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-rw-r--r--differ.scm331
1 files changed, 159 insertions, 172 deletions
diff --git a/differ.scm b/differ.scm
index 23b0e91..6acc253 100644
--- a/differ.scm
+++ b/differ.scm
@@ -1,5 +1,5 @@
;;;; "differ.scm" O(NP) Sequence Comparison Algorithm.
-;;; Copyright (C) 2001, 2002, 2003 Aubrey Jaffer
+;;; Copyright (C) 2001, 2002, 2003, 2004 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
@@ -25,14 +25,14 @@
;;S. Wu, E. Myers, U. Manber, and W. Miller,
;; "An O(NP) Sequence Comparison Algorithm,"
;; Information Processing Letters 35, 6 (1990), 317-323.
-;; @url{http://www.cs.arizona.edu/people/gene/vita.html}
+;; @url{http://www.cs.arizona.edu/people/gene/PAPERS/np_diff.ps}
;;@end example
;;@end ifinfo
;;@ifset html
;;S. Wu, <A HREF="http://www.cs.arizona.edu/people/gene/vita.html">
;;E. Myers,</A> U. Manber, and W. Miller,
;;<A HREF="http://www.cs.arizona.edu/people/gene/PAPERS/np_diff.ps">
-;;"An O(NP) Sequence Comparison Algorithm,"</A>
+;;"An O(NP) Sequence Comparison Algorithm"</A>,
;;Information Processing Letters 35, 6 (1990), 317-323.
;;@end ifset
;;
@@ -41,12 +41,24 @@
;;the degree of match between two sequences.
;;
;;@noindent
-;;Surprisingly, "An O(NP) Sequence Comparison Algorithm" does not
-;;derive the edit sequence; only the sequence length. Developing this
-;;linear-space sub-quadratic-time algorithm for computing the edit
-;;sequence required hundreds of hours of work. I have submitted a
-;;paper describing the algorithm to the Journal of Computational
-;;Biology.
+;;@code{diff:edits} and @code{diff:longest-common-subsequence} combine
+;;the algorithm with the divide-and-conquer method outlined in:
+;;
+;;@ifinfo
+;;@example
+;;E. Myers and W. Miller,
+;; "Optimal alignments in linear space",
+;; Computer Application in the Biosciences (CABIOS), 4(1):11-17, 1988.
+;; @url{http://www.cs.arizona.edu/people/gene/PAPERS/linear.ps}
+;;@end example
+;;@end ifinfo
+;;@ifset html
+;;<A HREF="http://www.cs.arizona.edu/people/gene/vita.html">
+;;E. Myers,</A> and W. Miller,
+;;<A HREF="http://www.cs.arizona.edu/people/gene/PAPERS/linear.ps">
+;;"Optimal alignments in linear space"</A>,
+;;Computer Application in the Biosciences (CABIOS), 4(1):11-17, 1988.
+;;@end ifset
;;
;;@noindent
;;If the items being sequenced are text lines, then the computed
@@ -55,24 +67,23 @@
;;lesser known @dfn{spiff} program.
(require 'array)
-(require 'sort)
;;; p-lim is half the number of gratuitous edits for strings of given
;;; lengths.
;;; When passed #f CC, fp:compare returns edit-distance if successful;
;;; #f otherwise (p > p-lim). When passed CC, fp:compare returns #f.
-(define (fp:compare fp CC A M B N =? p-lim)
+(define (fp:compare fp fpoff CC A M B N p-lim)
(define Delta (- N M))
;;(if (negative? Delta) (slib:error 'fp:compare (fp:subarray A 0 M) '> (fp:subarray B 0 N)))
;;(set! compares (+ 1 compares)) ;(print 'fp:compare M N p-lim)
(let loop ((p 0))
(do ((k (- p) (+ 1 k)))
((>= k Delta))
- (fp:run fp k A M B N =? CC p))
+ (fp:run fp fpoff k A M B N CC p))
(do ((k (+ Delta p) (+ -1 k)))
((<= k Delta))
- (fp:run fp k A M B N =? CC p))
- (let ((fpval (fp:run fp Delta A M B N =? CC p)))
+ (fp:run fp fpoff k A M B N CC p))
+ (let ((fpval (fp:run fp fpoff Delta A M B N CC p)))
;; At this point, the cost to (fpval-Delta, fpval) is Delta + 2*p
(cond ((and (not CC) (<= N fpval)) (+ Delta (* 2 p)))
((and (not (negative? p-lim)) (>= p p-lim)) #f)
@@ -81,11 +92,11 @@
;;; Traces runs of matches until they end; then set fp[k]=y.
;;; If CC is supplied, set each CC[y] = min(CC[y], cost) for run.
;;; Returns furthest y reached.
-(define (fp:run fp k A M B N =? CC p)
- (define y (max (+ 1 (array-ref fp (+ -1 k))) (array-ref fp (+ 1 k))))
+(define (fp:run fp fpoff k A M B N CC p)
(define cost (+ k p p))
- (let snloop ((x (- y k))
- (y y))
+ (let snloop ((y (max (+ (array-ref fp (+ -1 k fpoff)) 1)
+ (array-ref fp (+ 1 k fpoff)))))
+ (define x (- y k))
(and CC (<= y N)
(let ((xcst (- M x)))
(cond ((negative? xcst))
@@ -94,9 +105,9 @@
y)))))
;;(set! tick (+ 1 tick))
(cond ((and (< x M) (< y N)
- (=? (array-ref A x) (array-ref B y)))
- (snloop (+ 1 x) (+ 1 y)))
- (else (array-set! fp y k)
+ (eqv? (array-ref A x) (array-ref B y)))
+ (snloop (+ 1 y)))
+ (else (array-set! fp y (+ fpoff k))
y))))
;;; Check that only 1 and -1 steps between adjacent CC entries.
@@ -126,10 +137,7 @@
;; cdx))
;; CC)
-(define (diff:mid-split M N RR CC cost)
- (define b-splt N) ;Default
- (define bestrun 0)
- (define thisrun 0)
+(define (diff:mid-split N RR CC cost)
;; RR is not longer than CC. So do for each element of RR.
(let loop ((cdx (+ 1 (quotient N 2)))
(rdx (quotient N 2)))
@@ -143,18 +151,19 @@
(define (fp:subarray RA start end)
(define n-len (abs (- end start)))
(if (< end start)
- (make-shared-array RA (lambda (idx) (list (- start 1 idx))) n-len)
+ (make-shared-array RA (lambda (idx) (list (+ -1 (- start idx)))) n-len)
(make-shared-array RA (lambda (idx) (list (+ start idx))) n-len)))
-(define (fp:init! fp fill mindx maxdx)
- (do ((idx maxdx (+ -1 idx)))
- ((< idx mindx))
+(define (fp:init! fp fpoff fill mindx maxdx)
+ (define mlim (+ fpoff mindx))
+ (do ((idx (+ fpoff maxdx) (+ -1 idx)))
+ ((< idx mlim))
(array-set! fp fill idx)))
;;; Split A[start-a..end-a] (shorter array) into smaller and smaller chunks.
;;; EDX is index into EDITS.
;;; EPO is insert/delete polarity (+1 or -1)
-(define (diff:divide-and-conquer fp CCRR A start-a end-a B start-b end-b edits edx epo =? p-lim)
+(define (diff:divide-and-conquer fp fpoff CCRR A start-a end-a B start-b end-b edits edx epo p-lim)
(define mid-a (quotient (+ start-a end-a) 2))
(define len-b (- end-b start-b))
(define len-a (- end-a start-a))
@@ -163,18 +172,20 @@
(define RR (fp:subarray CCRR (+ len-b 1) (* 2 (+ len-b 1))))
(define M2 (- end-a mid-a))
(define M1 (- mid-a start-a))
- (fp:init! CC (+ len-a len-b) 0 len-b)
- (fp:init! fp -1 (- (+ 1 p-lim)) (+ 1 p-lim (- len-b M1)))
- (fp:compare fp CC
+ (fp:init! CC 0 (+ len-a len-b) 0 len-b)
+ (fp:init! fp fpoff -1 (- (+ 1 p-lim)) (+ 1 p-lim (- len-b M1)))
+ (fp:compare fp fpoff CC
(fp:subarray A start-a mid-a) M1
- (fp:subarray B start-b end-b) len-b =? (min p-lim len-a))
- (fp:init! RR (+ len-a len-b) 0 len-b)
- (fp:init! fp -1 (- (+ 1 p-lim)) (+ 1 p-lim (- len-b M2)))
- (fp:compare fp RR
+ (fp:subarray B start-b end-b) len-b
+ (min p-lim len-a))
+ (fp:init! RR 0 (+ len-a len-b) 0 len-b)
+ (fp:init! fp fpoff -1 (- (+ 1 p-lim)) (+ 1 p-lim (- len-b M2)))
+ (fp:compare fp fpoff RR
(fp:subarray A end-a mid-a) M2
- (fp:subarray B end-b start-b) len-b =? (min p-lim len-a))
+ (fp:subarray B end-b start-b) len-b
+ (min p-lim len-a))
;;(smooth-costs CC len-b) (smooth-costs RR len-b)
- (let ((b-splt (diff:mid-split len-a len-b RR CC tcst)))
+ (let ((b-splt (diff:mid-split len-b RR CC tcst)))
(define est-c (array-ref CC b-splt))
(define est-r (array-ref RR (- len-b b-splt)))
;;(set! splts (cons (/ b-splt (max .1 len-b)) splts))
@@ -183,49 +194,49 @@
;;(print 'cc cc) (print 'rr (fp:subarray RR (+ 1 len-b) 0))
;;(print (make-string (+ 7 (* 2 b-splt)) #\-) '^ (list b-splt))
(check-cost! 'CC est-c
- (diff2et fp CCRR
+ (diff2et fp fpoff CCRR
A start-a mid-a
B start-b (+ start-b b-splt)
- edits edx epo =?
+ edits edx epo
(quotient (- est-c (- b-splt (- mid-a start-a)))
2)))
(check-cost! 'RR est-r
- (diff2et fp CCRR
+ (diff2et fp fpoff CCRR
A mid-a end-a
B (+ start-b b-splt) end-b
- edits (+ est-c edx) epo =?
+ edits (+ est-c edx) epo
(quotient (- est-r (- (- len-b b-splt)
(- end-a mid-a)))
2)))
(+ est-c est-r))))
;;; Trim; then diff sub-arrays; either one longer. Returns edit-length
-(define (diff2et fp CCRR A start-a end-a B start-b end-b edits edx epo =? p-lim)
+(define (diff2et fp fpoff CCRR A start-a end-a B start-b end-b edits edx epo p-lim)
;; (if (< (- end-a start-a) p-lim) (slib:warn 'diff2et 'len-a (- end-a start-a) 'len-b (- end-b start-b) 'p-lim p-lim))
(do ((bdx (+ -1 end-b) (+ -1 bdx))
(adx (+ -1 end-a) (+ -1 adx)))
((not (and (<= start-b bdx)
(<= start-a adx)
- (=? (array-ref A adx) (array-ref B bdx))))
+ (eqv? (array-ref A adx) (array-ref B bdx))))
(do ((bsx start-b (+ 1 bsx))
(asx start-a (+ 1 asx)))
((not (and (< bsx bdx)
(< asx adx)
- (=? (array-ref A asx) (array-ref B bsx))))
+ (eqv? (array-ref A asx) (array-ref B bsx))))
;;(print 'trim-et (- asx start-a) '+ (- end-a adx))
(let ((delta (- (- bdx bsx) (- adx asx))))
(if (negative? delta)
- (diff2ez fp CCRR B bsx (+ 1 bdx) A asx (+ 1 adx)
- edits edx (- epo) =? (+ delta p-lim))
- (diff2ez fp CCRR A asx (+ 1 adx) B bsx (+ 1 bdx)
- edits edx epo =? p-lim))))
+ (diff2ez fp fpoff CCRR B bsx (+ 1 bdx) A asx (+ 1 adx)
+ edits edx (- epo) (+ delta p-lim))
+ (diff2ez fp fpoff CCRR A asx (+ 1 adx) B bsx (+ 1 bdx)
+ edits edx epo p-lim))))
;;(set! tick (+ 1 tick))
))
;;(set! tick (+ 1 tick))
))
;;; Diff sub-arrays, A not longer than B. Returns edit-length
-(define (diff2ez fp CCRR A start-a end-a B start-b end-b edits edx epo =? p-lim)
+(define (diff2ez fp fpoff CCRR A start-a end-a B start-b end-b edits edx epo p-lim)
(define len-a (- end-a start-a))
(define len-b (- end-b start-b))
;;(if (> len-a len-b) (slib:error 'diff2ez len-a '> len-b))
@@ -241,7 +252,7 @@
(edx edx (+ 1 edx)))
((>= idx end-b) (- len-b len-a))
(array-set! edits (* epo (+ 1 idx)) edx)))
- ((=? (array-ref A adx) (array-ref B bdx))
+ ((eqv? (array-ref A adx) (array-ref B bdx))
;;(set! tick (+ 1 tick))
(loop (+ 1 adx) (+ 1 bdx) edx))
(else (array-set! edits (* epo (+ 1 bdx)) edx)
@@ -250,65 +261,39 @@
((<= len-a p-lim) ; delete all A; insert all B
;;(if (< len-a p-lim) (slib:error 'diff2ez len-a len-b 'p-lim p-lim))
(do ((idx start-a (+ 1 idx))
- (edx edx (+ 1 edx)))
- ((>= idx end-a)
- (do ((jdx start-b (+ 1 jdx))
- (edx edx (+ 1 edx)))
- ((>= jdx end-b))
- (array-set! edits (* epo (+ 1 jdx)) edx)))
- (array-set! edits (* epo (- -1 idx)) edx))
- (+ len-a len-b))
+ (jdx start-b (+ 1 jdx)))
+ ((and (>= idx end-a) (>= jdx end-b)) (+ len-a len-b))
+ (cond ((< jdx end-b)
+ (array-set! edits (* epo (+ 1 jdx)) edx)
+ (set! edx (+ 1 edx))))
+ (cond ((< idx end-a)
+ (array-set! edits (* epo (- -1 idx)) edx)
+ (set! edx (+ 1 edx))))))
(else (diff:divide-and-conquer
- fp CCRR A start-a end-a B start-b end-b
- edits edx epo =? p-lim))))
+ fp fpoff CCRR A start-a end-a B start-b end-b
+ edits edx epo p-lim))))
-;;;Return new vector of edits in correct sequence
-(define (diff:order-edits edits cost sign)
- (if (negative? sign)
- (do ((idx (+ -1 cost) (+ -1 idx)))
- ((negative? idx))
- (array-set! edits (- (array-ref edits idx)) idx)))
- (if (zero? cost)
- edits
- (let ((sedits (sort! edits <))
- (nedits (create-array (As32) cost)))
- ;; Find -/+ boundary
- (define len-a (max 0 (- (array-ref sedits 0))))
- (define len-b (array-ref sedits (+ -1 cost)))
- (do ((idx 0 (+ 1 idx)))
- ((or (>= idx cost) (positive? (array-ref sedits idx)))
- (let loop ((ddx (+ -1 idx))
- (idx idx)
- (ndx 0)
- (adx 0)
- (bdx 0))
- (define del (if (negative? ddx) 0 (array-ref sedits ddx)))
- (define ins (if (>= idx cost) 0 (array-ref sedits idx)))
- (cond ((and (>= bdx len-b) (>= adx len-a)) nedits)
- ((and (negative? del) (>= adx (- -1 del))
- (positive? ins) (>= bdx (+ -1 ins)))
- (array-set! nedits del ndx)
- (array-set! nedits ins (+ 1 ndx))
- (loop (+ -1 ddx) (+ 1 idx) (+ 2 ndx)
- (+ 1 adx) (+ 1 bdx)))
- ((and (negative? del) (>= adx (- -1 del)))
- (array-set! nedits del ndx)
- (loop (+ -1 ddx) idx (+ 1 ndx) (+ 1 adx) bdx))
- ((and (positive? ins) (>= bdx (+ -1 ins)))
- (array-set! nedits ins ndx)
- (loop ddx (+ 1 idx) (+ 1 ndx) adx (+ 1 bdx)))
- (else
- (loop ddx idx ndx (+ 1 adx) (+ 1 bdx))))))))))
+(define (check-cost! name est cost)
+ (if (not (eqv? est cost))
+ (slib:warn name "cost check failed" est '!= cost)))
+
+;;;; Routines interfacing API layer to algorithms.
+
+(define (diff:invert-edits! edits)
+ (define cost (car (array-dimensions edits)))
+ (do ((idx (+ -1 cost) (+ -1 idx)))
+ ((negative? idx))
+ (array-set! edits (- (array-ref edits idx)) idx)))
;;; len-a < len-b
-(define (edits2lcs lcs edits cost A len-a len-b)
+(define (edits2lcs! lcs edits A)
+ (define cost (car (array-dimensions edits)))
+ (define len-a (car (array-dimensions A)))
(let loop ((edx 0)
(sdx 0)
(adx 0))
- (let ((edit (if (< edx cost)
- (array-ref edits edx)
- 0)))
- (cond ((>= adx len-a) lcs)
+ (let ((edit (if (< edx cost) (array-ref edits edx) 0)))
+ (cond ((>= adx len-a))
((positive? edit)
(loop (+ 1 edx) sdx adx))
((zero? edit)
@@ -321,67 +306,56 @@
(loop edx (+ 1 sdx) (+ 1 adx)))))))
;; A not longer than B (M <= N)
-(define (diff2edits A M B N =? p-lim)
- (define maxdx (if (negative? p-lim) (+ 2 N) (+ 1 p-lim (- N M))))
- (define mindx (if (negative? p-lim) (- (+ 1 M)) (- (+ 1 p-lim))))
- ;;(if (> M N) (slib:error 'diff2edits M '> N))
- (let ((fp (create-array (As32) (list mindx maxdx)))
- (CCRR (create-array (As32) (* 2 (+ N 1)))))
- (fp:init! fp -1 mindx maxdx)
- (let ((est (fp:compare fp #f A M B N =? p-lim)))
- (and est
- (let ((edits (create-array (As32) est)))
- (check-cost! 'diff2edits
- est
- (diff2et fp CCRR A 0 M B 0 N edits 0 1 =?
- (quotient (- est (- N M)) 2)))
- edits)))))
+(define (diff2edits! edits fp CCRR A B)
+ (define N (car (array-dimensions B)))
+ (define M (car (array-dimensions A)))
+ (define est (car (array-dimensions edits)))
+ (let ((p-lim (quotient (- est (- N M)) 2)))
+ (check-cost! 'diff2edits!
+ est
+ (diff2et fp (+ 1 p-lim)
+ CCRR A 0 M B 0 N edits 0 1 p-lim))))
;; A not longer than B (M <= N)
-(define (diff2editlen A M B N =? p-lim)
- (define maxdx (if (negative? p-lim) (+ 1 N) (+ 1 p-lim (- N M))))
- (define mindx (if (negative? p-lim) (- (+ 1 M)) (- (+ 1 p-lim))))
- (let ((fp (create-array (As32) (list mindx maxdx))))
- (fp:init! fp -1 mindx maxdx)
- (fp:compare fp #f A M B N =? p-lim)))
+(define (diff2editlen fp A B p-lim)
+ (define N (car (array-dimensions B)))
+ (define M (car (array-dimensions A)))
+ (let ((maxdx (if (negative? p-lim) (+ 1 N) (+ 1 p-lim (- N M))))
+ (mindx (if (negative? p-lim) (- (+ 1 M)) (- (+ 1 p-lim)))))
+ (fp:init! fp (- mindx) -1 mindx maxdx)
+ (fp:compare fp (- mindx) #f A M B N p-lim)))
-(define (check-cost! name est cost)
- (if (not (eqv? est cost))
- (slib:warn "%s: cost check failed %d != %d\\n" name est cost)))
+;;;; API
-;;@args array1 array2 =? p-lim
-;;@args array1 array2 =?
-;;@1 and @2 are one-dimensional arrays. The procedure @3 is used
-;;to compare sequence tokens for equality.
+;;@args array1 array2 p-lim
+;;@args array1 array2
+;;@1 and @2 are one-dimensional arrays.
;;
-;;The non-negative integer @4, if provided, is maximum number of
+;;The non-negative integer @3, if provided, is maximum number of
;;deletions of the shorter sequence to allow. @0 will return @code{#f}
;;if more deletions would be necessary.
;;
;;@0 returns a one-dimensional array of length @code{(quotient (- (+
;;len1 len2) (diff:edit-length @1 @2)) 2)} holding the longest sequence
;;common to both @var{array}s.
-(define (diff:longest-common-subsequence A B =? . p-lim)
- (define len-a (car (array-dimensions a)))
- (define len-b (car (array-dimensions b)))
+(define (diff:longest-common-subsequence A B . p-lim)
+ (define M (car (array-dimensions A)))
+ (define N (car (array-dimensions B)))
(set! p-lim (if (null? p-lim) -1 (car p-lim)))
- (let ((edits (if (< len-b len-a)
- (diff2edits B len-b A len-a =? p-lim)
- (diff2edits A len-a B len-b =? p-lim))))
+ (let ((edits (if (< N M)
+ (diff:edits B A p-lim)
+ (diff:edits A B p-lim))))
(and edits
(let* ((cost (car (array-dimensions edits)))
- (sedit (diff:order-edits edits cost (if (< len-b len-a) -1 1)))
- (lcs (create-array A (/ (- (+ len-b len-a) cost) 2))))
- (if (< len-b len-a)
- (edits2lcs lcs sedit cost B len-b len-a)
- (edits2lcs lcs sedit cost A len-a len-b))))))
+ (lcs (make-array A (/ (- (+ N M) cost) 2))))
+ (edits2lcs! lcs edits (if (< N M) B A))
+ lcs))))
-;;@args array1 array2 =? p-lim
-;;@args array1 array2 =?
-;;@1 and @2 are one-dimensional arrays. The procedure @3 is used
-;;to compare sequence tokens for equality.
+;;@args array1 array2 p-lim
+;;@args array1 array2
+;;@1 and @2 are one-dimensional arrays.
;;
-;;The non-negative integer @4, if provided, is maximum number of
+;;The non-negative integer @3, if provided, is maximum number of
;;deletions of the shorter sequence to allow. @0 will return @code{#f}
;;if more deletions would be necessary.
;;
@@ -395,44 +369,57 @@
;;@item @var{k} < 0
;;Deletes @code{(array-ref @2 (- -1 @var{k}))} from the sequence.
;;@end table
-(define (diff:edits A B =? . p-lim)
- (define len-a (car (array-dimensions a)))
- (define len-b (car (array-dimensions b)))
+(define (diff:edits A B . p-lim)
+ (define M (car (array-dimensions A)))
+ (define N (car (array-dimensions B)))
(set! p-lim (if (null? p-lim) -1 (car p-lim)))
- (let ((edits (if (< len-b len-a)
- (diff2edits B len-b A len-a =? p-lim)
- (diff2edits A len-a B len-b =? p-lim))))
- (and edits (diff:order-edits edits (car (array-dimensions edits))
- (if (< len-b len-a) -1 1)))))
+ (let ((fp (make-array (A:fixZ32b) (if (negative? p-lim)
+ (+ 3 M N)
+ (+ 3 (abs (- N M)) p-lim p-lim)))))
+ (define est (if (< N M)
+ (diff2editlen fp B A p-lim)
+ (diff2editlen fp A B p-lim)))
+ (and est
+ (let ((edits (make-array (A:fixZ32b) est))
+ (CCRR (make-array (A:fixZ32b) (* 2 (+ (max M N) 1)))))
+ (cond ((< N M)
+ (diff2edits! edits fp CCRR B A)
+ (diff:invert-edits! edits))
+ (else
+ (diff2edits! edits fp CCRR A B)))
+ ;;(diff:order-edits! edits est)
+ edits))))
-;;@args array1 array2 =? p-lim
-;;@args array1 array2 =?
-;;@1 and @2 are one-dimensional arrays. The procedure @3 is used
-;;to compare sequence tokens for equality.
+;;@args array1 array2 p-lim
+;;@args array1 array2
+;;@1 and @2 are one-dimensional arrays.
;;
-;;The non-negative integer @4, if provided, is maximum number of
+;;The non-negative integer @3, if provided, is maximum number of
;;deletions of the shorter sequence to allow. @0 will return @code{#f}
;;if more deletions would be necessary.
;;
;;@0 returns the length of the shortest sequence of edits transformaing
;;@1 to @2.
-(define (diff:edit-length A B =? . p-lim)
- (define M (car (array-dimensions a)))
- (define N (car (array-dimensions b)))
+(define (diff:edit-length A B . p-lim)
+ (define M (car (array-dimensions A)))
+ (define N (car (array-dimensions B)))
(set! p-lim (if (null? p-lim) -1 (car p-lim)))
- (if (< N M)
- (diff2editlen B N A M =? p-lim)
- (diff2editlen A M B N =? p-lim)))
+ (let ((fp (make-array (A:fixZ32b) (if (negative? p-lim)
+ (+ 3 M N)
+ (+ 3 (abs (- N M)) p-lim p-lim)))))
+ (if (< N M)
+ (diff2editlen fp B A p-lim)
+ (diff2editlen fp A B p-lim))))
;;@example
-;;(diff:longest-common-subsequence "fghiejcklm" "fgehijkpqrlm" eqv?)
+;;(diff:longest-common-subsequence "fghiejcklm" "fgehijkpqrlm")
;;@result{} "fghijklm"
;;
-;;(diff:edit-length "fghiejcklm" "fgehijkpqrlm" eqv?)
+;;(diff:edit-length "fghiejcklm" "fgehijkpqrlm")
;;@result{} 6
;;
-;;(diff:edits "fghiejcklm" "fgehijkpqrlm" eqv?)
-;;@result{} #As32(3 -5 -7 8 9 10)
+;;(diff:edits "fghiejcklm" "fgehijkpqrlm")
+;;@result{} #A:fixZ32b(3 -5 -7 8 9 10)
;; ; e c h p q r
;;@end example