summaryrefslogtreecommitdiffstats
path: root/differ.scm
blob: 6acc25389a26eee1aa8ccfd50d046fe64028f069 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
;;;; "differ.scm" O(NP) Sequence Comparison Algorithm.
;;; 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
;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.

(require 'array)

;;; 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)))

;;;; 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-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 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-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 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-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")
;;@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)