From: admin <admin@vouivredigital.com>
Date: Mon, 20 Nov 2023 07:56:37 +0000 (+0900)
Subject: Optimize garbage collection
X-Git-Tag: v0.2.0~11
X-Git-Url: https://git.vouivredigital.com/?a=commitdiff_plain;h=6f945ff1f9cae705f27d70ec18891df3ce3b50d4;p=vouivre.git

Optimize garbage collection

Instead of allocating memory on every index of every
differentiable function call we do it once per call
and use the buffer for all indices.
---

diff --git a/grad.scm b/grad.scm
index f0aa3c2..9e4ec76 100644
--- a/grad.scm
+++ b/grad.scm
@@ -3,6 +3,7 @@
   #:use-module (srfi srfi-1)
   #:use-module (srfi srfi-9)
   #:use-module (vouivre misc)
+  #:use-module (vouivre promises)
   #:export
   (*atype*
    adot
@@ -10,14 +11,17 @@
    contract-arrays
    differentiable-wrapper
    dot
+   do-times
+   ewise1
+   ewise2
    extend
    grad
-   internal-jacobian
+   make-batch
+   make-internal
    maximum
    mean
    rank-of
-   sum
-   )
+   sum)
   #:replace
   ((i:sqrt . sqrt)
    (i:exp . exp)
@@ -35,35 +39,24 @@
    (i:abs . abs)
    (i:identity . identity)
    (i:array-ref . array-ref)
-   )
+   (i:array-cell-ref . array-cell-ref))
   #:re-export
   (fold
    reduce))
 
 ;;;; array utilities
 
-(define (abs->rel index dimensions)
-  (let rec ((ds (cdr dimensions))
-	    (p (apply * (cdr dimensions)))
-	    (r index)
-	    (is '()))
-    (let ((i (quotient r p)))
-      (if (null? ds)
-	  (reverse (cons i is))
-	  (rec (cdr ds)
-	       (quotient p (car ds))
-	       (- r (* p i))
-	       (cons i is))))))
-
-(define (contracted-dims a b n)
-  (let ((dims-a (array-dimensions a))
-        (dims-b (array-dimensions b)))
-    (if (or (> n (array-rank a))
-            (> n (array-rank b)))
-      (error "can't contract arrays with size lower than" n)
-      (append (take dims-a (- (array-rank a)
-			      n))
-	      (drop dims-b n)))))
+(define (rel->abs indices dimensions)
+  (let rec ((s 0)
+	    (p 1)
+	    (is (reverse indices))
+	    (ds (reverse dimensions)))
+    (if (null? is)
+	s
+	(rec (+ s (* p (car is)))
+	     (* p (car ds))
+	     (cdr is)
+	     (cdr ds)))))
 
 (define(do-times n proc)
   (let rec ((i 0))
@@ -152,176 +145,232 @@ element-wise. All arrays must have the same dimension."
 ;;(define *atype* 'f32)
 (define *atype* #t)
 (define *grad* (make-parameter #f))
+(define *j* (make-parameter #f))
+
+(define-syntax-rule (w/j val body ...)
+  (parameterize ((*j* val))
+    body ...))
+
+(define (unwrap-fwd x)
+  (if (internal? x)
+      (internal-forward x)
+      x))
+
+(define (unwrap-jac x)
+  (if (internal? x)
+      (internal-jacobian x)
+      x))
+
+(define (dims-of x)
+  (if (number? x)
+      '()
+      (array-dimensions x)))
+
+(define (mov dst-buf n-dst-dims generator naked-inputs data j)
+  (do-times
+   n-dst-dims
+   (lambda (i)
+     (array-set!
+      dst-buf
+      (apply generator naked-inputs i j data)
+      i)))
+  dst-buf)
+
+(define (add dst-buf n-dst-dims generator naked-inputs data j)
+  (do-times
+   n-dst-dims
+   (lambda (i)
+     (array-set!
+      dst-buf
+      (+ (array-ref dst-buf i)
+	 (apply generator naked-inputs i j data))
+      i)))
+  dst-buf)
+
+(define (movc dst-buf n-dst-dims src-buf n-src-dims
+	      generator naked-inputs data)
+  "Contract the Jacobian column produced by the generator with the source buffer
+storing the result in the destination buffer."
+  (let ((s 0))
+    (do-times
+     n-dst-dims
+     (lambda (i)
+       (set! s 0)
+       (do-times
+	n-src-dims
+	(lambda (k)
+	  (set! s (+ s (* (apply generator naked-inputs i k data)
+			  (array-ref src-buf k))))))
+       (array-set! dst-buf s i))))
+  dst-buf)
+
+(define (addc dst-buf n-dst-dims src-buf n-src-dims
+	      generator naked-inputs data)
+  "Contract the Jacobian column produced by the generator with the source buffer
+adding the result to the destination buffer."
+  (let ((s 0))
+    (do-times
+     n-dst-dims
+     (lambda (i)
+       (set! s (array-ref dst-buf i))
+       (do-times
+	n-src-dims
+	(lambda (k)
+	  (set! s (+ s (* (apply generator naked-inputs i k data)
+			  (array-ref src-buf k))))))
+       (array-set! dst-buf s i))))
+  dst-buf)
 
 (define* (grad f #:optional (axis 0))
   (define (wrap x i)
     (if (= i axis)
-	(make-internal x #f)
+	(make-internal x 'input)
 	x))
   (lambda xs
-    (let* ((wrapped-xs (map wrap xs (list-tabulate (length xs) identity)))
-	   (y (internal-forward (list-ref wrapped-xs axis))))
-      ((if (*grad*)
-	   identity
-	   (lambda (boxed)
-	     (let ((fx (internal-forward boxed))
-		   (gfx (internal-jacobian boxed)))
-	       (cond
-		((and (number? fx) (number? y))
-		 (gfx '()))
-		((and (number? fx) (array? y))
-		 (apply produce-typed-array
-			(lambda js (gfx js))
-			*atype*
-			(array-dimensions y)))
-		((and (array? fx) (number? y))
-		 (gfx '()))
-		(else
-		 (let* ((dims-out (array-dimensions fx))
-			(dims-in (array-dimensions y))
-			(a (apply make-typed-array *atype* *unspecified* (append dims-out dims-in))))
-		   (for-indices-in-range
-		    (lambda js
-		      (let ((out (gfx js)))
-			(for-indices-in-range
-			 (lambda is
-			   (apply
-			    array-set!
-			    a
-			    (apply array-ref out is)
-			    (append is js)))
-			 (list-zeros (array-rank fx))
-			 dims-out)))
-		    (list-zeros (array-rank y))
-		    dims-in)
-		   a))))))
-       (parameterize (((@@ (vouivre grad) *grad*) y))
-	 (apply f wrapped-xs))))))
-
-(define (unbox-fwd x)
-  (if (internal? x)
-      (internal-forward x)
-      x))
-
-;; `n' is the number of arguments to `function'.
-;; `jacobian-generators is not a `Vec' but a `List' we only use the former to
-;; show its length.
+    (parameterize (((@@ (vouivre grad) *grad*) #t)
+		   ((@@ (vouivre grad) *promises*) (cons '() #f)))
+      (let* ((internal (apply f (map-indexed wrap xs)))
+	     (fx (internal-forward internal))
+	     (y (list-ref xs axis))  ; variable to differentiate w.r.t
+	     (pre-Jx (internal-jacobian internal))
+	     (Jx (cond
+		  ;; TODO: implement 'input case and test 'zero and 'input
+		  ((eq? pre-Jx 'zero)
+		   (lambda (j)
+		     (lambda (i)
+		       0)))
+		  ((eq? pre-Jx 'input)
+		   (error "TBD."))
+		  (else
+		   (lambda (j)
+		     (reset-promises (car (*promises*)))
+		     (let ((column-jac (w/j j (force pre-Jx))))
+		       (lambda (i)
+			 (array-ref column-jac i))))))))
+	(cond
+	 ((and (number? fx) (number? y))
+	  ((Jx 0) 0))
+	 ((and (number? fx) (array? y))
+	  (let* ((y-dims (array-dimensions y))
+		 (a (apply make-array *unspecified* y-dims))
+		 (ac (array-contents a)))
+	    (do-times
+	     (apply * y-dims)
+	     (lambda (j)
+	       (array-set! ac ((Jx j) 0)
+			   j)))
+	    a))
+	 ((and (array? fx) (number? y))
+	  (let* ((fx-dims (array-dimensions fx))
+		 (a (apply make-array *unspecified* fx-dims))
+		 (ac (array-contents a))
+		 (Jx (Jx 0)))
+	    (do-times
+	     (apply * fx-dims)
+	     (lambda (i)
+	       (array-set! ac (Jx i)
+			   i)))
+	    a))
+	 (else
+	  (let* ((fx-dims (array-dimensions fx))
+		 (y-dims (array-dimensions y))
+		 (n-fx-dims (apply * fx-dims))
+		 (n-y-dims (apply * y-dims))
+		 (a (apply make-array *unspecified* (append fx-dims y-dims)))
+		 (ac (array-contents a)))
+	    (do-times
+	     n-y-dims
+	     (lambda (j)
+	       (let ((Jx (Jx j)))
+		 (do-times
+		  n-fx-dims
+		  (lambda (i)
+		    (array-set! ac (Jx i)
+				(+ j (* n-y-dims i))))))))
+	    a)))))))
+
+
+;; In the comment that follows:
+;;
+;; `n' is the number of arguments to `proc'.
+;; `generators is not a `Vec' but a `List' we only use the former to illustrate
+;; its length.
 ;; `X1', ..., `Xn' are the types of inputs and thus `Array's of some dimension.
 ;; `I' is the type of multi-indices indexing the output of `function'.
 ;; `J' is the type of multi-indices indexing the input array being differentiated.
+;; `|I|' (resp. `|J|') is the type of absolute indices of `I' (resp. `J').
 ;; `Array I' is the type of arrays indexed by multi-indices of `I'.
 ;; `[X]' means that `X' is boxed in an internal as when returned by
-;;       `differentiable-wrapper' with the array being `X' and the function
-;;       taking a multi-index of `J' to return an array of the same shape as `X'.
-;; (∷ (→ (Vec n (→ X1 ... Xn I J Number))
-;;       (→ X1 ... Xn (Array I))
+;;       `differentiable-wrapper' with the array being `X' and the promise that
+;;       given a |J| we will get the change of `X' with a change of the
+;;       the differentiated argument at multi-index `J'.
+;; (∷ (→ (Vec n (→ X1 ... Xn |I| |J| Number))
+;;       (→ X1 ... Xn (Array I))*
 ;;       [X1] ... [Xn]
-;;       (Internal (Array I) (→ J (Array I)))))
-(define (differentiable-wrapper jacobian-generators function input . more)
-  ;; NOTE: Both the jacobian generators and the function act on naked inputs
-  ;;       (numbers or arrays not inside an internal object). The generators
-  ;;       additionaly take indices -- one for each dimension of what we are
-  ;;       differentiating with respect to (the content of `(*grad*)'). A
-  ;;       generator returns a jacobian column expressing the change of the
-  ;;       function's output when changing `(*grad*)' along the given indices.
-  ;;       In cases where an argument isn't meant to be differentiable its
-  ;;       corresponding generator should be `#f'.
-  (let* ((inputs (cons input more))
-	 (naked-inputs (map unbox-fwd inputs))
-	 (output (apply (if (procedure? function)
-			    function
-			    (car function))
-			naked-inputs))
-	 (data (if (procedure? function)
-		   '()
-		   (map (lambda (f) (apply f naked-inputs))
-			(cdr function)))))
+;;       (Internal (Array I) (Promise |J| (Array |I|)))))
+;;
+;; (*) We extend this definition to allow `proc' to be a list of procedures
+;;     the head of which is as described above and the remaining elements
+;;     are procedures of the same arguments but returning values that are
+;;     then fed as extra data to the generators.
+;;
+;; NOTE: In cases where an argument isn't meant to be differentiable its
+;;       corresponding generator should be `#f'.
+(define (differentiable-wrapper generators proc* arg . more)
+  (let* ((args (cons arg more))
+	 (proc (if (procedure? proc*)
+		   proc*
+		   (car proc*)))
+	 (naked-args (map unwrap-fwd args))
+	 (out (apply proc naked-args)))
     (ifn (*grad*)
-	 output
-	 (make-internal
-	  output
-	  (lambda (js)
-	    (or
-	     (fold
-	      (lambda (jacobian-generator input prev)
-		(ifn (internal? input)
-		     prev
-		     ((ifn prev identity (lambda (x) ((extend +) prev x)))
-		      (ifn (internal-jacobian input)
-			   (if (number? output)
-			       (apply jacobian-generator naked-inputs js data)
-			       (apply
-				produce-typed-array
-				(lambda is
-				  (apply jacobian-generator
-					 naked-inputs
-					 (append is js)
-					 data))
-				*atype*
-				(array-dimensions output)))
-			   (let ((b ((internal-jacobian input) js))
-				 (fwd (internal-forward input)))
-			     (cond
-			      ((and (number? output) (number? fwd))
-			       (* (apply jacobian-generator
-					 naked-inputs '() data)
-				  b))
-			      ((and (number? output) (array? fwd))
-			       (array-ref
-				(contract-arrays
-				 (apply
-				  produce-typed-array
-				  (lambda ks
-				    (apply jacobian-generator
-					   naked-inputs ks data))
-				  *atype*
-				  (array-dimensions fwd))
-				 b (array-rank fwd))))
-			      ((and (array? output) (number? fwd))
-			       (apply
-				produce-typed-array
-				(lambda is
-				  ((extend *)
-				   (apply jacobian-generator
-					  naked-inputs is data)
-				   b))
-				*atype*
-				(array-dimensions output)))
-			      (else
-			       (apply
-				produce-typed-array
-				(lambda is
-				  (array-ref
-				   (contract-arrays
-				    (apply
-				     produce-typed-array
-				     (lambda ks
-				       (apply jacobian-generator
-					      naked-inputs
-					      (append is ks)
-					      data))
-				     *atype*
-				     (array-dimensions fwd))
-				    b (array-rank fwd))))
-				*atype*
-				(array-dimensions output)))))))))
-	      #f jacobian-generators inputs)
-	     (if (number? output)
-		 0
-		 (apply make-typed-array *atype* 0 (array-dimensions output)))))))))
+	 out
+	 (let* ((data (if (procedure? proc*)
+			  '()
+			  (map (lambda (g)
+				 (apply g naked-args))
+			       (cdr proc*))))
+		(n-out-dims (apply * (dims-of out)))
+		(buf (make-array *unspecified* n-out-dims)))
+	   (make-internal
+	    out
+	    (fold
+	     (lambda (generator arg prev)
+	       (if (or (not (internal? arg))
+		       (eq? 'zero (internal-jacobian arg)))
+		   prev
+		   (let ((Jx (internal-jacobian arg))
+			 (n-fwd-dims (apply * (dims-of (unwrap-fwd arg)))))
+		     (if (eq? Jx 'input)
+			 (if (eq? prev 'zero)
+			     (delay
+			       (mov buf n-out-dims
+				    generator naked-args data (*j*)))
+			     (delay
+			       (add (force prev) n-out-dims
+				    generator naked-args data (*j*))))
+			 (if (eq? prev 'zero)
+			     (delay
+			       (movc buf n-out-dims (force Jx) n-fwd-dims
+				     generator naked-args data))
+			     (delay
+			       (addc (force prev) n-out-dims
+				     (force Jx) n-fwd-dims
+				     generator naked-args data)))))))
+	     'zero generators args))))))
 
 (define (ewise1 f)
-  (lambda (xs indices)
+  (lambda (xs i j)
     (let ((x (car xs)))
       (if (number? x)
 	  (f x)
-	  (receive (is js) (split-at indices (array-rank x))
-	    (if (equal? is js)
-		(f (apply array-ref x is))
-		0))))))
+	  (ifn (= i j)
+	       0
+	       (f (array-ref (array-contents x)
+			     j)))))))
 
 (define (ewise2 proc axis)
-  (lambda (xs indices)
+  (lambda (xs i j)
     (let ((x (car xs))
 	  (y (cadr xs)))
       (cond
@@ -329,25 +378,29 @@ element-wise. All arrays must have the same dimension."
 	(proc x y))
        ((and (number? x) (array? y))
 	(if (= axis 0)
-	    (proc x (apply array-ref y indices))
-	    (receive (is js) (split-at indices (array-rank y))
-	      (ifn (equal? is js)
-		   0
-		   (proc x (apply array-ref y is))))))
+	    (proc x (array-ref (array-contents y)
+			       i))
+	    (ifn (= i j)
+		 0
+		 (proc x (array-ref (array-contents y)
+				    j)))))
        ((and (array? x) (number? y))
 	(if (= axis 1)
-	    (proc (apply array-ref x indices) y)
-	    (receive (is js) (split-at indices (array-rank x))
-	      (ifn (equal? is js)
-		   0
-		   (proc (apply array-ref x is)
-			 y)))))
+	    (proc (array-ref (array-contents x)
+			     i)
+		  y)
+	    (ifn (= i j)
+		 0
+		 (proc (array-ref (array-contents x)
+				  j)
+		       y))))
        (else
-	(receive (is js) (split-at indices (array-rank x))
-	  (ifn (equal? is js)
-	       0
-	       (proc (apply array-ref x is)
-		     (apply array-ref y is)))))))))
+	(ifn (= i j)
+	     0
+	     (proc (array-ref (array-contents x)
+			      j)
+		   (array-ref (array-contents y)
+			      j))))))))
 
 (define (i:identity x)
   "Differentiable identity."
@@ -493,19 +546,19 @@ element-wise. All arrays must have the same dimension."
   "Differentiable mean on arrays."
   (differentiable-wrapper
    (list
-    (lambda (xs indices one-over-n)
+    (lambda (xs i j one-over-n)
       one-over-n))
    (let ((n 0))
-    (list
-     (lambda (x)
-       (let ((sum 0))
-	 (array-for-each
-	  (lambda (x)
-	    (set! sum (+ sum x))
-	    (set! n (1+ n)))
-	  x)
-	 (/ sum n)))
-     (lambda _ (/ n))))
+     (list
+      (lambda (x)
+	(let ((sum 0))
+	  (array-for-each
+	   (lambda (x)
+	     (set! sum (+ sum x))
+	     (set! n (1+ n)))
+	   x)
+	  (/ sum n)))
+      (lambda _ (/ n))))
    x))
 
 (define (i:array-ref x . indices)
@@ -513,20 +566,72 @@ element-wise. All arrays must have the same dimension."
   (apply
    differentiable-wrapper
    (cons
-    (lambda (xs js)
-      (if (equal? js indices)
+    (lambda (xs i j abs-index)
+      (if (= j abs-index)
 	  1
 	  0))
-    (list-tabulate (length indices) not))
-   array-ref
+    (map not indices))
+   (list
+    array-ref
+    (lambda (x . indices)
+      (rel->abs indices (array-dimensions x))))
+   x indices))
+
+(define (i:array-cell-ref x . indices)
+  (apply
+   differentiable-wrapper
+   (cons
+    (lambda (xs i j abs-index n-rst-dims)
+      (receive (j-ref j-rst) (euclidean/ j n-rst-dims)
+	(if (and (= j-ref abs-index)
+		 (= j-rst i))
+	    1
+	    0)))
+    (map not indices))
+   (list
+    array-cell-ref
+    (lambda (x . indices)
+      (rel->abs indices (take (array-dimensions x)
+			      (length indices))))
+    (lambda (x . indices)
+      (apply * (drop (array-dimensions x)
+		     (length indices)))))
    x indices))
 
+(define (make-batch elem . more)
+  (let ((batch-size (1+ (length more))))
+    (apply
+     differentiable-wrapper
+     (list-tabulate
+      batch-size
+      (lambda (b)
+	(lambda (xs i j n-rest-dims)
+	  (receive (i-batch i-rest) (euclidean/ i n-rest-dims)
+	    (if (and (= i-batch b)
+		     (= i-rest j))
+		1
+		0
+		)))))
+     (list
+      (lambda (elem . more)
+	(let ((a (apply make-typed-array *atype* *unspecified* batch-size
+			(dims-of elem))))
+	  (for-each
+	   (lambda (x b)
+	     (array-cell-set! a x b))
+	   (cons elem more)
+	   (list-tabulate batch-size identity))
+	  a))
+      (lambda (elem . more)
+	(apply * (dims-of elem))))
+     elem more)))
+
 (define (maximum x)
   "Differentiable maximum on arrays."
   (differentiable-wrapper
    (list
-    (lambda (xs indices max-indices)
-      (if (equal? indices max-indices)
+    (lambda (xs i j max-index)
+      (if (= j max-index)
 	  1
 	  0)))
    (let ((max-index 'TBD))
@@ -542,8 +647,7 @@ element-wise. All arrays must have the same dimension."
 	     (set! i (1+ i)))
 	   x)
 	  m))
-      (lambda (x)
-	(abs->rel max-index (array-dimensions x)))))
+      (lambda _ max-index)))
    x))
 
 (define (sum x)
@@ -559,115 +663,37 @@ element-wise. All arrays must have the same dimension."
        sum))
    x))
 
-(define (amap2 f x y)
-  (define (unbox-with proc x)
-    (ifn (internal? x)
-	 x
-	 (proc x)))
-  (define (dims-of x)
-    (if (number? x)
-	'()
-	(array-dimensions x)))
-  (define (boxed-ref x i)
-    (let ((xi (array-cell-ref (unbox-with internal-forward x)
-			      i)))
-      (ifn (internal? x)
-	   xi
-	   (make-internal
-	    xi
-	    (if (internal-jacobian x)
-		(lambda (js)
-		  (array-cell-ref
-		   ((internal-jacobian x)
-		    js)
-		   i))
-		(lambda (js)
-		  (if (number? xi)
-		      (if (= i (car js))
-			  1
-			  0)
-		      (apply
-		       produce-typed-array
-		       (lambda indices
-			 (if (and (= i (car js))
-				  (equal? indices (cdr js)))
-			     1
-			     0))
-		       (array-type xi)
-		       (array-dimensions xi)))))))))
-  (define (boxed-fi f i x y)
-    (f (boxed-ref x i)
-       (boxed-ref y i)))
-  (if (internal? f)
-      (error "unsupported application of `amap2' to internal object" f)
-      (let ((bs (first (array-dimensions (unbox-with internal-forward x))))
-	    (f0 (boxed-fi f 0 x y)))
-	(ifn (internal? f0)
-	     (let ((fwd (apply make-typed-array
-			       ;; TODO: use the correct type based on f0.
-			       *atype* *unspecified* bs (dims-of f0))))
-	       (for-indices-in-range
-		(lambda (i)
-		  (array-cell-set! fwd (boxed-fi f i x y) i))
-		'(0) (list bs))
-	       fwd)
-	     (let ((jac (make-array *unspecified* bs))
-		   (fwd (apply make-typed-array
-			       ;; TODO: use the correct type based on f0.
-			       *atype* *unspecified*
-			       bs (dims-of (internal-forward f0)))))
-	       (for-indices-in-range
-		(lambda (i)
-		  (let* ((fi (boxed-fi f i x y))
-			 (Jfi (internal-jacobian fi)))
-		    (array-set! jac (internal-jacobian fi) i)
-		    (array-cell-set! fwd (internal-forward fi) i)))
-		'(0) (list bs))
-	       (make-internal
-		fwd
-		(lambda (js)
-		  (let ((a (apply make-typed-array
-				  ;; TODO: use the correct type based on f0.
-				  *atype* *unspecified*
-				  bs (dims-of (internal-forward f0)))))
-		    (for-indices-in-range
-		     (lambda (batch)
-		       (array-cell-set!
-			a ((array-ref jac batch) js)
-			batch))
-		     '(0) (list bs))
-		    a))))))))
-
 (define (adot x y n)
   (differentiable-wrapper
    (list
-    (lambda (xs indices free-rank-x free-rank-y)
-      (let* ((y (cadr xs))
-	     (n (caddr xs))
-	     (out (take indices (+ free-rank-x free-rank-y)))
-	     (in (drop indices (+ free-rank-x free-rank-y)))
-	     (is-free1 (take out free-rank-x))
-	     (js-free (drop out free-rank-x))
-	     (is-free2 (take in free-rank-x))
-	     (is-bound (drop in free-rank-x)))
-	(ifn (equal? is-free1 is-free2)
-	     0
-	     (apply array-ref y (append is-bound js-free)))))
-    (lambda (xs indices free-rank-x free-rank-y)
-      (let* ((x (car xs))
-	     (n (caddr xs))
-	     (out (take indices (+ free-rank-x free-rank-y)))
-	     (in (drop indices (+ free-rank-x free-rank-y)))
-	     (is-free (take out free-rank-x))
-	     (js-free1 (drop out free-rank-x))
-	     (js-free2 (drop in n))
-	     (js-bound (take in n)))
-	(ifn (equal? js-free1 js-free2)
-	     0
-	     (apply array-ref x (append is-free js-bound)))))
+    (lambda (xs i j n-free-dims-y n-bound-dims)
+      (receive (i-x i-y) (euclidean/ i n-free-dims-y)
+	(receive (j-free j-bound) (euclidean/ j n-bound-dims)
+	  (ifn (= i-x j-free)
+	       0
+	       (array-ref (array-contents (cadr xs))
+			  (+ i-y (* n-free-dims-y j-bound)))))))
+    (lambda (xs i j n-free-dims-y n-bound-dims)
+      (receive (i-x i-y) (euclidean/ i n-free-dims-y)
+	(receive (j-bound j-free) (euclidean/ j n-free-dims-y)
+	  (ifn (= i-y j-free)
+	       0
+	       (array-ref (array-contents (car xs))
+			  (+ j-bound (* n-bound-dims i-x)))))))
     #f)
    (list
     contract-arrays
-    (lambda (x y n) (- (array-rank x) n))
-    (lambda (x y n) (- (array-rank y) n)))
+    (lambda (x y n)
+      (apply * (drop (array-dimensions y)
+		     n)))
+    (lambda (x y n)
+      (apply * (take (array-dimensions y)
+		     n))))
    x y n))
+
+(define (amap2 f x y)
+  (apply make-batch
+	 (list-tabulate (car (dims-of (unwrap-fwd x)))
+			(lambda (b)
+			  (f (i:array-cell-ref x b)
+			     (i:array-cell-ref y b))))))
diff --git a/misc.scm b/misc.scm
index 0437d7c..88f0073 100644
--- a/misc.scm
+++ b/misc.scm
@@ -46,14 +46,14 @@ order."
 (define (for-indices-in-range f starts ends)
   (define (for-indices-in-range% f indices starts ends)
     (if (null? starts)
-      (apply f (reverse indices))
-      (do ((i (car starts) (1+ i)))
-        ((= i (car ends)))
-        (for-indices-in-range%
-          f
-          (cons i indices)
-          (cdr starts)
-          (cdr ends)))))
+	(apply f (reverse indices))
+	(do ((i (car starts) (1+ i)))
+	    ((= i (car ends)))
+	  (for-indices-in-range%
+	   f
+           (cons i indices)
+           (cdr starts)
+           (cdr ends)))))
   (for-indices-in-range% f '() starts ends))
 
 ;;;; array utilities