;;; array
;;; 1997 - 2001 Jussi Piitulainen


;; This file is the result of
;; cat array.scm as-srfi-9-record.scm ix-ctor.scm op-ctor.scm > srfi-25.scm


;;; --- Intro ---

;;; This interface to arrays is based on Alan Bawden's array.scm of
;;; 1993 (earlier version in the Internet Repository and another
;;; version in SLIB). This is a complete rewrite, to be consistent
;;; with the rest of Scheme and to make arrays independent of lists.

;;; Some modifications are due to discussion in srfi-25 mailing list.

;;; (array? obj)
;;; (make-array shape [obj])             changed arguments
;;; (shape bound ...)                    new
;;; (array shape obj ...)                new
;;; (array-rank array)                   changed name back
;;; (array-start array dimension)        new
;;; (array-end array dimension)          new
;;; (array-ref array k ...)
;;; (array-ref array index)              new variant
;;; (array-set! array k ... obj)         changed argument order
;;; (array-set! array index obj)         new variant
;;; (share-array array shape proc)       changed arguments

;;; All other variables in this file have names in "array:".

;;; Should there be a way to make arrays with initial values mapped
;;; from indices? Sure. The current "initial object" is lame.
;;;
;;; Removed (array-shape array) from here. There is a new version
;;; in arlib though.

;;; --- Representation type dependencies ---

;;; The mapping from array indices to the index to the underlying vector
;;; is whatever array:optimize returns. The file "opt" provides three
;;; representations:
;;; 
;;; mbda) mapping is a procedure that allows an optional argument
;;; tter) mapping is two procedures that takes exactly the indices
;;; ctor) mapping is a vector of a constant term and coefficients
;;;
;;; Choose one in "opt" to make the optimizer. Then choose the matching
;;; implementation of array-ref and array-set!.
;;;
;;; These should be made macros to inline them. Or have a good compiler
;;; and plant the package as a module.

;;; 1. Pick an optimizer.
;;; 2. Pick matching index representation.
;;; 3. Pick a record implementation; as-procedure is generic; syntax inlines.
;;; 3. This file is otherwise portable.

;;; --- Portable R5RS (R4RS and multiple values) ---

;;; (array? obj)
;;; returns #t if `obj' is an array and #t or #f otherwise.

(define (array? obj)
   (array:array? obj))

;;; (make-array shape)
;;; (make-array shape obj)
;;; makes array of `shape' with each cell containing `obj' initially.

(define (make-array shape . rest)
  (or (array:good-shape? shape)
      (error "make-array: shape is not a shape"))
  (apply array:make-array shape rest))

(define (array:make-array shape . rest)
  (let ((size (array:size shape)))
    (array:make
     (if (pair? rest)
         (apply (lambda (o) (make-vector size o)) rest)
         (make-vector size))
     (if (= size 0)
         (array:optimize-empty
          (vector-ref (array:shape shape) 1))
         (array:optimize
          (array:make-index shape)
          (vector-ref (array:shape shape) 1)))
     (array:shape->vector shape))))

;;; (shape bound ...)
;;; makes a shape. Bounds must be an even number of exact, pairwise
;;; non-decreasing integers. Note that any such array can be a shape.

(define (shape . bounds)
  (let ((v (list->vector bounds)))
    (or (even? (vector-length v))
        (error (string-append "shape: uneven number of bounds: "
                              (array:list->string bounds))))
    (let ((shp (array:make
                v
                (if (pair? bounds)
                    (array:shape-index)
                    (array:empty-shape-index))
                (vector 0 (quotient (vector-length v) 2)
                        0 2))))
      (or (array:good-shape? shp)
          (error (string-append "shape: bounds are not pairwise "
                                "non-decreasing exact integers: "
                                (array:list->string bounds))))
      shp)))

;;; (array shape obj ...)
;;; is analogous to `vector'.

(define (array shape . elts)
  (or (array:good-shape? shape)
      (error (string-append "array: shape " (array:thing->string shape)
                            " is not a shape")))
  (let ((size (array:size shape)))
    (let ((vector (list->vector elts)))
      (or (= (vector-length vector) size)
          (error (string-append "array: an array of shape "
                                (array:shape-vector->string
                                 (array:vector shape))
                                " has "
                                (number->string size)
                                " elements but got "
                                (number->string (vector-length vector))
                                " values: "
                                (array:list->string elts))))
      (array:make
       vector
       (if (= size 0)
           (array:optimize-empty
            (vector-ref (array:shape shape) 1))
           (array:optimize
            (array:make-index shape)
            (vector-ref (array:shape shape) 1)))
       (array:shape->vector shape)))))

;;; (array-rank array)
;;; returns the number of dimensions of `array'.

(define (array-rank array)
   (quotient (vector-length (array:shape array)) 2))

;;; (array-start array k)
;;; returns the lower bound index of array along dimension k. This is
;;; the least valid index along that dimension if the dimension is not
;;; empty.

(define (array-start array d)
  (vector-ref (array:shape array) (+ d d)))

;;; (array-end array k)
;;; returns the upper bound index of array along dimension k. This is
;;; not a valid index. If the dimension is empty, this is the same as
;;; the lower bound along it.

(define (array-end array d)
  (vector-ref (array:shape array) (+ d d 1)))

;;; (share-array array shape proc)
;;; makes an array that shares elements of `array' at shape `shape'.
;;; The arguments to `proc' are indices of the result.  The values of
;;; `proc' are indices of `array'.

;;; Todo: in the error message, should recognise the mapping and show it.

(define (share-array array subshape f)
  (or (array:good-shape? subshape)
      (error (string-append "share-array: shape "
                            (array:thing->string subshape)
                            " is not a shape")))
  (let ((subsize (array:size subshape)))
    (or (array:good-share? subshape subsize f (array:shape array))
        (error (string-append "share-array: subshape "
                              (array:shape-vector->string
                               (array:vector subshape))
                              " does not map into supershape "
                              (array:shape-vector->string
                               (array:shape array))
                              " under mapping "
                              (array:map->string
                               f
                               (vector-ref (array:shape subshape) 1)))))    
    (let ((g (array:index array)))
      (array:make
       (array:vector array)
       (if (= subsize 0)
           (array:optimize-empty
            (vector-ref (array:shape subshape) 1))
           (array:optimize
            (lambda ks
              (call-with-values
               (lambda () (apply f ks))
               (lambda ks (array:vector-index g ks))))
            (vector-ref (array:shape subshape) 1)))
       (array:shape->vector subshape)))))

;;; --- Hrmph ---

;;; (array:share/index! ...)
;;; reuses a user supplied index object when recognising the
;;; mapping. The mind balks at the very nasty side effect that
;;; exposes the implementation. So this is not in the spec.
;;; But letting index objects in at all creates a pressure
;;; to go the whole hog. Arf.

;;; Use array:optimize-empty for an empty array to get a
;;; clearly invalid vector index.

;;; Surely it's perverse to use an actor for index here? But
;;; the possibility is provided for completeness.

(define (array:share/index! array subshape proc index)
  (array:make
   (array:vector array)
   (if (= (array:size subshape) 0)
       (array:optimize-empty
        (quotient (vector-length (array:shape array)) 2))
       ((if (vector? index)
            array:optimize/vector
            array:optimize/actor)
        (lambda (subindex)
          (let ((superindex (proc subindex)))
            (if (vector? superindex)
                (array:index/vector
                 (quotient (vector-length (array:shape array)) 2)
                 (array:index array)
                 superindex)
                (array:index/array
                 (quotient (vector-length (array:shape array)) 2)
                 (array:index array)
                 (array:vector superindex)
                 (array:index superindex)))))
        index))
   (array:shape->vector subshape)))

(define (array:optimize/vector f v)
  (let ((r (vector-length v)))
    (do ((k 0 (+ k 1)))
      ((= k r))
      (vector-set! v k 0))
    (let ((n0 (f v))
          (cs (make-vector (+ r 1)))
          (apply (array:applier-to-vector (+ r 1))))
      (vector-set! cs 0 n0)
      (let wok ((k 0))
        (if (< k r)
            (let ((k1 (+ k 1)))
              (vector-set! v k 1)
              (let ((nk (- (f v) n0)))
                (vector-set! v k 0)
                (vector-set! cs k1 nk)
                (wok k1)))))
      (apply (array:maker r) cs))))

(define (array:optimize/actor f a)
  (let ((r (array-end a 0))
        (v (array:vector a))
        (i (array:index a)))
    (do ((k 0 (+ k 1)))
      ((= k r))
      (vector-set! v (array:actor-index i k) 0))
    (let ((n0 (f a))
          (cs (make-vector (+ r 1)))
          (apply (array:applier-to-vector (+ r 1))))
      (vector-set! cs 0 n0)
      (let wok ((k 0))
        (if (< k r)
            (let ((k1 (+ k 1))
                  (t (array:actor-index i k)))
              (vector-set! v t 1)
              (let ((nk (- (f a) n0)))
                (vector-set! v t 0)
                (vector-set! cs k1 nk)
                (wok k1)))))
      (apply (array:maker r) cs))))

;;; --- Internals ---

(define (array:shape->vector shape)
  (let ((idx (array:index shape))
        (shv (array:vector shape))
        (rnk (vector-ref (array:shape shape) 1)))
    (let ((vec (make-vector (* rnk 2))))
      (do ((k 0 (+ k 1)))
        ((= k rnk)
         vec)
        (vector-set! vec (+ k k)
                     (vector-ref shv (array:shape-vector-index idx k 0)))
        (vector-set! vec (+ k k 1)
                     (vector-ref shv (array:shape-vector-index idx k 1)))))))

;;; (array:size shape)
;;; returns the number of elements in arrays of shape `shape'.

(define (array:size shape)
   (let ((idx (array:index shape))
         (shv (array:vector shape))
         (rnk (vector-ref (array:shape shape) 1)))
     (do   ((k 0 (+ k 1))
            (s 1 (* s
                    (- (vector-ref shv (array:shape-vector-index idx k 1))
                       (vector-ref shv (array:shape-vector-index idx k 0))))))
       ((= k rnk) s))))

;;; (array:make-index shape)
;;; returns an index function for arrays of shape `shape'. This is a
;;; runtime composition of several variable arity procedures, to be
;;; passed to array:optimize for recognition as an affine function of
;;; as many variables as there are dimensions in arrays of this shape.

(define (array:make-index shape)
   (let ((idx (array:index shape))
         (shv (array:vector shape))
         (rnk (vector-ref (array:shape shape) 1)))
     (do ((f (lambda () 0)
             (lambda (k . ks)
               (+ (* s (- k (vector-ref
                             shv
                             (array:shape-vector-index idx (- j 1) 0))))
                  (apply f ks))))
          (s 1 (* s (- (vector-ref
                        shv
                        (array:shape-vector-index idx (- j 1) 1))
                       (vector-ref
                        shv
                        (array:shape-vector-index idx (- j 1) 0)))))
          (j rnk (- j 1)))
       ((= j 0)
        f))))


;;; --- Error checking ---

;;; (array:good-shape? shape)
;;; returns true if `shape' is an array of the right shape and its
;;; elements are exact integers that pairwise bound intervals `[lo..hi)´.

(define (array:good-shape? shape)
  (and (array:array? shape)
       (let ((u (array:shape shape))
             (v (array:vector shape))
             (x (array:index shape)))
         (and (= (vector-length u) 4)
              (= (vector-ref u 0) 0)
              (= (vector-ref u 2) 0)
              (= (vector-ref u 3) 2))
         (let ((p (vector-ref u 1)))
           (do ((k 0 (+ k 1))
                (true #t (let ((lo (vector-ref
                                    v
                                    (array:shape-vector-index x k 0)))
                               (hi (vector-ref
                                    v
                                    (array:shape-vector-index x k 1))))
                           (and true
                                (integer? lo)
                                (exact? lo)
                                (integer? hi)
                                (exact? hi)
                                (<= lo hi)))))
             ((= k p) true))))))

;;; (array:good-share? subv subsize mapping superv)
;;; returns true if the extreme indices in the subshape vector map
;;; into the bounds in the supershape vector.

;;; If some interval in `subv' is empty, then `subv' is empty and its
;;; image under `f' is empty and it is trivially alright.  One must
;;; not call `f', though.

(define (array:good-share? subshape subsize f super)
  (or (zero? subsize)
      (letrec
          ((sub (array:vector subshape))
           (dex (array:index subshape))
           (ck (lambda (k ks)
		 (if (zero? k)
                     (call-with-values
                      (lambda () (apply f ks))
                      (lambda qs (array:good-indices? qs super)))
                     (and (ck (- k 1)
                              (cons (vector-ref
                                     sub
                                     (array:shape-vector-index
                                      dex
                                      (- k 1)
                                      0))
                                    ks))
                          (ck (- k 1)
                              (cons (- (vector-ref
                                        sub
                                        (array:shape-vector-index
                                         dex
                                         (- k 1)
                                         1))
                                       1)
                                    ks)))))))
        (let ((rnk (vector-ref (array:shape subshape) 1)))
          (or (array:unchecked-share-depth? rnk)
              (ck rnk '()))))))

;;; Check good-share on 10 dimensions at most. The trouble is,
;;; the cost of this check is exponential in the number of dimensions.

(define (array:unchecked-share-depth? rank)
  (if (> rank 10)
      (begin
        (display `(warning: unchecked depth in share:
                            ,rank subdimensions))
        (newline)
        #t)
      #f))

;;; (array:check-indices caller indices shape-vector)
;;; (array:check-indices.o caller indices shape-vector)
;;; (array:check-index-vector caller index-vector shape-vector)
;;; return if the index is in bounds, else signal error.
;;;
;;; Shape-vector is the internal representation, with
;;; b and e for dimension k at 2k and 2k + 1.

(define (array:check-indices who ks shv)
  (or (array:good-indices? ks shv)
      (error (array:not-in who ks shv))))

(define (array:check-indices.o who ks shv)
  (or (array:good-indices.o? ks shv)
      (error (array:not-in who (reverse (cdr (reverse ks))) shv))))

(define (array:check-index-vector who ks shv)
  (or (array:good-index-vector? ks shv)
      (error (array:not-in who (vector->list ks) shv))))

(define (array:check-index-actor who ks shv)
  (let ((shape (array:shape ks)))
    (or (and (= (vector-length shape) 2)
             (= (vector-ref shape 0) 0))
        (error "not an actor"))
    (or (array:good-index-actor?
         (vector-ref shape 1)
         (array:vector ks)
         (array:index ks)
         shv)
        (array:not-in who (do ((k (vector-ref shape 1) (- k 1))
                               (m '() (cons (vector-ref
                                             (array:vector ks)
                                             (array:actor-index
                                              (array:index ks)
                                              (- k 1)))
                                            m)))
                            ((= k 0) m))
                      shv))))

(define (array:good-indices? ks shv)
   (let ((d2 (vector-length shv)))
      (do ((kp ks (if (pair? kp)
                      (cdr kp)))
           (k 0 (+ k 2))
           (true #t (and true (pair? kp)
                         (array:good-index? (car kp) shv k))))
        ((= k d2)
         (and true (null? kp))))))

(define (array:good-indices.o? ks.o shv)
   (let ((d2 (vector-length shv)))
     (do   ((kp ks.o (if (pair? kp)
                         (cdr kp)))
            (k 0 (+ k 2))
            (true #t (and true (pair? kp)
                          (array:good-index? (car kp) shv k))))
       ((= k d2)
        (and true (pair? kp) (null? (cdr kp)))))))

(define (array:good-index-vector? ks shv)
  (let ((r2 (vector-length shv)))
    (and (= (* 2 (vector-length ks)) r2)
         (do ((j 0 (+ j 1))
              (k 0 (+ k 2))
              (true #t (and true
                            (array:good-index? (vector-ref ks j) shv k))))
           ((= k r2) true)))))

(define (array:good-index-actor? r v i shv)
  (and (= (* 2 r) (vector-length shv))
       (do ((j 0 (+ j 1))
            (k 0 (+ k 2))
            (true #t (and true
                          (array:good-index? (vector-ref
                                              v
                                              (array:actor-index i j))
                                             shv
                                             k))))
         ((= j r) true))))

;;; (array:good-index? index shape-vector 2d)
;;; returns true if index is within bounds for dimension 2d/2.

(define (array:good-index? w shv k)
  (and (integer? w)
       (exact? w)
       (<= (vector-ref shv k) w)
       (< w (vector-ref shv (+ k 1)))))

(define (array:not-in who ks shv)
  (let ((index (array:list->string ks))
        (bounds (array:shape-vector->string shv)))
    (error (string-append who
                          ": index " index
                          " not in bounds " bounds))))

(define (array:list->string ks)
  (do ((index "" (string-append index (array:thing->string (car ks)) " "))
       (ks ks (cdr ks)))
    ((null? ks) index)))

(define (array:shape-vector->string shv)
  (do ((bounds "" (string-append bounds
                                 "["
                                 (number->string (vector-ref shv t))
                                 ".."
                                 (number->string (vector-ref shv (+ t 1)))
                                 ")"
                                 " "))
       (t 0 (+ t 2)))
    ((= t (vector-length shv)) bounds)))

(define (array:thing->string thing)
  (cond
    ((number? thing) (number->string thing))
    ((symbol? thing) (string-append "#<symbol>" (symbol->string thing)))
    ((char? thing) "#<char>")
    ((string? thing) "#<string>")
    ((list? thing) (string-append "#" (number->string (length thing))
                                  "<list>"))
                                  
    ((pair? thing) "#<pair>")
    ((array? thing) "#<array>")
    ((vector? thing) (string-append "#" (number->string
                                         (vector-length thing))
                                    "<vector>"))
    ((procedure? thing) "#<procedure>")
    (else
     (case thing
       ((()) "()")
       ((#t) "#t")
       ((#f) "#f")
       (else
        "#<whatsit>")))))

;;; And to grok an affine map, vector->vector type. Column k of arr
;;; will contain coefficients n0 ... nm of 1 k1 ... km for kth value.
;;; 
;;; These are for the error message when share fails.

(define (array:index-ref ind k)
  (if (vector? ind)
      (vector-ref ind k)
      (vector-ref
       (array:vector ind)
       (array:actor-index (array:index ind) k))))

(define (array:index-set! ind k o)
  (if (vector? ind)
      (vector-set! ind k o)
      (vector-set!
       (array:vector ind)
       (array:actor-index (array:index ind) k)
       o)))

(define (array:index-length ind)
  (if (vector? ind)
      (vector-length ind)
      (vector-ref (array:shape ind) 1)))

(define (array:map->string proc r)
  (let* ((m (array:grok/arguments proc r))
         (s (vector-ref (array:shape m) 3)))
    (do ((i "" (string-append i c "k" (number->string k)))
         (c "" ", ")
         (k 1 (+ k 1)))
      ((< r k)
       (do ((o "" (string-append o c (array:map-column->string m r k)))
            (c "" ", ")
            (k 0 (+ k 1)))
         ((= k s)
          (string-append i " => " o)))))))

(define (array:map-column->string m r k)
  (let ((v (array:vector m))
        (i (array:index m)))
    (let ((n0 (vector-ref v (array:vector-index i (list 0 k)))))
      (let wok ((j 1)
                (e (if (= n0 0) "" (number->string n0))))
        (if (<= j r)
            (let ((nj (vector-ref v (array:vector-index i (list j k)))))
              (if (= nj 0)
                  (wok (+ j 1) e)
                  (let* ((nj (if (= nj 1) ""
                                 (if (= nj -1) "-"
                                     (string-append (number->string nj)
                                                    " "))))
                         (njkj (string-append nj "k" (number->string j))))
                    (if (string=? e "")
                        (wok (+ j 1) njkj)
                        (wok (+ j 1) (string-append e " + " njkj))))))
            (if (string=? e "") "0" e))))))

(define (array:grok/arguments proc r)
  (array:grok/index!
   (lambda (vec)
     (call-with-values
      (lambda ()
        (array:apply-to-vector r proc vec))
      vector))
   (make-vector r)))

(define (array:grok/index! proc in)
  (let ((m (array:index-length in)))
    (do ((k 0 (+ k 1)))
      ((= k m))
      (array:index-set! in k 0))
    (let* ((n0 (proc in))
           (n (array:index-length n0)))
      (let ((arr (make-array (shape 0 (+ m 1) 0 n))))  ; (*)
        (do ((k 0 (+ k 1)))
          ((= k n))
          (array-set! arr 0 k (array:index-ref n0 k))) ; (**)
        (do ((j 0 (+ j 1)))
          ((= j m))
          (array:index-set! in j 1)
          (let ((nj (proc in)))
            (array:index-set! in j 0)
            (do ((k 0 (+ k 1)))
              ((= k n))
              (array-set! arr (+ j 1) k (- (array:index-ref nj k) ; (**)
                                           (array:index-ref n0 k))))))
        arr))))
;; (*)  Should not use `make-array' and `shape' here
;; (**) Should not use `array-set!' here
;; Should use something internal to the library instead: either lower
;; level code (preferable but complex) or alternative names to these same.
;;; array as-srfi-9-record
;;; 2001 Jussi Piitulainen

;;; Untested.

(define-record-type
 array:srfi-9-record-type-descriptor
 (array:make vec ind shp)
 array:array?
 (vec array:vector)
 (ind array:index)
 (shp array:shape))
(define (array-ref a . xs)
  (or (array:array? a)
      (error "not an array"))
  (let ((shape (array:shape a)))
    (if (null? xs)
        (array:check-indices "array-ref" xs shape)
        (let ((x (car xs)))
          (if (vector? x)
              (array:check-index-vector "array-ref" x shape)
              (if (integer? x)
                  (array:check-indices "array-ref" xs shape)
                  (if (array:array? x)
                      (array:check-index-actor "array-ref" x shape)
                      (error "not an index object"))))))
    (vector-ref
     (array:vector a)
     (if (null? xs)
         (vector-ref (array:index a) 0)
         (let ((x (car xs)))
           (if (vector? x)
               (array:index/vector
                (quotient (vector-length shape) 2)
                (array:index a)
                x)
               (if (integer? x)
                   (array:vector-index (array:index a) xs)
                   (if (array:array? x)
                       (array:index/array
                        (quotient (vector-length shape) 2)
                        (array:index a)
                        (array:vector x)
                        (array:index x))
                       (error "array-ref: bad index object")))))))))

(define (array-set! a x . xs)
  (or (array:array? a)
      (error "array-set!: not an array"))
  (let ((shape (array:shape a)))
    (if (null? xs)
        (array:check-indices "array-set!" '() shape)
        (if (vector? x)
            (array:check-index-vector "array-set!" x shape)
            (if (integer? x)
                (array:check-indices.o "array-set!" (cons x xs) shape)
                (if (array:array? x)
                    (array:check-index-actor "array-set!" x shape)
                    (error "not an index object")))))
    (if (null? xs)
        (vector-set! (array:vector a) (vector-ref (array:index a) 0) x)
        (if (vector? x)
            (vector-set! (array:vector a)
                         (array:index/vector
                          (quotient (vector-length shape) 2)
                          (array:index a)
                          x)
                         (car xs))
            (if (integer? x)
                (let ((v (array:vector a))
                      (i (array:index a))
                      (r (quotient (vector-length shape) 2)))
                  (do ((sum (* (vector-ref i 0) x)
                            (+ sum (* (vector-ref i k) (car ks))))
                       (ks xs (cdr ks))
                       (k 1 (+ k 1)))
                    ((= k r)
                     (vector-set! v (+ sum (vector-ref i k)) (car ks)))))
                (if (array:array? x)
                    (vector-set! (array:vector a)
                                 (array:index/array
                                  (quotient (vector-length shape) 2)
                                  (array:index a)
                                  (array:vector x)
                                  (array:index x))
                                 (car xs))
                    (error (string-append
                            "array-set!: bad index object: "
                            (array:thing->string x)))))))))
(begin
  (define array:opt-args '(ctor (4)))
  (define (array:optimize f r)
    (case r
      ((0) (let ((n0 (f))) (array:0 n0)))
      ((1) (let ((n0 (f 0))) (array:1 n0 (- (f 1) n0))))
      ((2)
       (let ((n0 (f 0 0)))
         (array:2 n0 (- (f 1 0) n0) (- (f 0 1) n0))))
      ((3)
       (let ((n0 (f 0 0 0)))
         (array:3
           n0
           (- (f 1 0 0) n0)
           (- (f 0 1 0) n0)
           (- (f 0 0 1) n0))))
      (else
       (let ((v
              (do ((k 0 (+ k 1)) (v '() (cons 0 v)))
                  ((= k r) v))))
         (let ((n0 (apply f v)))
           (apply
            array:n
            n0
            (array:coefficients f n0 v v)))))))
  (define (array:optimize-empty r)
    (let ((x (make-vector (+ r 1) 0)))
      (vector-set! x r -1)
      x))
  (define (array:coefficients f n0 vs vp)
    (case vp
      ((()) '())
      (else
       (set-car! vp 1)
       (let ((n (- (apply f vs) n0)))
         (set-car! vp 0)
         (cons n (array:coefficients f n0 vs (cdr vp)))))))
  (define (array:vector-index x ks)
    (do ((sum 0 (+ sum (* (vector-ref x k) (car ks))))
         (ks ks (cdr ks))
         (k 0 (+ k 1)))
        ((null? ks) (+ sum (vector-ref x k)))))
  (define (array:shape-index) '#(2 1 0))
  (define (array:empty-shape-index) '#(0 0 -1))
  (define (array:shape-vector-index x r k)
    (+
     (* (vector-ref x 0) r)
     (* (vector-ref x 1) k)
     (vector-ref x 2)))
  (define (array:actor-index x k)
    (+ (* (vector-ref x 0) k) (vector-ref x 1)))
  (define (array:0 n0) (vector n0))
  (define (array:1 n0 n1) (vector n1 n0))
  (define (array:2 n0 n1 n2) (vector n1 n2 n0))
  (define (array:3 n0 n1 n2 n3) (vector n1 n2 n3 n0))
  (define (array:n n0 n1 n2 n3 n4 . ns)
    (apply vector n1 n2 n3 n4 (append ns (list n0))))
  (define (array:maker r)
    (case r
      ((0) array:0)
      ((1) array:1)
      ((2) array:2)
      ((3) array:3)
      (else array:n)))
  (define array:indexer/vector
    (let ((em
           (vector
             (lambda (x i) (+ (vector-ref x 0)))
             (lambda (x i)
               (+
                (* (vector-ref x 0) (vector-ref i 0))
                (vector-ref x 1)))
             (lambda (x i)
               (+
                (* (vector-ref x 0) (vector-ref i 0))
                (* (vector-ref x 1) (vector-ref i 1))
                (vector-ref x 2)))
             (lambda (x i)
               (+
                (* (vector-ref x 0) (vector-ref i 0))
                (* (vector-ref x 1) (vector-ref i 1))
                (* (vector-ref x 2) (vector-ref i 2))
                (vector-ref x 3)))
             (lambda (x i)
               (+
                (* (vector-ref x 0) (vector-ref i 0))
                (* (vector-ref x 1) (vector-ref i 1))
                (* (vector-ref x 2) (vector-ref i 2))
                (* (vector-ref x 3) (vector-ref i 3))
                (vector-ref x 4)))
             (lambda (x i)
               (+
                (* (vector-ref x 0) (vector-ref i 0))
                (* (vector-ref x 1) (vector-ref i 1))
                (* (vector-ref x 2) (vector-ref i 2))
                (* (vector-ref x 3) (vector-ref i 3))
                (* (vector-ref x 4) (vector-ref i 4))
                (vector-ref x 5)))
             (lambda (x i)
               (+
                (* (vector-ref x 0) (vector-ref i 0))
                (* (vector-ref x 1) (vector-ref i 1))
                (* (vector-ref x 2) (vector-ref i 2))
                (* (vector-ref x 3) (vector-ref i 3))
                (* (vector-ref x 4) (vector-ref i 4))
                (* (vector-ref x 5) (vector-ref i 5))
                (vector-ref x 6)))
             (lambda (x i)
               (+
                (* (vector-ref x 0) (vector-ref i 0))
                (* (vector-ref x 1) (vector-ref i 1))
                (* (vector-ref x 2) (vector-ref i 2))
                (* (vector-ref x 3) (vector-ref i 3))
                (* (vector-ref x 4) (vector-ref i 4))
                (* (vector-ref x 5) (vector-ref i 5))
                (* (vector-ref x 6) (vector-ref i 6))
                (vector-ref x 7)))
             (lambda (x i)
               (+
                (* (vector-ref x 0) (vector-ref i 0))
                (* (vector-ref x 1) (vector-ref i 1))
                (* (vector-ref x 2) (vector-ref i 2))
                (* (vector-ref x 3) (vector-ref i 3))
                (* (vector-ref x 4) (vector-ref i 4))
                (* (vector-ref x 5) (vector-ref i 5))
                (* (vector-ref x 6) (vector-ref i 6))
                (* (vector-ref x 7) (vector-ref i 7))
                (vector-ref x 8)))
             (lambda (x i)
               (+
                (* (vector-ref x 0) (vector-ref i 0))
                (* (vector-ref x 1) (vector-ref i 1))
                (* (vector-ref x 2) (vector-ref i 2))
                (* (vector-ref x 3) (vector-ref i 3))
                (* (vector-ref x 4) (vector-ref i 4))
                (* (vector-ref x 5) (vector-ref i 5))
                (* (vector-ref x 6) (vector-ref i 6))
                (* (vector-ref x 7) (vector-ref i 7))
                (* (vector-ref x 8) (vector-ref i 8))
                (vector-ref x 9)))))
          (it
           (lambda (w)
             (lambda (x i)
               (+
                (* (vector-ref x 0) (vector-ref i 0))
                (* (vector-ref x 1) (vector-ref i 1))
                (* (vector-ref x 2) (vector-ref i 2))
                (* (vector-ref x 3) (vector-ref i 3))
                (* (vector-ref x 4) (vector-ref i 4))
                (* (vector-ref x 5) (vector-ref i 5))
                (* (vector-ref x 6) (vector-ref i 6))
                (* (vector-ref x 7) (vector-ref i 7))
                (* (vector-ref x 8) (vector-ref i 8))
                (* (vector-ref x 9) (vector-ref i 9))
                (do ((xi
                      0
                      (+
                       (* (vector-ref x u) (vector-ref i u))
                       xi))
                     (u (- w 1) (- u 1)))
                    ((< u 10) xi))
                (vector-ref x w))))))
      (lambda (r) (if (< r 10) (vector-ref em r) (it r)))))
  (define array:indexer/array
    (let ((em
           (vector
             (lambda (x v i) (+ (vector-ref x 0)))
             (lambda (x v i)
               (+
                (*
                 (vector-ref x 0)
                 (vector-ref v (array:actor-index i 0)))
                (vector-ref x 1)))
             (lambda (x v i)
               (+
                (*
                 (vector-ref x 0)
                 (vector-ref v (array:actor-index i 0)))
                (*
                 (vector-ref x 1)
                 (vector-ref v (array:actor-index i 1)))
                (vector-ref x 2)))
             (lambda (x v i)
               (+
                (*
                 (vector-ref x 0)
                 (vector-ref v (array:actor-index i 0)))
                (*
                 (vector-ref x 1)
                 (vector-ref v (array:actor-index i 1)))
                (*
                 (vector-ref x 2)
                 (vector-ref v (array:actor-index i 2)))
                (vector-ref x 3)))
             (lambda (x v i)
               (+
                (*
                 (vector-ref x 0)
                 (vector-ref v (array:actor-index i 0)))
                (*
                 (vector-ref x 1)
                 (vector-ref v (array:actor-index i 1)))
                (*
                 (vector-ref x 2)
                 (vector-ref v (array:actor-index i 2)))
                (*
                 (vector-ref x 3)
                 (vector-ref v (array:actor-index i 3)))
                (vector-ref x 4)))
             (lambda (x v i)
               (+
                (*
                 (vector-ref x 0)
                 (vector-ref v (array:actor-index i 0)))
                (*
                 (vector-ref x 1)
                 (vector-ref v (array:actor-index i 1)))
                (*
                 (vector-ref x 2)
                 (vector-ref v (array:actor-index i 2)))
                (*
                 (vector-ref x 3)
                 (vector-ref v (array:actor-index i 3)))
                (*
                 (vector-ref x 4)
                 (vector-ref v (array:actor-index i 4)))
                (vector-ref x 5)))
             (lambda (x v i)
               (+
                (*
                 (vector-ref x 0)
                 (vector-ref v (array:actor-index i 0)))
                (*
                 (vector-ref x 1)
                 (vector-ref v (array:actor-index i 1)))
                (*
                 (vector-ref x 2)
                 (vector-ref v (array:actor-index i 2)))
                (*
                 (vector-ref x 3)
                 (vector-ref v (array:actor-index i 3)))
                (*
                 (vector-ref x 4)
                 (vector-ref v (array:actor-index i 4)))
                (*
                 (vector-ref x 5)
                 (vector-ref v (array:actor-index i 5)))
                (vector-ref x 6)))
             (lambda (x v i)
               (+
                (*
                 (vector-ref x 0)
                 (vector-ref v (array:actor-index i 0)))
                (*
                 (vector-ref x 1)
                 (vector-ref v (array:actor-index i 1)))
                (*
                 (vector-ref x 2)
                 (vector-ref v (array:actor-index i 2)))
                (*
                 (vector-ref x 3)
                 (vector-ref v (array:actor-index i 3)))
                (*
                 (vector-ref x 4)
                 (vector-ref v (array:actor-index i 4)))
                (*
                 (vector-ref x 5)
                 (vector-ref v (array:actor-index i 5)))
                (*
                 (vector-ref x 6)
                 (vector-ref v (array:actor-index i 6)))
                (vector-ref x 7)))
             (lambda (x v i)
               (+
                (*
                 (vector-ref x 0)
                 (vector-ref v (array:actor-index i 0)))
                (*
                 (vector-ref x 1)
                 (vector-ref v (array:actor-index i 1)))
                (*
                 (vector-ref x 2)
                 (vector-ref v (array:actor-index i 2)))
                (*
                 (vector-ref x 3)
                 (vector-ref v (array:actor-index i 3)))
                (*
                 (vector-ref x 4)
                 (vector-ref v (array:actor-index i 4)))
                (*
                 (vector-ref x 5)
                 (vector-ref v (array:actor-index i 5)))
                (*
                 (vector-ref x 6)
                 (vector-ref v (array:actor-index i 6)))
                (*
                 (vector-ref x 7)
                 (vector-ref v (array:actor-index i 7)))
                (vector-ref x 8)))
             (lambda (x v i)
               (+
                (*
                 (vector-ref x 0)
                 (vector-ref v (array:actor-index i 0)))
                (*
                 (vector-ref x 1)
                 (vector-ref v (array:actor-index i 1)))
                (*
                 (vector-ref x 2)
                 (vector-ref v (array:actor-index i 2)))
                (*
                 (vector-ref x 3)
                 (vector-ref v (array:actor-index i 3)))
                (*
                 (vector-ref x 4)
                 (vector-ref v (array:actor-index i 4)))
                (*
                 (vector-ref x 5)
                 (vector-ref v (array:actor-index i 5)))
                (*
                 (vector-ref x 6)
                 (vector-ref v (array:actor-index i 6)))
                (*
                 (vector-ref x 7)
                 (vector-ref v (array:actor-index i 7)))
                (*
                 (vector-ref x 8)
                 (vector-ref v (array:actor-index i 8)))
                (vector-ref x 9)))))
          (it
           (lambda (w)
             (lambda (x v i)
               (+
                (*
                 (vector-ref x 0)
                 (vector-ref v (array:actor-index i 0)))
                (*
                 (vector-ref x 1)
                 (vector-ref v (array:actor-index i 1)))
                (*
                 (vector-ref x 2)
                 (vector-ref v (array:actor-index i 2)))
                (*
                 (vector-ref x 3)
                 (vector-ref v (array:actor-index i 3)))
                (*
                 (vector-ref x 4)
                 (vector-ref v (array:actor-index i 4)))
                (*
                 (vector-ref x 5)
                 (vector-ref v (array:actor-index i 5)))
                (*
                 (vector-ref x 6)
                 (vector-ref v (array:actor-index i 6)))
                (*
                 (vector-ref x 7)
                 (vector-ref v (array:actor-index i 7)))
                (*
                 (vector-ref x 8)
                 (vector-ref v (array:actor-index i 8)))
                (*
                 (vector-ref x 9)
                 (vector-ref v (array:actor-index i 9)))
                (do ((xi
                      0
                      (+
                       (*
                        (vector-ref x u)
                        (vector-ref
                          v
                          (array:actor-index i u)))
                       xi))
                     (u (- w 1) (- u 1)))
                    ((< u 10) xi))
                (vector-ref x w))))))
      (lambda (r) (if (< r 10) (vector-ref em r) (it r)))))
  (define array:applier-to-vector
    (let ((em
           (vector
             (lambda (p v) (p))
             (lambda (p v) (p (vector-ref v 0)))
             (lambda (p v)
               (p (vector-ref v 0) (vector-ref v 1)))
             (lambda (p v)
               (p
                (vector-ref v 0)
                (vector-ref v 1)
                (vector-ref v 2)))
             (lambda (p v)
               (p
                (vector-ref v 0)
                (vector-ref v 1)
                (vector-ref v 2)
                (vector-ref v 3)))
             (lambda (p v)
               (p
                (vector-ref v 0)
                (vector-ref v 1)
                (vector-ref v 2)
                (vector-ref v 3)
                (vector-ref v 4)))
             (lambda (p v)
               (p
                (vector-ref v 0)
                (vector-ref v 1)
                (vector-ref v 2)
                (vector-ref v 3)
                (vector-ref v 4)
                (vector-ref v 5)))
             (lambda (p v)
               (p
                (vector-ref v 0)
                (vector-ref v 1)
                (vector-ref v 2)
                (vector-ref v 3)
                (vector-ref v 4)
                (vector-ref v 5)
                (vector-ref v 6)))
             (lambda (p v)
               (p
                (vector-ref v 0)
                (vector-ref v 1)
                (vector-ref v 2)
                (vector-ref v 3)
                (vector-ref v 4)
                (vector-ref v 5)
                (vector-ref v 6)
                (vector-ref v 7)))
             (lambda (p v)
               (p
                (vector-ref v 0)
                (vector-ref v 1)
                (vector-ref v 2)
                (vector-ref v 3)
                (vector-ref v 4)
                (vector-ref v 5)
                (vector-ref v 6)
                (vector-ref v 7)
                (vector-ref v 8)))))
          (it
           (lambda (r)
             (lambda (p v)
               (apply
                p
                (vector-ref v 0)
                (vector-ref v 1)
                (vector-ref v 2)
                (vector-ref v 3)
                (vector-ref v 4)
                (vector-ref v 5)
                (vector-ref v 6)
                (vector-ref v 7)
                (vector-ref v 8)
                (vector-ref v 9)
                (do ((k r (- k 1))
                     (r
                      '()
                      (cons (vector-ref v (- k 1)) r)))
                    ((= k 10) r)))))))
      (lambda (r) (if (< r 10) (vector-ref em r) (it r)))))
  (define array:applier-to-actor
    (let ((em
           (vector
             (lambda (p a) (p))
             (lambda (p a) (p (array-ref a 0)))
             (lambda (p a)
               (p (array-ref a 0) (array-ref a 1)))
             (lambda (p a)
               (p
                (array-ref a 0)
                (array-ref a 1)
                (array-ref a 2)))
             (lambda (p a)
               (p
                (array-ref a 0)
                (array-ref a 1)
                (array-ref a 2)
                (array-ref a 3)))
             (lambda (p a)
               (p
                (array-ref a 0)
                (array-ref a 1)
                (array-ref a 2)
                (array-ref a 3)
                (array-ref a 4)))
             (lambda (p a)
               (p
                (array-ref a 0)
                (array-ref a 1)
                (array-ref a 2)
                (array-ref a 3)
                (array-ref a 4)
                (array-ref a 5)))
             (lambda (p a)
               (p
                (array-ref a 0)
                (array-ref a 1)
                (array-ref a 2)
                (array-ref a 3)
                (array-ref a 4)
                (array-ref a 5)
                (array-ref a 6)))
             (lambda (p a)
               (p
                (array-ref a 0)
                (array-ref a 1)
                (array-ref a 2)
                (array-ref a 3)
                (array-ref a 4)
                (array-ref a 5)
                (array-ref a 6)
                (array-ref a 7)))
             (lambda (p a)
               (p
                (array-ref a 0)
                (array-ref a 1)
                (array-ref a 2)
                (array-ref a 3)
                (array-ref a 4)
                (array-ref a 5)
                (array-ref a 6)
                (array-ref a 7)
                (array-ref a 8)))))
          (it
           (lambda (r)
             (lambda (p a)
               (apply
                a
                (array-ref a 0)
                (array-ref a 1)
                (array-ref a 2)
                (array-ref a 3)
                (array-ref a 4)
                (array-ref a 5)
                (array-ref a 6)
                (array-ref a 7)
                (array-ref a 8)
                (array-ref a 9)
                (do ((k r (- k 1))
                     (r '() (cons (array-ref a (- k 1)) r)))
                    ((= k 10) r)))))))
      (lambda (r)
        "These are high level, hiding implementation at call site."
        (if (< r 10) (vector-ref em r) (it r)))))
  (define array:applier-to-backing-vector
    (let ((em
           (vector
             (lambda (p ai av) (p))
             (lambda (p ai av)
               (p (vector-ref av (array:actor-index ai 0))))
             (lambda (p ai av)
               (p
                (vector-ref av (array:actor-index ai 0))
                (vector-ref av (array:actor-index ai 1))))
             (lambda (p ai av)
               (p
                (vector-ref av (array:actor-index ai 0))
                (vector-ref av (array:actor-index ai 1))
                (vector-ref av (array:actor-index ai 2))))
             (lambda (p ai av)
               (p
                (vector-ref av (array:actor-index ai 0))
                (vector-ref av (array:actor-index ai 1))
                (vector-ref av (array:actor-index ai 2))
                (vector-ref av (array:actor-index ai 3))))
             (lambda (p ai av)
               (p
                (vector-ref av (array:actor-index ai 0))
                (vector-ref av (array:actor-index ai 1))
                (vector-ref av (array:actor-index ai 2))
                (vector-ref av (array:actor-index ai 3))
                (vector-ref av (array:actor-index ai 4))))
             (lambda (p ai av)
               (p
                (vector-ref av (array:actor-index ai 0))
                (vector-ref av (array:actor-index ai 1))
                (vector-ref av (array:actor-index ai 2))
                (vector-ref av (array:actor-index ai 3))
                (vector-ref av (array:actor-index ai 4))
                (vector-ref av (array:actor-index ai 5))))
             (lambda (p ai av)
               (p
                (vector-ref av (array:actor-index ai 0))
                (vector-ref av (array:actor-index ai 1))
                (vector-ref av (array:actor-index ai 2))
                (vector-ref av (array:actor-index ai 3))
                (vector-ref av (array:actor-index ai 4))
                (vector-ref av (array:actor-index ai 5))
                (vector-ref av (array:actor-index ai 6))))
             (lambda (p ai av)
               (p
                (vector-ref av (array:actor-index ai 0))
                (vector-ref av (array:actor-index ai 1))
                (vector-ref av (array:actor-index ai 2))
                (vector-ref av (array:actor-index ai 3))
                (vector-ref av (array:actor-index ai 4))
                (vector-ref av (array:actor-index ai 5))
                (vector-ref av (array:actor-index ai 6))
                (vector-ref av (array:actor-index ai 7))))
             (lambda (p ai av)
               (p
                (vector-ref av (array:actor-index ai 0))
                (vector-ref av (array:actor-index ai 1))
                (vector-ref av (array:actor-index ai 2))
                (vector-ref av (array:actor-index ai 3))
                (vector-ref av (array:actor-index ai 4))
                (vector-ref av (array:actor-index ai 5))
                (vector-ref av (array:actor-index ai 6))
                (vector-ref av (array:actor-index ai 7))
                (vector-ref av (array:actor-index ai 8))))))
          (it
           (lambda (r)
             (lambda (p ai av)
               (apply
                p
                (vector-ref av (array:actor-index ai 0))
                (vector-ref av (array:actor-index ai 1))
                (vector-ref av (array:actor-index ai 2))
                (vector-ref av (array:actor-index ai 3))
                (vector-ref av (array:actor-index ai 4))
                (vector-ref av (array:actor-index ai 5))
                (vector-ref av (array:actor-index ai 6))
                (vector-ref av (array:actor-index ai 7))
                (vector-ref av (array:actor-index ai 8))
                (vector-ref av (array:actor-index ai 9))
                (do ((k r (- k 1))
                     (r
                      '()
                      (cons
                       (vector-ref
                         av
                         (array:actor-index ai (- k 1)))
                       r)))
                    ((= k 10) r)))))))
      (lambda (r)
        "These are low level, exposing implementation at call site."
        (if (< r 10) (vector-ref em r) (it r)))))
  (define (array:index/vector r x v)
    ((array:indexer/vector r) x v))
  (define (array:index/array r x av ai)
    ((array:indexer/array r) x av ai))
  (define (array:apply-to-vector r p v)
    ((array:applier-to-vector r) p v))
  (define (array:apply-to-actor r p a)
    ((array:applier-to-actor r) p a)))
