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|
;;;;"array.scm" Arrays for Scheme
; Copyright (C) 2001, 2003, 2005, 2006 Aubrey Jaffer
;
;Permission to copy this software, to modify it, to redistribute it,
;to distribute modified versions, and to use it for any purpose is
;granted, subject to the following restrictions and understandings.
;
;1. Any copy made of this software must include this copyright notice
;in full.
;
;2. I have made no warranty or representation that the operation of
;this software will be error-free, and I am under no obligation to
;provide any services, by way of maintenance, update, or otherwise.
;
;3. In conjunction with products arising from the use of this
;material, there shall be no use of my name in any advertising,
;promotional, or sales literature without prior written consent in
;each case.
;;@code{(require 'array)} or @code{(require 'srfi-63)}
;;@ftindex array
(require 'record)
(define array:rtd
(make-record-type "array"
'(dimensions
scales ;list of dimension scales
offset ;exact integer
store ;data
)))
(define array:dimensions
(let ((dimensions (record-accessor array:rtd 'dimensions)))
(lambda (array)
(cond ((vector? array) (list (vector-length array)))
((string? array) (list (string-length array)))
(else (dimensions array))))))
(define array:scales
(let ((scales (record-accessor array:rtd 'scales)))
(lambda (obj)
(cond ((string? obj) '(1))
((vector? obj) '(1))
(else (scales obj))))))
(define array:store
(let ((store (record-accessor array:rtd 'store)))
(lambda (obj)
(cond ((string? obj) obj)
((vector? obj) obj)
(else (store obj))))))
(define array:offset
(let ((offset (record-accessor array:rtd 'offset)))
(lambda (obj)
(cond ((string? obj) 0)
((vector? obj) 0)
(else (offset obj))))))
(define array:construct
(record-constructor array:rtd '(dimensions scales offset store)))
;;@args obj
;;Returns @code{#t} if the @1 is an array, and @code{#f} if not.
(define array?
(let ((array:array? (record-predicate array:rtd)))
(lambda (obj) (or (string? obj) (vector? obj) (array:array? obj)))))
;;@noindent
;;@emph{Note:} Arrays are not disjoint from other Scheme types.
;;Vectors and possibly strings also satisfy @code{array?}.
;;A disjoint array predicate can be written:
;;
;;@example
;;(define (strict-array? obj)
;; (and (array? obj) (not (string? obj)) (not (vector? obj))))
;;@end example
;;@body
;;Returns @code{#t} if @1 and @2 have the same rank and dimensions and the
;;corresponding elements of @1 and @2 are @code{equal?}.
;;@body
;;@0 recursively compares the contents of pairs, vectors, strings, and
;;@emph{arrays}, applying @code{eqv?} on other objects such as numbers
;;and symbols. A rule of thumb is that objects are generally @0 if
;;they print the same. @0 may fail to terminate if its arguments are
;;circular data structures.
;;
;;@example
;;(equal? 'a 'a) @result{} #t
;;(equal? '(a) '(a)) @result{} #t
;;(equal? '(a (b) c)
;; '(a (b) c)) @result{} #t
;;(equal? "abc" "abc") @result{} #t
;;(equal? 2 2) @result{} #t
;;(equal? (make-vector 5 'a)
;; (make-vector 5 'a)) @result{} #t
;;(equal? (make-array (A:fixN32b 4) 5 3)
;; (make-array (A:fixN32b 4) 5 3)) @result{} #t
;;(equal? (make-array '#(foo) 3 3)
;; (make-array '#(foo) 3 3)) @result{} #t
;;(equal? (lambda (x) x)
;; (lambda (y) y)) @result{} @emph{unspecified}
;;@end example
(define (equal? obj1 obj2)
(cond ((eqv? obj1 obj2) #t)
((or (pair? obj1) (pair? obj2))
(and (pair? obj1) (pair? obj2)
(equal? (car obj1) (car obj2))
(equal? (cdr obj1) (cdr obj2))))
((and (string? obj1) (string? obj2))
(string=? obj1 obj2))
((and (vector? obj1) (vector? obj2))
(and (equal? (vector-length obj1) (vector-length obj2))
(do ((idx (+ -1 (vector-length obj1)) (+ -1 idx)))
((or (negative? idx)
(not (equal? (vector-ref obj1 idx)
(vector-ref obj2 idx))))
(negative? idx)))))
((and (array? obj1) (array? obj2))
(and (equal? (array:dimensions obj1) (array:dimensions obj2))
(letrec ((rascan
(lambda (dims idxs)
(if (null? dims)
(equal? (apply array-ref obj1 idxs)
(apply array-ref obj2 idxs))
(do ((res #t (rascan (cdr dims) (cons idx idxs)))
(idx (+ -1 (car dims)) (+ -1 idx)))
((or (not res) (negative? idx)) res))))))
(rascan (reverse (array:dimensions obj1)) '()))))
(else #f)))
;;@body
;;Returns the number of dimensions of @1. If @1 is not an array, 0 is
;;returned.
(define (array-rank obj)
(if (array? obj) (length (array:dimensions obj)) 0))
;;@args array
;;Returns a list of dimensions.
;;
;;@example
;;(array-dimensions (make-array '#() 3 5))
;; @result{} (3 5)
;;@end example
(define array-dimensions array:dimensions)
;;@args prototype k1 @dots{}
;;
;;Creates and returns an array of type @1 with dimensions @2, @dots{}
;;and filled with elements from @1. @1 must be an array, vector, or
;;string. The implementation-dependent type of the returned array
;;will be the same as the type of @1; except if that would be a vector
;;or string with rank not equal to one, in which case some variety of
;;array will be returned.
;;
;;If the @1 has no elements, then the initial contents of the returned
;;array are unspecified. Otherwise, the returned array will be filled
;;with the element at the origin of @1.
(define (make-array prototype . dimensions)
(define prot (array:store prototype))
(define pdims (array:dimensions prototype))
(define onedim? (eqv? 1 (length dimensions)))
(define tcnt (apply * dimensions))
(let ((initializer
(if (zero? (apply * pdims)) '()
(list
(apply array-ref prototype
(map (lambda (x) 0) pdims))))))
(cond ((and onedim? (string? prot))
(apply make-string (car dimensions) initializer))
((and onedim? (vector? prot))
(apply make-vector (car dimensions) initializer))
(else
(let ((store
(if (string? prot)
(apply make-string tcnt initializer)
(apply make-vector tcnt initializer))))
(define (loop dims scales)
(if (null? dims)
(array:construct dimensions (cdr scales) 0 store)
(loop (cdr dims)
(cons (* (car dims) (car scales)) scales))))
(loop (reverse dimensions) '(1)))))))
;;@args prototype k1 @dots{}
;;@0 is an alias for @code{make-array}.
(define create-array make-array)
;;@args array mapper k1 @dots{}
;;@0 can be used to create shared subarrays of other
;;arrays. The @var{mapper} is a function that translates coordinates in
;;the new array into coordinates in the old array. A @var{mapper} must be
;;linear, and its range must stay within the bounds of the old array, but
;;it can be otherwise arbitrary. A simple example:
;;
;;@example
;;(define fred (make-array '#(#f) 8 8))
;;(define freds-diagonal
;; (make-shared-array fred (lambda (i) (list i i)) 8))
;;(array-set! freds-diagonal 'foo 3)
;;(array-ref fred 3 3)
;; @result{} FOO
;;(define freds-center
;; (make-shared-array fred (lambda (i j) (list (+ 3 i) (+ 3 j)))
;; 2 2))
;;(array-ref freds-center 0 0)
;; @result{} FOO
;;@end example
(define (make-shared-array array mapper . dimensions)
(define odl (array:scales array))
(define rank (length dimensions))
(define shape
(map (lambda (dim) (if (list? dim) dim (list 0 (+ -1 dim)))) dimensions))
(do ((idx (+ -1 rank) (+ -1 idx))
(uvt (if (zero? rank)
'()
(append (cdr (vector->list (make-vector rank 0))) '(1)))
(append (cdr uvt) '(0)))
(uvts '() (cons uvt uvts)))
((negative? idx)
(let ((ker0 (apply + (map * odl (apply mapper uvt)))))
(array:construct
(map (lambda (dim) (+ 1 (- (cadr dim) (car dim)))) shape)
(map (lambda (uvt) (- (apply + (map * odl (apply mapper uvt))) ker0))
uvts)
(apply +
(array:offset array)
(map * odl (apply mapper (map car shape))))
(array:store array))))))
;;@args rank proto list
;;@3 must be a rank-nested list consisting of all the elements, in
;;row-major order, of the array to be created.
;;
;;@0 returns an array of rank @1 and type @2 consisting of all the
;;elements, in row-major order, of @3. When @1 is 0, @3 is the lone
;;array element; not necessarily a list.
;;
;;@example
;;(list->array 2 '#() '((1 2) (3 4)))
;; @result{} #2A((1 2) (3 4))
;;(list->array 0 '#() 3)
;; @result{} #0A 3
;;@end example
(define (list->array rank proto lst)
(define dimensions
(do ((shp '() (cons (length row) shp))
(row lst (car lst))
(rnk (+ -1 rank) (+ -1 rnk)))
((negative? rnk) (reverse shp))))
(let ((nra (apply make-array proto dimensions)))
(define (l2ra dims idxs row)
(cond ((null? dims)
(apply array-set! nra row (reverse idxs)))
((if (not (eqv? (car dims) (length row)))
(slib:error 'list->array
'non-rectangular 'array dims dimensions))
(do ((idx 0 (+ 1 idx))
(row row (cdr row)))
((>= idx (car dims)))
(l2ra (cdr dims) (cons idx idxs) (car row))))))
(l2ra dimensions '() lst)
nra))
;;@args array
;;Returns a rank-nested list consisting of all the elements, in
;;row-major order, of @1. In the case of a rank-0 array, @0 returns
;;the single element.
;;
;;@example
;;(array->list #2A((ho ho ho) (ho oh oh)))
;; @result{} ((ho ho ho) (ho oh oh))
;;(array->list #0A ho)
;; @result{} ho
;;@end example
(define (array->list ra)
(define (ra2l dims idxs)
(if (null? dims)
(apply array-ref ra (reverse idxs))
(do ((lst '() (cons (ra2l (cdr dims) (cons idx idxs)) lst))
(idx (+ -1 (car dims)) (+ -1 idx)))
((negative? idx) lst))))
(ra2l (array:dimensions ra) '()))
;;@args vect proto dim1 @dots{}
;;@1 must be a vector of length equal to the product of exact
;;nonnegative integers @3, @dots{}.
;;
;;@0 returns an array of type @2 consisting of all the elements, in
;;row-major order, of @1. In the case of a rank-0 array, @1 has a
;;single element.
;;
;;@example
;;(vector->array #(1 2 3 4) #() 2 2)
;; @result{} #2A((1 2) (3 4))
;;(vector->array '#(3) '#())
;; @result{} #0A 3
;;@end example
(define (vector->array vect prototype . dimensions)
(define vdx (vector-length vect))
(if (not (eqv? vdx (apply * dimensions)))
(slib:error 'vector->array vdx '<> (cons '* dimensions)))
(let ((ra (apply make-array prototype dimensions)))
(define (v2ra dims idxs)
(cond ((null? dims)
(set! vdx (+ -1 vdx))
(apply array-set! ra (vector-ref vect vdx) (reverse idxs)))
(else
(do ((idx (+ -1 (car dims)) (+ -1 idx)))
((negative? idx) vect)
(v2ra (cdr dims) (cons idx idxs))))))
(v2ra dimensions '())
ra))
;;@args array
;;Returns a new vector consisting of all the elements of @1 in
;;row-major order.
;;
;;@example
;;(array->vector #2A ((1 2)( 3 4)))
;; @result{} #(1 2 3 4)
;;(array->vector #0A ho)
;; @result{} #(ho)
;;@end example
(define (array->vector ra)
(define dims (array:dimensions ra))
(let* ((vdx (apply * dims))
(vect (make-vector vdx)))
(define (ra2v dims idxs)
(if (null? dims)
(let ((val (apply array-ref ra (reverse idxs))))
(set! vdx (+ -1 vdx))
(vector-set! vect vdx val))
(do ((idx (+ -1 (car dims)) (+ -1 idx)))
((negative? idx) vect)
(ra2v (cdr dims) (cons idx idxs)))))
(ra2v dims '())
vect))
(define (array:in-bounds? array indices)
(do ((bnds (array:dimensions array) (cdr bnds))
(idxs indices (cdr idxs)))
((or (null? bnds)
(null? idxs)
(not (integer? (car idxs)))
(not (< -1 (car idxs) (car bnds))))
(and (null? bnds) (null? idxs)))))
;;@args array index1 @dots{}
;;Returns @code{#t} if its arguments would be acceptable to
;;@code{array-ref}.
(define (array-in-bounds? array . indices)
(array:in-bounds? array indices))
;;@args array k1 @dots{}
;;Returns the (@2, @dots{}) element of @1.
(define (array-ref array . indices)
(define store (array:store array))
(or (array:in-bounds? array indices)
(slib:error 'array-ref 'bad-indices indices))
((if (string? store) string-ref vector-ref)
store (apply + (array:offset array) (map * (array:scales array) indices))))
;;@args array obj k1 @dots{}
;;Stores @2 in the (@3, @dots{}) element of @1. The value returned
;;by @0 is unspecified.
(define (array-set! array obj . indices)
(define store (array:store array))
(or (array:in-bounds? array indices)
(slib:error 'array-set! 'bad-indices indices))
((if (string? store) string-set! vector-set!)
store (apply + (array:offset array) (map * (array:scales array) indices))
obj))
;;@noindent
;;These functions return a prototypical uniform-array enclosing the
;;optional argument (which must be of the correct type). If the
;;uniform-array type is supported by the implementation, then it is
;;returned; defaulting to the next larger precision type; resorting
;;finally to vector.
(define (make-prototype-checker name pred? creator)
(lambda args
(case (length args)
((1) (if (pred? (car args))
(creator (car args))
(slib:error name 'incompatible 'type (car args))))
((0) (creator))
(else (slib:error name 'wrong 'number 'of 'args args)))))
(define (integer-bytes?? n)
(lambda (obj)
(and (integer? obj)
(exact? obj)
(or (negative? n) (not (negative? obj)))
(do ((num obj (quotient num 256))
(n (+ -1 (abs n)) (+ -1 n)))
((or (zero? num) (negative? n))
(zero? num))))))
;;@args z
;;@args
;;Returns an inexact 128.bit flonum complex uniform-array prototype.
(define A:floC128b (make-prototype-checker 'A:floC128b complex? vector))
;;@args z
;;@args
;;Returns an inexact 64.bit flonum complex uniform-array prototype.
(define A:floC64b (make-prototype-checker 'A:floC64b complex? vector))
;;@args z
;;@args
;;Returns an inexact 32.bit flonum complex uniform-array prototype.
(define A:floC32b (make-prototype-checker 'A:floC32b complex? vector))
;;@args z
;;@args
;;Returns an inexact 16.bit flonum complex uniform-array prototype.
(define A:floC16b (make-prototype-checker 'A:floC16b complex? vector))
;;@args z
;;@args
;;Returns an inexact 128.bit flonum real uniform-array prototype.
(define A:floR128b (make-prototype-checker 'A:floR128b real? vector))
;;@args z
;;@args
;;Returns an inexact 64.bit flonum real uniform-array prototype.
(define A:floR64b (make-prototype-checker 'A:floR64b real? vector))
;;@args z
;;@args
;;Returns an inexact 32.bit flonum real uniform-array prototype.
(define A:floR32b (make-prototype-checker 'A:floR32b real? vector))
;;@args z
;;@args
;;Returns an inexact 16.bit flonum real uniform-array prototype.
(define A:floR16b (make-prototype-checker 'A:floR16b real? vector))
;;@args z
;;@args
;;Returns an exact 128.bit decimal flonum rational uniform-array prototype.
(define A:floR128b (make-prototype-checker 'A:floR128b real? vector))
;;@args z
;;@args
;;Returns an exact 64.bit decimal flonum rational uniform-array prototype.
(define A:floR64b (make-prototype-checker 'A:floR64b real? vector))
;;@args z
;;@args
;;Returns an exact 32.bit decimal flonum rational uniform-array prototype.
(define A:floR32b (make-prototype-checker 'A:floR32b real? vector))
;;@args n
;;@args
;;Returns an exact binary fixnum uniform-array prototype with at least
;;64 bits of precision.
(define A:fixZ64b (make-prototype-checker 'A:fixZ64b (integer-bytes?? -8) vector))
;;@args n
;;@args
;;Returns an exact binary fixnum uniform-array prototype with at least
;;32 bits of precision.
(define A:fixZ32b (make-prototype-checker 'A:fixZ32b (integer-bytes?? -4) vector))
;;@args n
;;@args
;;Returns an exact binary fixnum uniform-array prototype with at least
;;16 bits of precision.
(define A:fixZ16b (make-prototype-checker 'A:fixZ16b (integer-bytes?? -2) vector))
;;@args n
;;@args
;;Returns an exact binary fixnum uniform-array prototype with at least
;;8 bits of precision.
(define A:fixZ8b (make-prototype-checker 'A:fixZ8b (integer-bytes?? -1) vector))
;;@args k
;;@args
;;Returns an exact non-negative binary fixnum uniform-array prototype with at
;;least 64 bits of precision.
(define A:fixN64b (make-prototype-checker 'A:fixN64b (integer-bytes?? 8) vector))
;;@args k
;;@args
;;Returns an exact non-negative binary fixnum uniform-array prototype with at
;;least 32 bits of precision.
(define A:fixN32b (make-prototype-checker 'A:fixN32b (integer-bytes?? 4) vector))
;;@args k
;;@args
;;Returns an exact non-negative binary fixnum uniform-array prototype with at
;;least 16 bits of precision.
(define A:fixN16b (make-prototype-checker 'A:fixN16b (integer-bytes?? 2) vector))
;;@args k
;;@args
;;Returns an exact non-negative binary fixnum uniform-array prototype with at
;;least 8 bits of precision.
(define A:fixN8b (make-prototype-checker 'A:fixN8b (integer-bytes?? 1) vector))
;;@args bool
;;@args
;;Returns a boolean uniform-array prototype.
(define A:bool (make-prototype-checker 'A:bool boolean? vector))
|