316 lines
10 KiB
Scheme
316 lines
10 KiB
Scheme
; Copyright (c) 1993, 1994 Richard Kelsey and Jonathan Rees. See file COPYING.
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; (make-array <initial-value> <bound1> ...)
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; (array-shape <array>)
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; (array-ref <array> <index1> ...)
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; (array-set! <array> <value> <index1> ...)
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; (make-shared-array <array> <linear-map> <bound1> ...)
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; (copy-array <array>)
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; (array->vector <array>)
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; (array <bounds> . <elements>)
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;
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; All arrays are zero based.
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;
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; ARRAY-MAP returns a list containing the array's bounds.
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;
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; The <linear-map> argument to MAKE-SHARED-ARRAY is a linear function
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; that maps indices into the shared array into a list of indices into
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; the original array. The array returned by MAKE-SHARED-ARRAY shares
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; storage with the original array.
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;
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; (array-ref (make-shared-array a f i1 i2 ... iN) j1 j2 ... jM)
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; <==>
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; (apply array-ref a (f j1 j2 ... jM))
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;
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; ARRAY->VECTOR returns a vector containing the elements of an array
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; in row-major order.
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; An array consists of a vector containing the bounds of the array,
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; a vector containing the elements of the array, and a linear map
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; expressed as a vector of coefficients and one constant.
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; If the map is #(c1 c2 ... cN C0) then the index into the vector of
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; elements for (array-ref a i1 i2 ... iN) is
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; (+ (* i1 c1) (* i2 c2) ... (* iN cN) C0).
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; Interface due to Alan Bawden.
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; Implementation by Richard Kelsey.
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(define-record-type array
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(bounds ; vector of array bounds
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map ; vector of coefficients + one constant
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elements) ; vector of actual elements
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())
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(define (array-shape array)
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(vector->list (array-bounds array)))
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; Calculate the index into an array's element vector that corresponds to
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; INDICES. MAP is the array's linear map.
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(define (fast-array-index indices map)
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(let ((size (- (vector-length map) 1)))
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(do ((i 0 (+ i 1))
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(j (vector-ref map size)
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(+ j (* (vector-ref indices i)
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(vector-ref map i)))))
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((>= i size) j))))
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; The same thing with bounds checking added.
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(define (array-index array indices)
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(let ((bounds (array-bounds array))
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(coefficients (array-map array)))
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(let loop ((is indices)
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(i 0)
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(index (vector-ref coefficients (vector-length bounds))))
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(cond ((null? is)
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(if (= i (vector-length bounds))
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index
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(error "wrong number of array indices" array indices)))
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((>= i (vector-length bounds))
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(error "wrong number of array indices" array indices))
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(else
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(let ((j (car is)))
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(if (and (>= j 0)
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(< j (vector-ref bounds i)))
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(loop (cdr is)
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(+ i 1)
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(+ index (* j (vector-ref coefficients i))))
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(error "array index out of range" array indices))))))))
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(define (array-ref array . indices)
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(vector-ref (array-elements array) (array-index array indices)))
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(define (array-set! array value . indices)
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(vector-set! (array-elements array) (array-index array indices) value))
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; This is mostly error checking.
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(define (make-array initial bound1 . bounds)
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(let* ((all-bounds (cons bound1 bounds))
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(bounds (make-vector (length all-bounds)))
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(size (do ((bs all-bounds (cdr bs))
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(i 0 (+ i 1))
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(s 1 (* s (car bs))))
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((null? bs) s)
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(let ((b (car bs)))
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(vector-set! bounds i b)
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(if (not (and (integer? b)
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(exact? b)
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(< 0 b)))
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(error "illegal array bounds" all-bounds))))))
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(array-maker bounds
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(bounds->map bounds)
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(make-vector size initial))))
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(define (array bounds . elts)
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(let* ((array (apply make-array #f bounds))
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(elements (array-elements array))
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(size (vector-length elements)))
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(if (not (= (length elts) size))
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(error "ARRAY got the wrong number of elements" bounds elts))
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(do ((i 0 (+ i 1))
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(elts elts (cdr elts)))
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((null? elts))
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(vector-set! elements i (car elts)))
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array))
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; Determine the linear map that corresponds to a simple array with the
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; given bounds.
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(define (bounds->map bounds)
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(do ((i (- (vector-length bounds) 1) (- i 1))
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(s 1 (* s (vector-ref bounds i)))
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(l '() (cons s l)))
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((< i 0)
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(list->vector (reverse (cons 0 (reverse l)))))))
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; This is mostly error checking. Two different procedures are used to
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; check that the shared array does not extend past the original. The
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; full check does a complete check, but, as it must check every corner
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; of the shared array, it gets very slow as the number of dimensions
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; goes up. The simple check just verifies that the all elements of
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; the shared array map to elements in the vector of the original.
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(define (make-shared-array array linear-map . bounds)
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(let ((map (make-shared-array-map array linear-map bounds)))
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(if (if (<= (length bounds) maximum-full-bounds-check)
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(full-array-bounds-okay? linear-map bounds (array-bounds array))
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(simple-array-bounds-okay? map bounds (vector-length
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(array-elements array))))
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(array-maker (list->vector bounds)
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map
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(array-elements array))
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(error "shared array out of bounds" array linear-map bounds))))
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(define maximum-full-bounds-check 5)
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; Check that every corner of the array specified by LINEAR and NEW-BOUNDS
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; is within OLD-BOUNDS. This checks every corner of the new array.
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(define (full-array-bounds-okay? linear new-bounds old-bounds)
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(let ((old-bounds (vector->list old-bounds)))
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(let label ((bounds (reverse new-bounds)) (args '()))
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(if (null? bounds)
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(let loop ((res (apply linear args)) (bounds old-bounds))
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(cond ((null? res)
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(null? bounds))
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((and (not (null? bounds))
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(<= 0 (car res))
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(< (car res) (car bounds)))
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(loop (cdr res) (cdr bounds)))
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(else #f)))
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(and (label (cdr bounds) (cons 0 args))
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(label (cdr bounds) (cons (- (car bounds) 1) args)))))))
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; Check that the maximum and minimum possible vector indices possible with
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; the given bounds and map would fit in an array of the given size.
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(define (simple-array-bounds-okay? map bounds size)
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(do ((map (vector->list map) (cdr map))
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(bounds bounds (cdr bounds))
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(min 0 (if (> 0 (car map))
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(+ min (* (car map) (- (car bounds) 1)))
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min))
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(max 0 (if (< 0 (car map))
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(+ max (* (car map) (- (car bounds) 1)))
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max)))
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((null? bounds)
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(and (>= 0 (+ min (car map)))
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(< size (+ max (car map)))))))
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; Determine the coefficients and constant of the composition of
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; LINEAR-MAP and the linear map of ARRAY. BOUNDS is used only to
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; determine the rank of LINEAR-MAP's domain.
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;
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; The coefficients are determined by applying first LINEAR-MAP and then
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; ARRAY's map to the vectors (1 0 0 ... 0), (0 1 0 ... 0), ..., (0 ... 0 1).
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; Applying them to (0 ... 0) gives the constant of the composition.
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(define (make-shared-array-map array linear-map bounds)
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(let* ((zero (map (lambda (ignore) 0) bounds))
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(do-vector (lambda (v)
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(or (apply-map array (apply linear-map v))
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(error "bad linear map for shared array"
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linear-map array bounds))))
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(base (do-vector zero)))
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(let loop ((bs bounds) (ces '()) (unit (cons 1 (cdr zero))))
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(if (null? bs)
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(list->vector (reverse (cons base ces)))
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(loop (cdr bs)
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(cons (- (do-vector unit) base) ces)
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(rotate unit))))))
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; Apply ARRAY's linear map to the indices in the list VALUES and
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; return the resulting vector index. #F is returned if VALUES is not
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; the correct length or if any of its elements are out of range.
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(define (apply-map array values)
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(let ((map (array-map array))
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(bounds (array-bounds array)))
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(let loop ((values values)
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(i 0)
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(index (vector-ref map (vector-length bounds))))
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(cond ((null? values)
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(if (= i (vector-length bounds))
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index
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#f))
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((>= i (vector-length bounds))
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#f)
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(else
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(let ((j (car values)))
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(if (and (>= j 0)
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(< j (vector-ref bounds i)))
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(loop (cdr values)
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(+ i 1)
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(+ index (* j (vector-ref map i))))
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#f)))))))
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; Return LIST with its last element moved to the front.
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(define (rotate list)
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(let ((l (reverse list)))
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(cons (car l) (reverse (cdr l)))))
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; Copy an array, shrinking the vector if this is subarray that does not
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; use all of the original array's elements.
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(define (copy-array array)
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(array-maker (array-bounds array)
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(bounds->map (array-bounds array))
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(array->vector array)))
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; Make a new vector and copy the elements into it. If ARRAY's map is
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; the simple map for it's bounds, then the elements are already in the
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; appropriate order and we can just copy the element vector.
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(define (array->vector array)
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(let* ((size (array-element-count array))
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(new (make-vector size)))
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(if (and (= size (vector-length (array-elements array)))
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(equal? (array-map array) (bounds->map (array-bounds array))))
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(copy-vector (array-elements array) new)
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(copy-elements array new))
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new))
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(define (array-element-count array)
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(let ((bounds (array-bounds array)))
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(do ((i 0 (+ i 1))
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(s 1 (* s (vector-ref bounds i))))
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((>= i (vector-length bounds))
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s))))
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(define (copy-vector from to)
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(do ((i (- (vector-length to) 1) (- i 1)))
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((< i 0))
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(vector-set! to i (vector-ref from i))))
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; Copy the elements of ARRAY into the vector TO. The copying is done one
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; row at a time. POSN is a vector containing the index of the row that
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; we are currently copying. After the row is copied, POSN is updated so
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; that the next row can be copied. A little more cleverness would make
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; this faster by replacing the call to FAST-ARRAY-INDEX with some simple
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; arithmetic on J.
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(define (copy-elements array to)
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(let ((bounds (array-bounds array))
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(elements (array-elements array))
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(map (array-map array)))
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(let* ((size (vector-length bounds))
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(posn (make-vector size 0))
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(step-size (vector-ref bounds (- size 1)))
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(delta (vector-ref map (- size 1))))
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(let loop ((i 0))
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(do ((i2 i (+ i2 1))
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(j (fast-array-index posn map) (+ j delta)))
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((>= i2 (+ i step-size)))
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(vector-set! to i2 (vector-ref elements j)))
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(cond ((< (+ i step-size) (vector-length to))
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(let loop2 ((k (- size 2)))
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(cond ((= (+ (vector-ref posn k) 1) (vector-ref bounds k))
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(vector-set! posn k 0)
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(loop2 (- k 1)))
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(else
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(vector-set! posn k (+ 1 (vector-ref posn k))))))
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(loop (+ i step-size))))))))
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; Testing.
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; (define a1 (make-array 0 4 5))
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; 0 1 2 3
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; 4 5 6 7
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; 8 9 10 11
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; 12 13 14 15
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; 16 17 18 19
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; (make-shared-array-map a1 (lambda (x) (list x x)) '(3))
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; 0 5 10, #(5 0)
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; (make-shared-array-map a1 (lambda (x) (list 2 (- 4 x))) '(3))
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; 18 14 10 #(-4 18)
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; (make-shared-array-map a1 (lambda (x y) (list (+ x 1) y)) '(2 4))
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; 1 2
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; 5 6
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; 9 10
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; 13 14
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; #(1 4 1)
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