9092974268256817]
 end
 
+# PR #17300: loop fusion
+@test (x->x+1).((x->x+2).((x->x+3).(1:10))) == collect(7:16)
+let A = [sqrt(i)+j for i = 1:3, j=1:4]
+    @test atan2.(log.(A), sum(A,1)) == broadcast(atan2, broadcast(log, A), sum(A, 1))
+end
+let x = sin.(1:10)
+    @test atan2.((x->x+1).(x), (x->x+2).(x)) == atan2(x+1, x+2) == atan2(x.+1, x.+2)
+    @test sin.(atan2.([x+1,x+2]...)) == sin.(atan2.(x+1,x+2))
+    @test sin.(atan2.(x, 3.7)) == broadcast(x -> sin(atan2(x,3.7)), x)
+    @test atan2.(x, 3.7) == broadcast(x -> atan2(x,3.7), x) == broadcast(atan2, x, 3.7)
+end
+# Use side effects to check for loop fusion.  Note that, due to #17314,
+# a broadcasted function is currently called an extra time with an argument 1.
+let g = Int[]
+    f17300(x) = begin; push!(g, x); x+1; end
+    f17300.(f17300.(f17300.(1:3)))
+    @test g == [1,2,3, 1,2,3, 2,3,4, 3,4,5]
+end
+# fusion with splatted args:
+let x = sin.(1:10), a = [x]
+    @test cos.(x) == cos.(a...)
+    @test atan2.(x,x) == atan2.(a..., a...) == atan2.([x, x]...)
+    @test atan2.(x, cos.(x)) == atan2.(a..., cos.(x)) == atan2(x, cos.(a...)) == atan2(a..., cos.(a...))
+    @test ((args...)->cos(args[1])).(x) == cos.(x) == ((y,args...)->cos(y)).(x)
+end
+@test atan2.(3,4) == atan2(3,4) == (() -> atan2(3,4)).()
+# fusion with keyword args:
+let x = [1:4;]
+    f17300kw(x; y=0) = x + y
+    @test f17300kw.(x) == x
+    @test f17300kw.(x, y=1) == f17300kw.(x; y=1) == f17300kw.(x; [(:y,1)]...) == x .+ 1
+    @test f17300kw.(sin.(x), y=1) == f17300kw.(sin.(x); y=1) == sin.(x) .+ 1
+    @test sin.(f17300kw.(x, y=1)) == sin.(f17300kw.(x; y=1)) == sin.(x .+ 1)
+end
+
 # PR 16988
 @test Base.promote_op(+, Bool) === Int
 @test isa(broadcast(+, [true]), Array{Int,1})