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+;;; "differ.scm" O(NP) Sequence Comparison Algorithm.
+;;; Copyright (C) 2001, 2002, 2003, 2004 Aubrey Jaffer
+
+;;;
+;;; Taken from Slib 3a2 and adapated by Ludovic Courtès
+;;; <ludovic.courtes@laas.fr> to use Guile's native API (March 2007).
+;;;
+
+(define-module (differ)
+ :export (diff:longest-common-subsequence diff:edits
+ diff:edit-length))
+
+;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.
+
+;;@noindent
+;;@code{diff:edit-length} implements the algorithm:
+;;
+;;@ifinfo
+;;@example
+;;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/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>,
+;;Information Processing Letters 35, 6 (1990), 317-323.
+;;@end ifset
+;;
+;;@noindent
+;;The values returned by @code{diff:edit-length} can be used to gauge
+;;the degree of match between two sequences.
+;;
+;;@noindent
+;;@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
+;;edit-list is equivalent to the output of the @dfn{diff} utility
+;;program. If the items being sequenced are words, then it is like the
+;;lesser known @dfn{spiff} program.
+
+
+;;; 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 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 fpoff k A M B N CC p))
+ (do ((k (+ Delta p) (+ -1 k)))
+ ((<= k Delta))
+ (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)
+ (else (loop (+ 1 p)))))))
+
+;;; 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 fpoff k A M B N CC p)
+ (define cost (+ k p p))
+ (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))
+ (else (array-set! CC
+ (min (+ xcst cost) (array-ref CC y))
+ y)))))
+ ;;(set! tick (+ 1 tick))
+ (cond ((and (< x M) (< y N)
+ (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.
+;;(define (fp:step-check A M B N CC)
+;; (do ((cdx (+ -1 N) (+ -1 cdx)))
+;; ((negative? cdx))
+;; (case (- (array-ref CC cdx) (array-ref CC (+ 1 cdx)))
+;; ((1 -1) #t)
+;; (else (cond ((> 30 (car (array-dimensions CC)))
+;; (display "A: ") (print A)
+;; (display "B: ") (print B)))
+;; (slib:warn
+;; "CC" (append (list (max 0 (+ -5 cdx)) ': (min (+ 1 N) (+ 5 cdx))
+;; 'of)
+;; (array-dimensions CC))
+;; (fp:subarray CC (max 0 (+ -5 cdx)) (min (+ 1 N) (+ 5 cdx))))))))
+
+;;; Correct cost jumps left by fp:compare [which visits only a few (x,y)].
+;;(define (smooth-costs CC N)
+;; (do ((cdx (+ -1 N) (+ -1 cdx))) ; smooth from end
+;; ((negative? cdx))
+;; (array-set! CC (min (array-ref CC cdx) (+ 1 (array-ref CC (+ 1 cdx))))
+;; cdx))
+;; (do ((cdx 1 (+ 1 cdx))) ; smooth toward end
+;; ((> cdx N))
+;; (array-set! CC (min (array-ref CC cdx) (+ 1 (array-ref CC (+ -1 cdx))))
+;; cdx))
+;; CC)
+
+(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)))
+ ;;(if (negative? rdx) (slib:error 'negative? 'rdx))
+ (cond ((eqv? cost (+ (array-ref CC rdx) (array-ref RR (- N rdx)))) rdx)
+ ((eqv? cost (+ (array-ref CC cdx) (array-ref RR (- N cdx)))) cdx)
+ (else (loop (+ 1 cdx) (+ -1 rdx))))))
+
+;;; Return 0-based shared array.
+;;; Reverse RA if END < START.
+(define (fp:subarray RA start end)
+ (define n-len (abs (- end start)))
+ (if (< end start)
+ (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 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 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))
+ (let ((tcst (+ p-lim p-lim (- len-b len-a))))
+ (define CC (fp:subarray CCRR 0 (+ len-b 1)))
+ (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 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 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))
+ ;;(smooth-costs CC len-b) (smooth-costs RR len-b)
+ (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))
+ ;;(display "A: ") (array-for-each display (fp:subarray A start-a mid-a)) (display " + ") (array-for-each display (fp:subarray A mid-a end-a)) (newline)
+ ;;(display "B: ") (array-for-each display (fp:subarray B start-b end-b)) (newline)
+ ;;(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 fpoff CCRR
+ A start-a mid-a
+ B start-b (+ start-b b-splt)
+ edits edx epo
+ (quotient (- est-c (- b-splt (- mid-a start-a)))
+ 2)))
+ (check-cost! 'RR est-r
+ (diff2et fp fpoff CCRR
+ A mid-a end-a
+ B (+ start-b b-splt) end-b
+ 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 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)
+ (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)
+ (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 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 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))
+ (cond ((zero? p-lim) ; B inserts only
+ (if (= len-b len-a)
+ 0 ; A = B; no edits
+ (let loop ((adx start-a)
+ (bdx start-b)
+ (edx edx))
+ (cond ((>= bdx end-b) (- len-b len-a))
+ ((>= adx end-a)
+ (do ((idx bdx (+ 1 idx))
+ (edx edx (+ 1 edx)))
+ ((>= idx end-b) (- len-b len-a))
+ (array-set! edits (* epo (+ 1 idx)) edx)))
+ ((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)
+ ;;(set! tick (+ 1 tick))
+ (loop adx (+ 1 bdx) (+ 1 edx)))))))
+ ((<= 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))
+ (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 fpoff CCRR A start-a end-a B start-b end-b
+ edits edx epo p-lim))))
+
+(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 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))
+ ((positive? edit)
+ (loop (+ 1 edx) sdx adx))
+ ((zero? edit)
+ (array-set! lcs (array-ref A adx) sdx)
+ (loop edx (+ 1 sdx) (+ 1 adx)))
+ ((>= adx (- -1 edit))
+ (loop (+ 1 edx) sdx (+ 1 adx)))
+ (else
+ (array-set! lcs (array-ref A adx) sdx)
+ (loop edx (+ 1 sdx) (+ 1 adx)))))))
+
+;; A not longer than B (M <= N)
+(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 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)))
+
+
+;;;
+;;; Public API.
+;;;
+
+;;@args array1 array2 p-lim
+;;@args array1 array2
+;;@1 and @2 are one-dimensional arrays.
+;;
+;;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 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 (< N M)
+ (diff:edits B A p-lim)
+ (diff:edits A B p-lim))))
+ (and edits
+ (let* ((cost (car (array-dimensions edits)))
+ (lcs (make-typed-array (array-type A) *unspecified*
+ (/ (- (+ 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 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 vector of length @code{(diff:edit-length @1 @2)} composed
+;;of a shortest sequence of edits transformaing @1 to @2.
+;;
+;;Each edit is an integer:
+;;@table @asis
+;;@item @var{k} > 0
+;;Inserts @code{(array-ref @1 (+ -1 @var{j}))} into the sequence.
+;;@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 M (car (array-dimensions A)))
+ (define N (car (array-dimensions B)))
+ (set! p-lim (if (null? p-lim) -1 (car p-lim)))
+ (let ((fp (make-typed-array 's32 0
+ (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-typed-array 's32 0 est))
+ (CCRR (make-typed-array 's32 0 (* 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 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)))
+ (set! p-lim (if (null? p-lim) -1 (car p-lim)))
+ (let ((fp (make-typed-array 's32 0
+ (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")
+;;@result{} "fghijklm"
+;;
+;;(diff:edit-length "fghiejcklm" "fgehijkpqrlm")
+;;@result{} 6
+;;
+;;(diff:edits "fghiejcklm" "fgehijkpqrlm")
+;;@result{} #A:fixZ32b(3 -5 -7 8 9 10)
+;; ; e c h p q r
+;;@end example
+
+;;(trace-all "/home/jaffer/slib/differ.scm")(set! *qp-width* 333)(untrace fp:run fp:subarray)
+
+
+;;;arch-tag: 8e80eb1d-fb11-4872-895a-8adcee26580d
generated by cgit v1.2.3 (git 2.45.0) at 2024-07-05 22:12:40 +0000