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Re: SRFI 43 Reference Implementation vector-map bug
On Fri, 4 Feb 2005, Will M. Farr wrote:
> Hello,
>
> I just grabbed your reference implementation of SRFI 43 (vector-lib)
> from srfi.schemers.org, and I found a bug in vector-map. The
> correction is to replace the lines
>
> (loop f target vec (- len 1)) and (loop f target vectors (- len 1))
>
> in %vector-map1! and %vector-map2+! with
>
> (loop f target vec len) and (loop f target vectors len)
>
> You already subtract one when using a given index in
> vector-ref/vector-set, so you don't need to do it entering the loop. I
> don't know if this matters (most of the ports of vector-lib don't seem
> to use the reference implementation), but I thought you might want to
> know.
Thanks for reporting that bug. This prompted me to review the code
again, which I noticed several more bugs in. I could swear I tested my
last modifications before I committed them, but it seems that there was
quite a bit that was somewhat broken. I've attached a new reference
implementation, which is much less buggy & which I've moved into the
public domain.
(What other Scheme systems did you find implemented SRFI 43 from
scratch, by the way? The only system I know of that already boasts
SRFI 43 support is Chicken, and there it's just a modification of an
old version of my reference implementation.)
;;;;;; SRFI 43: Vector library -*- Scheme -*-
;;; Taylor Campbell wrote this code; he places it in the public domain.
;;; --------------------
;;; Exported procedure index
;;;
;;; * Constructors
;;; make-vector vector
;;; vector-unfold vector-unfold-right
;;; vector-copy vector-reverse-copy
;;; vector-append vector-concatenate
;;;
;;; * Predicates
;;; vector?
;;; vector-empty?
;;; vector=
;;;
;;; * Selectors
;;; vector-ref
;;; vector-length
;;;
;;; * Iteration
;;; vector-fold vector-fold-right
;;; vector-map vector-map!
;;; vector-for-each
;;; vector-count
;;;
;;; * Searching
;;; vector-index vector-skip
;;; vector-index-right vector-skip-right
;;; vector-binary-search
;;; vector-any vector-every
;;;
;;; * Mutators
;;; vector-set!
;;; vector-swap!
;;; vector-fill!
;;; vector-reverse!
;;; vector-copy! vector-reverse-copy!
;;; vector-reverse!
;;;
;;; * Conversion
;;; vector->list reverse-vector->list
;;; list->vector reverse-list->vector
;;; --------------------
;;; Commentary on efficiency of the code
;;; This code is somewhat tuned for efficiency. There are several
;;; internal routines that can be optimized greatly to greatly improve
;;; the performance of much of the library. These internal procedures
;;; are already carefully tuned for performance, and lambda-lifted by
;;; hand. Some other routines are lambda-lifted by hand, but only the
;;; loops are lambda-lifted, and only if some routine has two possible
;;; loops -- a fast path and an n-ary case --, whereas _all_ of the
;;; internal routines' loops are lambda-lifted so as to never cons a
;;; closure in their body (VECTOR-PARSE-START+END doesn't have a loop),
;;; even in Scheme systems that perform no loop optimization (which is
;;; most of them, unfortunately).
;;;
;;; Fast paths are provided for common cases in most of the loops in
;;; this library.
;;;
;;; All calls to primitive vector operations are protected by a prior
;;; type check; they can be safely converted to use unsafe equivalents
;;; of the operations, if available. Ideally, the compiler should be
;;; able to determine this, but the state of Scheme compilers today is
;;; not a happy one.
;;;
;;; Efficiency of the actual algorithms is a rather mundane point to
;;; mention; vector operations are rarely beyond being straightforward.
;;; --------------------
;;; Utilities
;;; SRFI 8, too trivial to put in the dependencies list.
(define-syntax receive
(syntax-rules ()
((receive ?formals ?producer ?body1 ?body2 ...)
(call-with-values (lambda () ?producer)
(lambda ?formals ?body1 ?body2 ...)))))
;;; Not the best LET*-OPTIONALS, but not the worst, either. Use Olin's
;;; if it's available to you.
(define-syntax let*-optionals
(syntax-rules ()
((let*-optionals (?x ...) ((?var ?default) ...) ?body1 ?body2 ...)
(let ((args (?x ...)))
(let*-optionals args ((?var ?default) ...) ?body1 ?body2 ...)))
((let*-optionals ?args ((?var ?default) ...) ?body1 ?body2 ...)
(let*-optionals:aux ?args ?args ((?var ?default) ...)
?body1 ?body2 ...))))
(define-syntax let*-optionals:aux
(syntax-rules ()
((aux ?orig-args-var ?args-var () ?body1 ?body2 ...)
(if (null? ?args-var)
(let () ?body1 ?body2 ...)
(error "too many arguments" (length ?orig-args-var)
?orig-args-var)))
((aux ?orig-args-var ?args-var
((?var ?default) ?more ...)
?body1 ?body2 ...)
(if (null? ?args-var)
(let* ((?var ?default) ?more ...) ?body1 ?body2 ...)
(let ((?var (car ?args-var))
(new-args (cdr ?args-var)))
(let*-optionals:aux ?orig-args-var new-args
(?more ...)
?body1 ?body2 ...))))))
(define (nonneg-int? x)
(and (integer? x)
(not (negative? x))))
(define (between? x y z)
(and (< x y)
(<= y z)))
(define (unspecified-value) (if #f #f))
;++ This should be implemented more efficiently. It shouldn't cons a
;++ closure, and the cons cells used in the loops when using this could
;++ be reused.
(define (vectors-ref vectors i)
(map (lambda (v) (vector-ref v i)) vectors))
;;; --------------------
;;; Error checking
;;; Error signalling (not checking) is done in a way that tries to be
;;; as helpful to the person who gets the debugging prompt as possible.
;;; That said, error _checking_ tries to be as unredundant as possible.
;;; I don't use any sort of general condition mechanism; I use simply
;;; SRFI 23's ERROR, even in cases where it might be better to use such
;;; a general condition mechanism. Fix that when porting this to a
;;; Scheme implementation that has its own condition system.
;;; In argument checks, upon receiving an invalid argument, the checker
;;; procedure recursively calls itself, but in one of the arguments to
;;; itself is a call to ERROR; this mechanism is used in the hopes that
;;; the user may be thrown into a debugger prompt, proceed with another
;;; value, and let it be checked again.
;;; Type checking is pretty basic, but easily factored out and replaced
;;; with whatever your implementation's preferred type checking method
;;; is. I doubt there will be many other methods of index checking,
;;; though the index checkers might be better implemented natively.
;;; (CHECK-TYPE <type-predicate?> <value> <callee>) -> value
;;; Ensure that VALUE satisfies TYPE-PREDICATE?; if not, signal an
;;; error stating that VALUE did not satisfy TYPE-PREDICATE?, showing
;;; that this happened while calling CALLEE. Return VALUE if no
;;; error was signalled.
(define (check-type pred? value callee)
(if (pred? value)
value
;; Recur: when (or if) the user gets a debugger prompt, he can
;; proceed where the call to ERROR was with the correct value.
(check-type pred?
(error "erroneous value"
(list pred? value)
`(while calling ,callee))
callee)))
;;; (CHECK-INDEX <vector> <index> <callee>) -> index
;;; Ensure that INDEX is a valid index into VECTOR; if not, signal an
;;; error stating that it is not and that this happened in a call to
;;; CALLEE. Return INDEX when it is valid. (Note that this does NOT
;;; check that VECTOR is indeed a vector.)
(define (check-index vec index callee)
(let ((index (check-type integer? index callee)))
(cond ((< index 0)
(check-index vec
(error "vector index too low"
index
`(into vector ,vec)
`(while calling ,callee))
callee))
((>= index (vector-length vec))
(check-index vec
(error "vector index too high"
index
`(into vector ,vec)
`(while calling ,callee))
callee))
(else index))))
;;; (CHECK-INDICES <vector>
;;; <start> <start-name>
;;; <end> <end-name>
;;; <caller>) -> [start end]
;;; Ensure that START and END are valid bounds of a range within
;;; VECTOR; if not, signal an error stating that they are not, with
;;; the message being informative about what the argument names were
;;; called -- by using START-NAME & END-NAME --, and that it occurred
;;; while calling CALLEE. Also ensure that VEC is in fact a vector.
;;; Returns no useful value.
(define (check-indices vec start start-name end end-name callee)
(let ((lose (lambda things
(apply error "vector range out of bounds"
(append things
`(vector was ,vec)
`(,start-name was ,start)
`(,end-name was ,end)
`(while calling ,callee)))))
(start (check-type integer? start callee))
(end (check-type integer? end callee)))
(cond ((> start end)
;; I'm not sure how well this will work. The intent is that
;; the programmer tells the debugger to proceed with both a
;; new START & a new END by returning multiple values
;; somewhere.
(receive (new-start new-end)
(lose `(,end-name < ,start-name))
(check-indices vec
new-start start-name
new-end end-name
callee)))
((< start 0)
(check-indices vec
(lose `(,start-name < 0))
start-name
end end-name
callee))
((>= start (vector-length vec))
(check-indices vec
(lose `(,start-name > len)
`(len was ,(vector-length vec)))
start-name
end end-name
callee))
((> end (vector-length vec))
(check-indices vec
start start-name
(lose `(,end-name > len)
`(len was ,(vector-length vec)))
end-name
callee))
(else
(values start end)))))
;;; --------------------
;;; Internal routines
;;; These should all be integrated, native, or otherwise optimized --
;;; they're used a _lot_ --. All of the loops and LETs inside loops
;;; are lambda-lifted by hand, just so as not to cons closures in the
;;; loops. (If your compiler can do better than that if they're not
;;; lambda-lifted, then lambda-drop (?) them.)
;;; (VECTOR-PARSE-START+END <vector> <arguments>
;;; <start-name> <end-name>
;;; <callee>)
;;; -> [start end]
;;; Return two values, composing a valid range within VECTOR, as
;;; extracted from ARGUMENTS or defaulted from VECTOR -- 0 for START
;;; and the length of VECTOR for END --; START-NAME and END-NAME are
;;; purely for error checking.
(define (vector-parse-start+end vec args start-name end-name callee)
(let ((len (vector-length vec)))
(cond ((null? args)
(values 0 len))
((null? (cdr args))
(check-indices vec
(car args) start-name
len end-name
callee))
((null? (cddr args))
(check-indices vec
(car args) start-name
(cadr args) end-name
callee))
(else
(error "too many arguments"
`(extra args were ,(cddr args))
`(while calling ,callee))))))
(define-syntax let-vector-start+end
(syntax-rules ()
((let-vector-start+end ?callee ?vec ?args (?start ?end)
?body1 ?body2 ...)
(let ((?vec (check-type vector? ?vec ?callee)))
(receive (?start ?end)
(vector-parse-start+end ?vec ?args '?start '?end
?callee)
?body1 ?body2 ...)))))
;;; (%SMALLEST-LENGTH <vector-list> <default-length> <callee>)
;;; -> exact, nonnegative integer
;;; Compute the smallest length of VECTOR-LIST. DEFAULT-LENGTH is
;;; the length that is returned if VECTOR-LIST is empty. Common use
;;; of this is in n-ary vector routines:
;;; (define (f vec . vectors)
;;; (let ((vec (check-type vector? vec f)))
;;; ...(%smallest-length vectors (vector-length vec) f)...))
;;; %SMALLEST-LENGTH takes care of the type checking -- which is what
;;; the CALLEE argument is for --; thus, the design is tuned for
;;; avoiding redundant type checks.
(define %smallest-length
(letrec ((loop (lambda (vector-list length callee)
(if (null? vector-list)
length
(loop (cdr vector-list)
(min (vector-length
(check-type vector?
(car vector-list)
callee))
length)
callee)))))
loop))
;;; (%VECTOR-COPY! <target> <tstart> <source> <sstart> <send>)
;;; Copy elements at locations SSTART to SEND from SOURCE to TARGET,
;;; starting at TSTART in TARGET.
;;;
;;; Optimize this! Probably with some combination of:
;;; - Force it to be integrated.
;;; - Let it use unsafe vector element dereferencing routines: bounds
;;; checking already happens outside of it. (Or use a compiler
;;; that figures this out, but Olin Shivers' PhD thesis seems to
;;; have been largely ignored in actual implementations...)
;;; - Implement it natively as a VM primitive: the VM can undoubtedly
;;; perform much faster than it can make Scheme perform, even with
;;; bounds checking.
;;; - Implement it in assembly: you _want_ the fine control that
;;; assembly can give you for this.
;;; I already lambda-lift it by hand, but you should be able to make it
;;; even better than that.
(define %vector-copy!
(letrec ((loop/l->r (lambda (target source send i j)
(cond ((< i send)
(vector-set! target j
(vector-ref source i))
(loop/l->r target source send
(+ i 1) (+ j 1))))))
(loop/r->l (lambda (target source sstart i j)
(cond ((>= i sstart)
(vector-set! target j
(vector-ref source i))
(loop/r->l target source sstart
(- i 1) (- j 1)))))))
(lambda (target tstart source sstart send)
(if (> sstart tstart) ; Make sure we don't copy over
; ourselves.
(loop/l->r target source send sstart tstart)
(loop/r->l target source sstart (- send 1)
(+ -1 tstart send (- sstart)))))))
;;; (%VECTOR-REVERSE-COPY! <target> <tstart> <source> <sstart> <send>)
;;; Copy elements from SSTART to SEND from SOURCE to TARGET, in the
;;; reverse order.
(define %vector-reverse-copy!
(letrec ((loop (lambda (target source sstart i j)
(cond ((>= i sstart)
(vector-set! target j (vector-ref source i))
(loop target source sstart
(- i 1)
(+ j 1)))))))
(lambda (target tstart source sstart send)
(loop target source sstart
(- send 1)
tstart))))
(define %vector-reverse!
(letrec ((loop (lambda (vec i j)
(cond ((<= i j)
(let ((v (vector-ref vec i)))
(vector-set! vec i (vector-ref vec j))
(vector-set! vec j v)
(loop vec (+ i 1) (- j 1))))))))
(lambda (vec start end)
(loop vec start (- end 1)))))
(define %vector-fold1
(letrec ((loop (lambda (kons knil len vec i)
(if (= i len)
knil
(loop kons
(kons i knil (vector-ref vec i))
len vec (+ i 1))))))
(lambda (kons knil len vec)
(loop kons knil len vec 0))))
(define %vector-fold2+
(letrec ((loop (lambda (kons knil len vectors i)
(if (= i len)
knil
(loop kons
(apply kons i knil
(vectors-ref vectors i))
len vectors (+ i 1))))))
(lambda (kons knil len vectors)
(loop kons knil len vectors 0))))
(define %vector-map1!
(letrec ((loop (lambda (f target vec i)
(if (zero? i)
target
(let ((j (- i 1)))
(vector-set! target j
(f j (vector-ref vec j)))
(loop f target vec j))))))
(lambda (f target vec len)
(loop f target vec len))))
(define %vector-map2+!
(letrec ((loop (lambda (f target vectors i)
(if (zero? i)
target
(let ((j (- i 1)))
(vector-set! target j
(apply f j (vectors-ref vectors j)))
(loop f target vectors j))))))
(lambda (f target vectors len)
(loop f target vectors len))))
;;;;;;;;;;;;;;;;;;;;;;;; ***** vector-lib ***** ;;;;;;;;;;;;;;;;;;;;;;;
;;; --------------------
;;; Constructors
;;; (MAKE-VECTOR <size> [<fill>]) -> vector
;;; [R5RS] Create a vector of length LENGTH. If FILL is present,
;;; initialize each slot in the vector with it; if not, the vector's
;;; initial contents are unspecified.
(define make-vector make-vector)
;;; (VECTOR <elt> ...) -> vector
;;; [R5RS] Create a vector containing ELEMENT ..., in order.
(define vector vector)
;;; This ought to be able to be implemented much more efficiently -- if
;;; we have the number of arguments available to us, we can create the
;;; vector without using LENGTH to determine the number of elements it
;;; should have.
;(define (vector . elements) (list->vector elements))
;;; (VECTOR-UNFOLD <f> <length> <initial-seed> ...) -> vector
;;; (F <index> <seed> ...) -> [elt seed' ...]
;;; The fundamental vector constructor. Creates a vector whose
;;; length is LENGTH and iterates across each index K between 0 and
;;; LENGTH, applying F at each iteration to the current index and the
;;; current seeds to receive N+1 values: first, the element to put in
;;; the Kth slot and then N new seeds for the next iteration.
(define vector-unfold
(letrec ((tabulate! ; Special zero-seed case.
(lambda (f vec i len)
(cond ((< i len)
(vector-set! vec i (f i))
(tabulate! f vec (+ i 1) len)))))
(unfold1! ; Fast path for one seed.
(lambda (f vec i len seed)
(if (< i len)
(receive (elt new-seed)
(f i seed)
(vector-set! vec i elt)
(unfold1! f vec (+ i 1) len new-seed)))))
(unfold2+! ; Slower variant for N seeds.
(lambda (f vec i len seeds)
(if (< i len)
(receive (elt . new-seeds)
(apply f i seeds)
(vector-set! vec i elt)
(unfold2+! f vec (+ i 1) len new-seeds))))))
(lambda (f len . initial-seeds)
(let ((f (check-type procedure? f vector-unfold))
(len (check-type nonneg-int? len vector-unfold)))
(let ((vec (make-vector len)))
(cond ((null? initial-seeds)
(tabulate! f vec 0 len))
((null? (cdr initial-seeds))
(unfold1! f vec 0 len (car initial-seeds)))
(else
(unfold2+! f vec 0 len initial-seeds)))
vec)))))
;;; (VECTOR-UNFOLD-RIGHT <f> <length> <initial-seed> ...) -> vector
;;; (F <seed> ...) -> [seed' ...]
;;; Like VECTOR-UNFOLD, but it generates elements from LENGTH to 0
;;; (still exclusive with LENGTH and inclusive with 0), not 0 to
;;; LENGTH as with VECTOR-UNFOLD.
(define vector-unfold-right
(letrec ((tabulate!
(lambda (f vec i)
(cond ((>= i 0)
(vector-set! vec i (f i))
(tabulate! f vec (- i 1))))))
(unfold1!
(lambda (f vec i seed)
(if (>= i 0)
(receive (elt new-seed)
(f i seed)
(vector-set! vec i elt)
(unfold1! f vec (- i 1) new-seed)))))
(unfold2+!
(lambda (f vec i seeds)
(if (>= i 0)
(receive (elt . new-seeds)
(apply f i seeds)
(vector-set! vec i elt)
(unfold2+! f vec (- i 1) new-seeds))))))
(lambda (f len . initial-seeds)
(let ((f (check-type procedure? f vector-unfold-right))
(len (check-type nonneg-int? len vector-unfold-right)))
(let ((vec (make-vector len))
(i (- len 1)))
(cond ((null? initial-seeds)
(tabulate! f vec i))
((null? (cdr initial-seeds))
(unfold1! f vec i (car initial-seeds)))
(else
(unfold2+! f vec i initial-seeds)))
vec)))))
;++ Flush VECTOR-TABULATE: it's superseded by VECTOR-UNFOLD.
;;; (VECTOR-TABULATE <f> <length>) -> vector
;;; (F <index>)
;;; Create a vector whose length is LENGTH. Initialize it with the
;;; results of (f INDEX) for every INDEX in the resulting vector.
;;; The order of applications of F is unspecified.
;++(define (vector-tabulate f len)
;++ (check-type procedure? f vector-tabulate)
;++ (check-type nonneg-int? len vector-tabulate)
;++ (let ((new-vector (make-vector len)))
;++ (do ((i 0 (+ i 1)))
;++ ((= i len) new-vector)
;++ (vector-set! new-vector i (f i)))))
;;; (VECTOR-COPY <vector> [<start> <end> <fill>]) -> vector
;;; Create a newly allocated vector containing the elements from the
;;; range [START,END) in VECTOR. START defaults to 0; END defaults
;;; to the length of VECTOR. END may be greater than the length of
;;; VECTOR, in which case the vector is enlarged; if FILL is passed,
;;; the new locations from which there is no respective element in
;;; VECTOR are filled with FILL.
(define (vector-copy vec . args)
(let ((vec (check-type vector? vec vector-copy)))
;; We can't use LET-VECTOR-START+END, because we have one more
;; argument, and we want finer control, too.
;;
;; Olin's implementation of LET*-OPTIONALS would prove useful here:
;; the built-in argument-checks-as-you-go-along produces almost
;; _exactly_ the same code as VECTOR-COPY:PARSE-ARGS.
(receive (start end fill)
(vector-copy:parse-args vec args)
(let ((new-vector (make-vector (- end start) fill)))
(%vector-copy! new-vector 0
vec start
(if (> end (vector-length vec))
(vector-length vec)
end))
new-vector))))
;;; Auxiliary for VECTOR-COPY.
(define (vector-copy:parse-args vec args)
(if (null? args)
(values 0 (vector-length vec) (unspecified-value))
(let ((start (check-index vec (car args) vector-copy)))
(if (null? (cdr args))
(values start (vector-length vec) (unspecified-value))
(let ((end (check-type nonneg-int? (cadr args)
vector-copy)))
(cond ((>= start (vector-length vec))
(error "start bound out of bounds"
`(start was ,start)
`(end was ,end)
`(vector was ,vec)
`(while calling ,vector-copy)))
((> start end)
(error "can't invert a vector copy!"
`(start was ,start)
`(end was ,end)
`(vector was ,vec)
`(while calling ,vector-copy)))
((null? (cddr args))
(values start end (unspecified-value)))
(else
(let ((fill (caddr args)))
(if (null? (cdddr args))
(values start end fill)
(error "too many arguments"
vector-copy
(cdddr args)))))))))))
;;; (VECTOR-REVERSE-COPY <vector> [<start> <end>]) -> vector
;;; Create a newly allocated vector whose elements are the reversed
;;; sequence of elements between START and END in VECTOR. START's
;;; default is 0; END's default is the length of VECTOR.
(define (vector-reverse-copy vec . maybe-start+end)
(let-vector-start+end vector-reverse-copy vec maybe-start+end
(start end)
(let ((new (make-vector (- end start))))
(%vector-reverse-copy! new 0 vec start end)
new)))
;;; (VECTOR-APPEND <vector> ...) -> vector
;;; Append VECTOR ... into a newly allocated vector and return that
;;; new vector.
(define (vector-append . vectors)
(vector-concatenate:aux vectors vector-append))
;;; (VECTOR-CONCATENATE <vector-list>) -> vector
;;; Concatenate the vectors in VECTOR-LIST. This is equivalent to
;;; (apply vector-append VECTOR-LIST)
;;; but VECTOR-APPEND tends to be implemented in terms of
;;; VECTOR-CONCATENATE, and some Schemes bork when the list to apply
;;; a function to is too long.
;;;
;;; Actually, they're both implemented in terms of an internal routine.
(define (vector-concatenate vector-list)
(vector-concatenate:aux vector-list vector-concatenate))
;;; Auxiliary for VECTOR-APPEND and VECTOR-CONCATENATE
(define vector-concatenate:aux
(letrec ((compute-length
(lambda (vectors len callee)
(if (null? vectors)
len
(let ((vec (check-type vector? (car vectors)
callee)))
(compute-length (cdr vectors)
(+ (vector-length vec) len)
callee)))))
(concatenate!
(lambda (vectors target to)
(if (null? vectors)
target
(let* ((vec1 (car vectors))
(len (vector-length vec1)))
(%vector-copy! target to vec1 0 len)
(concatenate! (cdr vectors) target
(+ to len)))))))
(lambda (vectors callee)
(cond ((null? vectors) ;+++
(make-vector 0))
((null? (cdr vectors)) ;+++
;; Blech, we still have to allocate a new one.
(let* ((vec (check-type vector? (car vectors) callee))
(len (vector-length vec))
(new (make-vector len)))
(%vector-copy! new 0 vec 0 len)
new))
(else
(let ((new-vector
(make-vector (compute-length vectors 0 callee))))
(concatenate! vectors new-vector 0)
new-vector))))))
;;; --------------------
;;; Predicates
;;; (VECTOR? <value>) -> boolean
;;; [R5RS] Return #T if VALUE is a vector and #F if not.
(define vector? vector?)
;;; (VECTOR-EMPTY? <vector>) -> boolean
;;; Return #T if VECTOR has zero elements in it, i.e. VECTOR's length
;;; is 0, and #F if not.
(define (vector-empty? vec)
(let ((vec (check-type vector? vec vector-empty?)))
(zero? (vector-length vec))))
;;; (VECTOR= <elt=?> <vector> ...) -> boolean
;;; (ELT=? <value> <value>) -> boolean
;;; Determine vector equality generalized across element comparators.
;;; Vectors A and B are equal iff their lengths are the same and for
;;; each respective elements E_a and E_b (element=? E_a E_b) returns
;;; a true value. ELT=? is always applied to two arguments. Element
;;; comparison must be consistent wtih EQ?; that is, if (eq? E_a E_b)
;;; results in a true value, then (ELEMENT=? E_a E_b) must result in a
;;; true value. This may be exploited to avoid multiple unnecessary
;;; element comparisons. (This implementation does, but does not deal
;;; with the situation that ELEMENT=? is EQ? to avoid more unnecessary
;;; comparisons, but I believe this optimization is probably fairly
;;; insignificant.)
;;;
;;; If the number of vector arguments is zero or one, then #T is
;;; automatically returned. If there are N vector arguments,
;;; VECTOR_1 VECTOR_2 ... VECTOR_N, then VECTOR_1 & VECTOR_2 are
;;; compared; if they are equal, the vectors VECTOR_2 ... VECTOR_N
;;; are compared. The precise order in which ELT=? is applied is not
;;; specified.
(define (vector= elt=? . vectors)
(let ((elt=? (check-type procedure? elt=? vector=)))
(cond ((null? vectors)
#t)
((null? (cdr vectors))
(check-type vector? (car vectors) vector=)
#t)
(else
(let loop ((vecs vectors))
(let ((vec1 (check-type vector? (car vecs) vector=))
(vec2+ (cdr vecs)))
(or (null? vec2+)
(and (binary-vector= elt=? vec1 (car vec2+))
(loop vec2+)))))))))
(define (binary-vector= elt=? vector-a vector-b)
(or (eq? vector-a vector-b) ;+++
(let ((length-a (vector-length vector-a))
(length-b (vector-length vector-b)))
(letrec ((loop (lambda (i)
(or (= i length-a)
(and (< i length-b)
(test (vector-ref vector-a i)
(vector-ref vector-b i)
i)))))
(test (lambda (elt-a elt-b i)
(and (or (eq? elt-a elt-b) ;+++
(elt=? elt-a elt-b))
(loop (+ i 1))))))
(and (= length-a length-b)
(loop 0))))))
;;; --------------------
;;; Selectors
;;; (VECTOR-REF <vector> <index>) -> value
;;; [R5RS] Return the value that the location in VECTOR at INDEX is
;;; mapped to in the store.
(define vector-ref vector-ref)
;;; (VECTOR-LENGTH <vector>) -> exact, nonnegative integer
;;; [R5RS] Return the length of VECTOR.
(define vector-length vector-length)
;;; --------------------
;;; Iteration
;;; (VECTOR-FOLD <kons> <initial-knil> <vector> ...) -> knil
;;; (KONS <knil> <elt> ...) -> knil' ; N vectors -> N+1 args
;;; The fundamental vector iterator. KONS is iterated over each
;;; index in all of the vectors in parallel, stopping at the end of
;;; the shortest; KONS is applied to an argument list of (list I
;;; STATE (vector-ref VEC I) ...), where STATE is the current state
;;; value -- the state value begins with KNIL and becomes whatever
;;; KONS returned at the respective iteration --, and I is the
;;; current index in the iteration. The iteration is strictly left-
;;; to-right.
;;; (vector-fold KONS KNIL (vector E_1 E_2 ... E_N))
;;; <=>
;;; (KONS (... (KONS (KONS KNIL E_1) E_2) ... E_N-1) E_N)
(define (vector-fold kons knil vec . vectors)
(let ((kons (check-type procedure? kons vector-fold))
(vec (check-type vector? vec vector-fold)))
(if (null? vectors)
(%vector-fold1 kons knil (vector-length vec) vec)
(%vector-fold2+ kons knil
(%smallest-length vectors
(vector-length vec)
vector-fold)
(cons vec vectors)))))
;;; (VECTOR-FOLD-RIGHT <kons> <initial-knil> <vector> ...) -> knil
;;; (KONS <knil> <elt> ...) -> knil' ; N vectors => N+1 args
;;; The fundamental vector recursor. Iterates in parallel across
;;; VECTOR ... right to left, applying KONS to the elements and the
;;; current state value; the state value becomes what KONS returns
;;; at each next iteration. KNIL is the initial state value.
;;; (vector-fold-right KONS KNIL (vector E_1 E_2 ... E_N))
;;; <=>
;;; (KONS (... (KONS (KONS KNIL E_N) E_N-1) ... E_2) E_1)
;;;
;;; Not implemented in terms of a more primitive operations that might
;;; called %VECTOR-FOLD-RIGHT due to the fact that it wouldn't be very
;;; useful elsewhere.
(define vector-fold-right
(letrec ((loop1 (lambda (kons knil vec i)
(if (negative? i)
knil
(loop1 kons (kons i knil (vector-ref vec i))
vec
(+ i 1)))))
(loop2+ (lambda (kons knil vectors i)
(if (negative? i)
knil
(loop2+ kons
(apply kons i knil
(vectors-ref vectors i))
vectors
(+ i 1))))))
(lambda (kons knil vec . vectors)
(let ((kons (check-type procedure? kons vector-fold-right))
(vec (check-type vector? vec vector-fold-right)))
(if (null? vectors)
(loop1 kons knil vec (- (vector-length vec) 1))
(loop2+ kons knil (cons vec vectors)
(- (%smallest-length vectors
(vector-length vec)
vector-fold-right)
1)))))))
;;; (VECTOR-MAP <f> <vector> ...) -> vector
;;; (F <elt> ...) -> value ; N vectors -> N args
;;; Constructs a new vector of the shortest length of the vector
;;; arguments. Each element at index I of the new vector is mapped
;;; from the old vectors by (F I (vector-ref VECTOR I) ...). The
;;; dynamic order of application of F is unspecified.
(define (vector-map f vec . vectors)
(let ((f (check-type procedure? f vector-map))
(vec (check-type vector? vec vector-map)))
(if (null? vectors)
(let ((len (vector-length vec)))
(%vector-map1! f (make-vector len) vec len))
(let ((len (%smallest-length vectors
(vector-length vec)
vector-map)))
(%vector-map2+! f (make-vector len) vectors len)))))
;;; (VECTOR-MAP! <f> <vector> ...) -> unspecified
;;; (F <elt> ...) -> element' ; N vectors -> N args
;;; Similar to VECTOR-MAP, but rather than mapping the new elements
;;; into a new vector, the new mapped elements are destructively
;;; inserted into the first vector. Again, the dynamic order of
;;; application of F is unspecified, so it is dangerous for F to
;;; manipulate the first VECTOR.
(define (vector-map! f vec . vectors)
(let ((f (check-type procedure? f vector-map!))
(vec (check-type vector? vec vector-map!)))
(if (null? vectors)
(%vector-map1! f vec vec (vector-length vec))
(%vector-map2+! f vec (cons vec vectors)
(%smallest-length vectors
(vector-length vec)
vector-map!)))
(unspecified-value)))
;;; (VECTOR-FOR-EACH <f> <vector> ...) -> unspecified
;;; (F <elt> ...) ; N vectors -> N args
;;; Simple vector iterator: applies F to each index in the range [0,
;;; LENGTH), where LENGTH is the length of the smallest vector
;;; argument passed, and the respective element at that index. In
;;; contrast with VECTOR-MAP, F is reliably applied to each
;;; subsequent elements, starting at index 0 from left to right, in
;;; the vectors.
(define vector-for-each
(letrec ((for-each1
(lambda (f vec i len)
(cond ((< i len)
(f i (vector-ref vec i))
(for-each1 f vec (+ i 1) len)))))
(for-each2+
(lambda (f vecs i len)
(cond ((< i len)
(apply f i (vectors-ref vecs i))
(for-each2+ f vecs (+ i 1) len))))))
(lambda (f vec . vectors)
(let ((f (check-type procedure? f vector-for-each))
(vec (check-type vector? vec vector-for-each)))
(if (null? vectors)
(for-each1 f vec 0 (vector-length vec))
(for-each2+ f (cons vec vectors) 0
(%smallest-length vectors
(vector-length vec)
vector-for-each)))))))
;;; (VECTOR-COUNT <predicate?> <vector> ...)
;;; -> exact, nonnegative integer
;;; (PREDICATE? <index> <value> ...) ; N vectors -> N+1 args
;;; PREDICATE? is applied element-wise to the elements of VECTOR ...,
;;; and a count is tallied of the number of elements for which a
;;; true value is produced by PREDICATE?. This count is returned.
(define (vector-count pred? vec . vectors)
(let ((pred? (check-type procedure? pred? vector-count))
(vec (check-type vector? vec vector-count)))
(if (null? vectors)
(%vector-fold1 (lambda (index count elt)
(if (pred? index elt)
(+ count 1)
count))
0
(vector-length vec)
vec)
(%vector-fold2+ (lambda (index count . elts)
(if (apply pred? index elts)
(+ count 1)
count))
0
(%smallest-length vectors
(vector-length vec)
vector-count)
(cons vec vectors)))))
;;; --------------------
;;; Searching
;;; (VECTOR-INDEX <predicate?> <vector> ...)
;;; -> exact, nonnegative integer or #F
;;; (PREDICATE? <elt> ...) -> boolean ; N vectors -> N args
;;; Search left-to-right across VECTOR ... in parallel, returning the
;;; index of the first set of values VALUE ... such that (PREDICATE?
;;; VALUE ...) returns a true value; if no such set of elements is
;;; reached, return #F.
(define (vector-index pred? vec . vectors)
(vector-index/skip pred? vec vectors vector-index))
;;; (VECTOR-SKIP <predicate?> <vector> ...)
;;; -> exact, nonnegative integer or #F
;;; (PREDICATE? <elt> ...) -> boolean ; N vectors -> N args
;;; (vector-index (lambda elts (not (apply PREDICATE? elts)))
;;; VECTOR ...)
;;; Like VECTOR-INDEX, but find the index of the first set of values
;;; that do _not_ satisfy PREDICATE?.
(define (vector-skip pred? vec . vectors)
(vector-index/skip (lambda elts (not (apply pred? elts)))
vec vectors
vector-skip))
;;; Auxiliary for VECTOR-INDEX & VECTOR-SKIP
(define vector-index/skip
(letrec ((loop1 (lambda (pred? vec len i)
(cond ((= i len) #f)
((pred? (vector-ref vec i)) i)
(else (loop1 pred? vec len (+ i 1))))))
(loop2+ (lambda (pred? vectors len i)
(cond ((= i len) #f)
((apply pred? (vectors-ref vectors i)) i)
(else (loop2+ pred? vectors len
(+ i 1)))))))
(lambda (pred? vec vectors callee)
(let ((pred? (check-type procedure? pred? callee))
(vec (check-type vector? vec callee)))
(if (null? vectors)
(loop1 pred? vec (vector-length vec) 0)
(loop2+ pred? (cons vec vectors)
(%smallest-length vectors
(vector-length vec)
callee)
0))))))
;;; (VECTOR-INDEX-RIGHT <predicate?> <vector> ...)
;;; -> exact, nonnegative integer or #F
;;; (PREDICATE? <elt> ...) -> boolean ; N vectors -> N args
;;; Right-to-left variant of VECTOR-INDEX.
(define (vector-index-right pred? vec . vectors)
(vector-index/skip-right pred? vec vectors vector-index-right))
;;; (VECTOR-SKIP-RIGHT <predicate?> <vector> ...)
;;; -> exact, nonnegative integer or #F
;;; (PREDICATE? <elt> ...) -> boolean ; N vectors -> N args
;;; Right-to-left variant of VECTOR-SKIP.
(define (vector-skip-right pred? vec . vectors)
(vector-index/skip-right (lambda elts (not (apply pred? elts)))
vec vectors
vector-index-right))
(define vector-index/skip-right
(letrec ((loop1 (lambda (pred? vec i)
(cond ((negative? i) #f)
((pred? (vector-ref vec i)) i)
(else (loop1 pred? vec (- i 1))))))
(loop2+ (lambda (pred? vectors i)
(cond ((negative? i) #f)
((apply pred? (vectors-ref vectors i)) i)
(else (loop2+ pred? vectors (- i 1)))))))
(lambda (pred? vec vectors callee)
(let ((pred? (check-type procedure? pred? callee))
(vec (check-type vector? vec callee)))
(if (null? vectors)
(loop1 pred? vec (- (vector-length vec) 1))
(loop2+ pred? (cons vec vectors)
(- (%smallest-length vectors
(vector-length vec)
callee)
1)))))))
;;; (VECTOR-BINARY-SEARCH <vector> <value> <cmp> [<start> <end>])
;;; -> exact, nonnegative integer or #F
;;; (CMP <value1> <value2>) -> integer
;;; positive -> VALUE1 > VALUE2
;;; zero -> VALUE1 = VALUE2
;;; negative -> VALUE1 < VALUE2
;;; Perform a binary search through VECTOR for VALUE, comparing each
;;; element to VALUE with CMP.
(define (vector-binary-search vec value cmp . maybe-start+end)
(let ((cmp (check-type procedure? cmp vector-binary-search)))
(let-vector-start+end vector-binary-search vec maybe-start+end
(start end)
(let loop ((start start) (end end) (j #f))
(let ((i (quotient (+ start end) 2)))
(if (and j (= i j))
#f
(let ((comparison
(check-type integer?
(cmp (vector-ref vec i) value)
`(,cmp for ,vector-binary-search))))
(cond ((zero? comparison) i)
((positive? comparison) (loop start i i))
(else (loop i end i))))))))))
;;; (VECTOR-ANY <pred?> <vector> ...) -> value
;;; Apply PRED? to each parallel element in each VECTOR ...; if PRED?
;;; should ever return a true value, immediately stop and return that
;;; value; otherwise, when the shortest vector runs out, return #F.
;;; The iteration and order of application of PRED? across elements
;;; is of the vectors is strictly left-to-right.
(define vector-any
(letrec ((loop1 (lambda (pred? vec i len len-1)
(and (not (= i len))
(if (= i len-1)
(pred? (vector-ref vec i))
(or (pred? (vector-ref vec i))
(loop1 pred? vec (+ i 1)
len len-1))))))
(loop2+ (lambda (pred? vectors i len len-1)
(and (not (= i len))
(if (= i len-1)
(apply pred? (vectors-ref vectors i))
(or (apply pred? (vectors-ref vectors i))
(loop2+ pred? vectors (+ i 1)
len len-1)))))))
(lambda (pred? vec . vectors)
(let ((pred? (check-type procedure? pred? vector-any))
(vec (check-type vector? vec vector-any)))
(if (null? vectors)
(let ((len (vector-length vec)))
(loop1 pred? vec 0 len (- len 1)))
(let ((len (%smallest-length vectors
(vector-length vec)
vector-any)))
(loop2+ pred? (cons vec vectors) 0 len (- len 1))))))))
;;; (VECTOR-EVERY <pred?> <vector> ...) -> value
;;; Apply PRED? to each parallel value in each VECTOR ...; if PRED?
;;; should ever return #F, immediately stop and return #F; otherwise,
;;; if PRED? should return a true value for each element, stopping at
;;; the end of the shortest vector, return the last value that PRED?
;;; returned. In the case that there is an empty vector, return #T.
;;; The iteration and order of application of PRED? across elements
;;; is of the vectors is strictly left-to-right.
(define vector-every
(letrec ((loop1 (lambda (pred? vec i len len-1)
(or (= i len)
(if (= i len-1)
(pred? (vector-ref vec i))
(and (pred? (vector-ref vec i))
(loop1 pred? vec (+ i 1)
len len-1))))))
(loop2+ (lambda (pred? vectors i len len-1)
(or (= i len)
(if (= i len-1)
(apply pred? (vectors-ref vectors i))
(and (apply pred? (vectors-ref vectors i))
(loop2+ pred? vectors (+ i 1)
len len-1)))))))
(lambda (pred? vec . vectors)
(let ((pred? (check-type procedure? pred? vector-every))
(vec (check-type vector? vec vector-every)))
(if (null? vectors)
(let ((len (vector-length vec)))
(loop1 pred? vec 0 len (- len 1)))
(let ((len (%smallest-length vectors
(vector-length vec)
vector-every)))
(loop2+ pred? (cons vec vectors) 0 len (- len 1))))))))
;;; --------------------
;;; Mutators
;;; (VECTOR-SET! <vector> <index> <value>) -> unspecified
;;; [R5RS] Assign the location at INDEX in VECTOR to VALUE.
(define vector-set! vector-set!)
;;; (VECTOR-SWAP! <vector> <index1> <index2>) -> unspecified
;;; Swap the values in the locations at INDEX1 and INDEX2.
(define (vector-swap! vec i j)
(let ((vec (check-type vector? vec vector-swap!)))
(let ((i (check-index vec i vector-swap!))
(j (check-index vec j vector-swap!)))
(let ((x (vector-ref vec i)))
(vector-set! vec i (vector-ref vec j))
(vector-set! vec j x)))))
;;; (VECTOR-FILL! <vector> <value> [<start> <end>]) -> unspecified
;;; [R5RS+] Fill the locations in VECTOR between START, whose default
;;; is 0, and END, whose default is the length of VECTOR, with VALUE.
;;;
;;; This one can probably be made really fast natively.
(define vector-fill!
(let ((%vector-fill! vector-fill!)) ; Take the native one, under
; the assumption that it's
; faster, so we can use it if
; there are no optional
; arguments.
(lambda (vec value . maybe-start+end)
(if (null? maybe-start+end)
(%vector-fill! vec value) ;+++
(let-vector-start+end vector-fill! vec maybe-start+end
(start end)
(do ((i start (+ i 1)))
((= i end))
(vector-set! vec i value)))))))
;;; (VECTOR-COPY! <target> <tstart> <source> [<sstart> <send>])
;;; -> unspecified
;;; Copy the values in the locations in [SSTART,SEND) from SOURCE to
;;; to TARGET, starting at TSTART in TARGET.
(define (vector-copy! target tstart source . maybe-sstart+send)
(let* ((target (check-type vector? target vector-copy!))
(tstart (check-index target tstart vector-copy!)))
(let-vector-start+end vector-copy! source maybe-sstart+send
(sstart send)
(let* ((source-length (vector-length source))
(lose (lambda (argument)
(error "vector range out of bounds"
argument
`(while calling ,vector-copy!)
`(target was ,target)
`(target-length was ,(vector-length target))
`(tstart was ,tstart)
`(source was ,source)
`(source-length was ,source-length)
`(sstart was ,sstart)
`(send was ,send)))))
(cond ((< sstart 0)
(lose '(sstart < 0)))
((< send 0)
(lose '(send < 0)))
((> sstart send)
(lose '(sstart > send)))
((>= sstart source-length)
(lose '(sstart >= source-length)))
((> send source-length)
(lose '(send > source-length)))
(else
(%vector-copy! target tstart
source sstart send)))))))
;;; (VECTOR-REVERSE-COPY! <target> <tstart> <source> [<sstart> <send>])
(define (vector-reverse-copy! target tstart source . maybe-sstart+send)
(let* ((target (check-type vector? target vector-reverse-copy!))
(tstart (check-index target tstart vector-reverse-copy!)))
(let-vector-start+end vector-reverse-copy source maybe-sstart+send
(sstart send)
(let* ((source-length (vector-length source))
(lose (lambda (argument)
(error "vector range out of bounds"
argument
`(while calling ,vector-reverse-copy!)
`(target was ,target)
`(target-length was ,(vector-length target))
`(tstart was ,tstart)
`(source was ,source)
`(source-length was ,source-length)
`(sstart was ,sstart)
`(send was ,send)))))
(cond ((< sstart 0)
(lose '(sstart < 0)))
((< send 0)
(lose '(send < 0)))
((> sstart send)
(lose '(sstart > send)))
((>= sstart source-length)
(lose '(sstart >= source-length)))
((> send source-length)
(lose '(send > source-length)))
((and (eq? target source)
(= sstart tstart))
(%vector-reverse! target tstart send))
((and (eq? target source)
(or (between? sstart tstart send)
(between? sstart (+ tstart (- send sstart))
send)))
(error "vector range for self-copying overlaps"
vector-reverse-copy!
`(vector was ,target)
`(tstart was ,tstart)
`(sstart was ,sstart)
`(send was ,send)))
(else
(%vector-reverse-copy! target tstart
source sstart send)))))))
;;; (VECTOR-REVERSE! <vector> [<start> <end>]) -> unspecified
;;; Destructively reverse the contents of the sequence of locations
;;; in VECTOR between START, whose default is 0, and END, whose
;;; default is the length of VECTOR.
(define (vector-reverse! vec . start+end)
(let-vector-start+end vector-reverse! vec start+end
(start end)
(%vector-reverse! vec start end)))
;;; --------------------
;;; Conversion
;;; (VECTOR->LIST <vector> [<start> <end>]) -> list
;;; [R5RS+] Produce a list containing the elements in the locations
;;; between START, whose default is 0, and END, whose default is the
;;; length of VECTOR, from VECTOR.
(define vector->list
(let ((%vector->list vector->list))
(lambda (vec . maybe-start+end)
(if (null? maybe-start+end) ; Oughta use CASE-LAMBDA.
(%vector->list vec) ;+++
(let-vector-start+end vector->list vec maybe-start+end
(start end)
;(unfold (lambda (i) ; No SRFI 1.
; (< i start))
; (lambda (i) (vector-ref vec i))
; (lambda (i) (- i 1))
; (- end 1))
(do ((i (- end 1) (- i 1))
(result '() (cons (vector-ref vec i) result)))
((< i start) result)))))))
;;; (REVERSE-VECTOR->LIST <vector> [<start> <end>]) -> list
;;; Produce a list containing the elements in the locations between
;;; START, whose default is 0, and END, whose default is the length
;;; of VECTOR, from VECTOR, in reverse order.
(define (reverse-vector->list vec . maybe-start+end)
(let-vector-start+end reverse-vector->list vec maybe-start+end
(start end)
;(unfold (lambda (i) (= i end)) ; No SRFI 1.
; (lambda (i) (vector-ref vec i))
; (lambda (i) (+ i 1))
; start)
(do ((i start (+ i 1))
(result '() (cons (vector-ref vec i) result)))
((= i end) result))))
;;; (LIST->VECTOR <list> [<start> <end>]) -> vector
;;; [R5RS+] Produce a vector containing the elements in LIST, which
;;; must be a proper list, between START, whose default is 0, & END,
;;; whose default is the length of LIST. It is suggested that if the
;;; length of LIST is known in advance, the START and END arguments
;;; be passed, so that LIST->VECTOR need not call LENGTH to determine
;;; the the length.
;;;
;;; This implementation diverges on circular lists, unless LENGTH fails
;;; and causes - to fail as well. Given a LENGTH* that computes the
;;; length of a list's cycle, this wouldn't diverge, and would work
;;; great for circular lists.
(define list->vector
(let ((%list->vector list->vector))
(lambda (lst . maybe-start+end)
;; Checking the type of a proper list is expensive, so we do it
;; amortizedly, or let %LIST->VECTOR or LIST-TAIL do it.
(if (null? maybe-start+end) ; Oughta use CASE-LAMBDA.
(%list->vector lst) ;+++
;; We can't use LET-VECTOR-START+END, because we're using the
;; bounds of a _list_, not a vector.
(let*-optionals maybe-start+end
((start 0)
(end (length lst))) ; Ugh -- LENGTH
(let ((start (check-type nonneg-int? start list->vector))
(end (check-type nonneg-int? end list->vector)))
((lambda (f)
(vector-unfold f (- end start) lst))
(lambda (l)
(cond ((null? l)
(error "list was too short"
`(list was ,lst)
`(attempted end was ,end)
`(while calling ,list->vector)))
((pair? l)
(values (car l) (cdr l)))
(else
;; Make this look as much like what CHECK-TYPE
;; would report as possible.
(error "erroneous value"
;; We want SRFI 1's PROPER-LIST?, but it
;; would be a waste to link all of SRFI
;; 1 to this module for only the single
;; function PROPER-LIST?.
(list list? lst)
`(while calling
,list->vector))))))))))))
;;; (REVERSE-LIST->VECTOR <list> [<start> <end>]) -> vector
;;; Produce a vector containing the elements in LIST, which must be a
;;; proper list, between START, whose default is 0, and END, whose
;;; default is the length of LIST, in reverse order. It is suggested
;;; that if the length of LIST is known in advance, the START and END
;;; arguments be passed, so that REVERSE-LIST->VECTOR need not call
;;; LENGTH to determine the the length.
;;;
;;; This also diverges on circular lists unless, again, LENGTH returns
;;; something that makes - bork.
(define (reverse-list->vector lst . maybe-start+end)
(let*-optionals maybe-start+end
((start 0)
(end (length lst))) ; Ugh -- LENGTH
(let ((start (check-type nonneg-int? start reverse-list->vector))
(end (check-type nonneg-int? end reverse-list->vector)))
((lambda (f)
(vector-unfold-right f (- end start) lst))
(lambda (index l)
(cond ((null? l)
(error "list too short"
`(list was ,lst)
`(attempted end was ,end)
`(while calling ,reverse-list->vector)))
((pair? l)
(values (car l) (cdr l)))
(else
(error "erroneous value"
(list list? lst)
`(while calling ,reverse-list->vector)))))))))