src/code/sort.lisp

   1 ;;;; SORT and friends
   2
   3 ;;;; This software is part of the SBCL system. See the README file for
   4 ;;;; more information.
   5 ;;;;
   6 ;;;; This software is derived from the CMU CL system, which was
   7 ;;;; written at Carnegie Mellon University and released into the
   8 ;;;; public domain. The software is in the public domain and is
   9 ;;;; provided with absolutely no warranty. See the COPYING and CREDITS
  10 ;;;; files for more information.
  11
  12 (in-package "SB!IMPL")
  13
  14 (defun sort-vector (vector start end predicate-fun key-fun-or-nil)
  15   (sort-vector vector start end predicate-fun key-fun-or-nil))
  16
  17 ;;; This is MAYBE-INLINE because it's not too hard to have an
  18 ;;; application where sorting is a major bottleneck, and inlining it
  19 ;;; allows the compiler to make enough optimizations that it might be
  20 ;;; worth the (large) cost in space.
  21 (declaim (maybe-inline sort stable-sort))
  22 (defun sort (sequence predicate &rest args &key key)
  23   #!+sb-doc
  24   "Destructively sort SEQUENCE. PREDICATE should return non-NIL if
  25    ARG1 is to precede ARG2."
  26   (declare (truly-dynamic-extent args))
  27   (let ((predicate-fun (%coerce-callable-to-fun predicate)))
  28     (seq-dispatch sequence
  29       (stable-sort-list sequence
  30                         predicate-fun
  31                         (if key (%coerce-callable-to-fun key) #'identity))
  32       (let ((key-fun-or-nil (and key (%coerce-callable-to-fun key))))
  33         (with-array-data ((vector (the vector sequence))
  34                           (start)
  35                           (end)
  36                           :check-fill-pointer t)
  37           (sort-vector vector start end predicate-fun key-fun-or-nil))
  38         sequence)
  39       (apply #'sb!sequence:sort sequence predicate args))))
  40 \f
  41 ;;;; stable sorting
  42 (defun stable-sort (sequence predicate &rest args &key key)
  43   #!+sb-doc
  44   "Destructively sort SEQUENCE. PREDICATE should return non-NIL if
  45    ARG1 is to precede ARG2."
  46   (declare (truly-dynamic-extent args))
  47   (let ((predicate-fun (%coerce-callable-to-fun predicate)))
  48     (seq-dispatch sequence
  49       (stable-sort-list sequence
  50                         predicate-fun
  51                         (if key (%coerce-callable-to-fun key) #'identity))
  52       (if (typep sequence 'simple-vector)
  53           (stable-sort-simple-vector sequence
  54                                      predicate-fun
  55                                      (and key (%coerce-callable-to-fun key)))
  56           (stable-sort-vector sequence
  57                               predicate-fun
  58                               (and key (%coerce-callable-to-fun key))))
  59       (apply #'sb!sequence:stable-sort sequence predicate args))))
  60 \f
  61 ;;; FUNCALL-USING-KEY saves us a function call sometimes.
  62 (eval-when (:compile-toplevel :execute)
  63   (sb!xc:defmacro funcall2-using-key (pred key one two)
  64     `(if ,key
  65          (funcall ,pred (funcall ,key ,one)
  66                   (funcall ,key  ,two))
  67          (funcall ,pred ,one ,two)))
  68 ) ; EVAL-WHEN
  69 \f
  70 ;;;; stable sort of lists
  71 (declaim (maybe-inline merge-lists* stable-sort-list))
  72
  73 ;;; Destructively merge LIST-1 with LIST-2 (given that they're already
  74 ;;; sorted w.r.t. PRED-FUN on KEY-FUN, giving output sorted the same
  75 ;;; way). In the resulting list, elements of LIST-1 are guaranteed to
  76 ;;; come before equal elements of LIST-2.
  77 ;;;
  78 ;;; Enqueues the values in the right order in HEAD's cdr, and returns
  79 ;;; the merged list.
  80 (defun merge-lists* (head list1 list2 test key &aux (tail head))
  81   (declare (type cons head list1 list2)
  82            (type function test key)
  83            (optimize speed))
  84   (let ((key1 (funcall key (car list1)))
  85         (key2 (funcall key (car list2))))
  86     (macrolet ((merge-one (l1 k1 l2)
  87                  `(progn
  88                     (setf (cdr tail) ,l1
  89                           tail       ,l1)
  90                     (let ((rest (cdr ,l1)))
  91                       (cond (rest
  92                              (setf ,l1 rest
  93                                    ,k1 (funcall key (first rest))))
  94                             (t
  95                              (setf (cdr ,l1) ,l2)
  96                              (return (cdr head))))))))
  97       (loop
  98        (if (funcall test key2           ; this way, equivalent
  99                          key1)          ; values are first popped
 100            (merge-one list2 key2 list1) ; from list1
 101            (merge-one list1 key1 list2))))))
 102
 103 ;;; Convenience wrapper for CL:MERGE
 104 (declaim (inline merge-lists))
 105 (defun merge-lists (list1 list2 test key)
 106   (cond ((null list1)
 107          list2)
 108         ((null list2)
 109          list1)
 110         (t
 111          (let ((head (cons nil nil)))
 112            (declare (dynamic-extent head))
 113            (merge-lists* head list1 list2 test key)))))
 114
 115 ;;; Small specialised stable sorts
 116 (declaim (inline stable-sort-list-2 stable-sort-list-3))
 117 (defun stable-sort-list-2 (list test key)
 118   (declare (type cons list)
 119            (type function test key))
 120   (let ((second (cdr list)))
 121     (declare (type cons second))
 122     (when (funcall test (funcall key (car second))
 123                         (funcall key (car list)))
 124       (rotatef (car list) (car second)))
 125     (values list second (shiftf (cdr second) nil))))
 126
 127 (defun stable-sort-list-3 (list test key)
 128   (declare (type cons list)
 129            (type function test key))
 130   (let* ((second (cdr list))
 131          (third  (cdr second))
 132          (x (car list))
 133          (y (car second))
 134          (z (car third)))
 135     (declare (type cons second third))
 136     (when (funcall test (funcall key y)
 137                         (funcall key x))
 138       (rotatef x y))
 139     (let ((key-z (funcall key z)))
 140       (when (funcall test key-z
 141                           (funcall key y))
 142         (if (funcall test key-z
 143                           (funcall key x))
 144             (rotatef x z y)
 145             (rotatef z y))))
 146     (setf (car list)   x
 147           (car second) y
 148           (car third)  z)
 149     (values list third (shiftf (cdr third) nil))))
 150
 151 ;;; STABLE-SORT-LIST implements a top-down merge sort. See the closest
 152 ;;; intro to algorithms book.  Benchmarks have shown significantly
 153 ;;; improved performance over the previous (hairier) bottom-up
 154 ;;; implementation, particularly on non-power-of-two sizes: bottom-up
 155 ;;; recursed on power-of-two-sized subsequences, which can result in
 156 ;;; very unbalanced recursion trees.
 157
 158 ;;; The minimum length at which list merge sort will try and detect
 159 ;;; it can merge disjoint ranges (e.g. sorted inputs) in constant time.
 160 (defconstant +stable-sort-fast-merge-limit+ 8)
 161
 162 (defun stable-sort-list (list test key &aux (head (cons :head list)))
 163   (declare (type list list)
 164            (type function test key)
 165            (dynamic-extent head))
 166   (labels ((merge* (size list1 tail1 list2 tail2 rest)
 167              (declare (optimize speed)
 168                       (type (and fixnum unsigned-byte) size)
 169                       (type cons list1 tail1 list2 tail2))
 170              (when (>= size +stable-sort-fast-merge-limit+)
 171                (cond ((not (funcall test (funcall key (car list2))   ; stability
 172                                          (funcall key (car tail1)))) ; trickery
 173                       (setf (cdr tail1) list2)
 174                       (return-from merge* (values list1 tail2 rest)))
 175                      ((funcall test (funcall key (car tail2))
 176                                     (funcall key (car list1)))
 177                       (setf (cdr tail2) list1)
 178                       (return-from merge* (values list2 tail1 rest)))))
 179                (values (merge-lists* head list1 list2 test key)
 180                        (if (null (cdr tail1))
 181                            tail1
 182                            tail2)
 183                        rest))
 184            (recur (list size)
 185              (declare (optimize speed)
 186                       (type cons list)
 187                       (type (and fixnum unsigned-byte) size))
 188              (cond ((> size 3)
 189                     (let ((half (ash size -1)))
 190                       (multiple-value-bind (list1 tail1 rest)
 191                           (recur list half)
 192                         (multiple-value-bind (list2 tail2 rest)
 193                             (recur rest (- size half))
 194                           (merge* size list1 tail1 list2 tail2 rest)))))
 195                    ((= size 3)
 196                     (stable-sort-list-3 list test key))
 197                    ((= size 2)
 198                     (stable-sort-list-2 list test key))
 199                    (t ; (= size 1)
 200                     (values list list (shiftf (cdr list) nil))))))
 201     (when list
 202       (values (recur list (length list))))))
 203 \f
 204 ;;;; stable sort of vectors
 205
 206 ;;; Stable sorting vectors is done with the same algorithm used for
 207 ;;; lists, using a temporary vector to merge back and forth between it
 208 ;;; and the given vector to sort.
 209
 210 (eval-when (:compile-toplevel :execute)
 211
 212 ;;; STABLE-SORT-MERGE-VECTORS* takes a source vector with subsequences,
 213 ;;;    start-1 (inclusive) ... end-1 (exclusive) and
 214 ;;;    end-1 (inclusive) ... end-2 (exclusive),
 215 ;;; and merges them into a target vector starting at index start-1.
 216
 217 (sb!xc:defmacro stable-sort-merge-vectors* (source target start-1 end-1 end-2
 218                                                      pred key source-ref
 219                                                      target-ref)
 220   (let ((i (gensym))
 221         (j (gensym))
 222         (target-i (gensym)))
 223     `(let ((,i ,start-1)
 224            (,j ,end-1) ; start-2
 225            (,target-i ,start-1))
 226        (declare (fixnum ,i ,j ,target-i))
 227        (loop
 228         (cond ((= ,i ,end-1)
 229                (loop (if (= ,j ,end-2) (return))
 230                      (setf (,target-ref ,target ,target-i)
 231                            (,source-ref ,source ,j))
 232                      (incf ,target-i)
 233                      (incf ,j))
 234                (return))
 235               ((= ,j ,end-2)
 236                (loop (if (= ,i ,end-1) (return))
 237                      (setf (,target-ref ,target ,target-i)
 238                            (,source-ref ,source ,i))
 239                      (incf ,target-i)
 240                      (incf ,i))
 241                (return))
 242               ((funcall2-using-key ,pred ,key
 243                                    (,source-ref ,source ,j)
 244                                    (,source-ref ,source ,i))
 245                (setf (,target-ref ,target ,target-i)
 246                      (,source-ref ,source ,j))
 247                (incf ,j))
 248               (t (setf (,target-ref ,target ,target-i)
 249                        (,source-ref ,source ,i))
 250                  (incf ,i)))
 251         (incf ,target-i)))))
 252
 253 ;;; VECTOR-MERGE-SORT is the same algorithm used to stable sort lists,
 254 ;;; but it uses a temporary vector. DIRECTION determines whether we
 255 ;;; are merging into the temporary (T) or back into the given vector
 256 ;;; (NIL).
 257 (sb!xc:defmacro vector-merge-sort (vector pred key vector-ref)
 258   (with-unique-names
 259       (vector-len n direction unsorted start-1 end-1 end-2 temp i)
 260     `(let* ((,vector-len (length (the vector ,vector)))
 261             (,n 1)            ; bottom-up size of contiguous runs to be merged
 262             (,direction t)    ; t vector --> temp    nil temp --> vector
 263             (,temp (make-array ,vector-len))
 264             (,unsorted 0)   ; unsorted..vector-len are the elements that need
 265                                         ; to be merged for a given n
 266             (,start-1 0))   ; one n-len subsequence to be merged with the next
 267        (declare (fixnum ,vector-len ,n ,unsorted ,start-1)
 268                 (simple-vector ,temp))
 269        (loop
 270          ;; for each n, we start taking n-runs from the start of the vector
 271          (setf ,unsorted 0)
 272          (loop
 273            (setf ,start-1 ,unsorted)
 274            (let ((,end-1 (+ ,start-1 ,n)))
 275              (declare (fixnum ,end-1))
 276              (cond ((< ,end-1 ,vector-len)
 277                     ;; there are enough elements for a second run
 278                     (let ((,end-2 (+ ,end-1 ,n)))
 279                       (declare (fixnum ,end-2))
 280                       (if (> ,end-2 ,vector-len) (setf ,end-2 ,vector-len))
 281                       (setf ,unsorted ,end-2)
 282                       (if ,direction
 283                           (stable-sort-merge-vectors*
 284                            ,vector ,temp
 285                            ,start-1 ,end-1 ,end-2 ,pred ,key ,vector-ref svref)
 286                           (stable-sort-merge-vectors*
 287                            ,temp ,vector
 288                            ,start-1 ,end-1 ,end-2 ,pred ,key svref ,vector-ref))
 289                       (if (= ,unsorted ,vector-len) (return))))
 290                    ;; if there is only one run, copy those elements to the end
 291                    (t (if ,direction
 292                           (do ((,i ,start-1 (1+ ,i)))
 293                               ((= ,i ,vector-len))
 294                             (declare (fixnum ,i))
 295                             (setf (svref ,temp ,i) (,vector-ref ,vector ,i)))
 296                           (do ((,i ,start-1 (1+ ,i)))
 297                               ((= ,i ,vector-len))
 298                             (declare (fixnum ,i))
 299                             (setf (,vector-ref ,vector ,i) (svref ,temp ,i))))
 300                       (return)))))
 301          ;; If the inner loop only executed once, then there were only enough
 302          ;; elements for two subsequences given n, so all the elements have
 303          ;; been merged into one list. Start-1 will have remained 0 upon exit.
 304          (when (zerop ,start-1)
 305            (when ,direction
 306              ;; if we just merged into the temporary, copy it all back
 307              ;; to the given vector.
 308              (dotimes (,i ,vector-len)
 309                (setf (,vector-ref ,vector ,i) (svref ,temp ,i))))
 310            ;; Kill the new vector to prevent garbage from being retained.
 311            (%shrink-vector ,temp 0)
 312            (return ,vector))
 313          (setf ,n (ash ,n 1))           ; (* 2 n)
 314          (setf ,direction (not ,direction))))))
 315
 316 ) ; EVAL-when
 317
 318 (defun stable-sort-simple-vector (vector pred key)
 319   (declare (type simple-vector vector)
 320            (type function pred)
 321            (type (or null function) key))
 322   (vector-merge-sort vector pred key svref))
 323
 324 (defun stable-sort-vector (vector pred key)
 325   (declare (type function pred)
 326            (type (or null function) key))
 327   (vector-merge-sort vector pred key aref))
 328 \f
 329 ;;;; merging
 330
 331 (eval-when (:compile-toplevel :execute)
 332
 333 ;;; MERGE-VECTORS returns a new vector which contains an interleaving
 334 ;;; of the elements of VECTOR-1 and VECTOR-2. Elements from VECTOR-2
 335 ;;; are chosen only if they are strictly less than elements of
 336 ;;; VECTOR-1, (PRED ELT-2 ELT-1), as specified in the manual.
 337 (sb!xc:defmacro merge-vectors (vector-1 length-1 vector-2 length-2
 338                                result-vector pred key access)
 339   (let ((result-i (gensym))
 340         (i (gensym))
 341         (j (gensym)))
 342     `(let* ((,result-i 0)
 343             (,i 0)
 344             (,j 0))
 345        (declare (fixnum ,result-i ,i ,j))
 346        (loop
 347         (cond ((= ,i ,length-1)
 348                (loop (if (= ,j ,length-2) (return))
 349                      (setf (,access ,result-vector ,result-i)
 350                            (,access ,vector-2 ,j))
 351                      (incf ,result-i)
 352                      (incf ,j))
 353                (return ,result-vector))
 354               ((= ,j ,length-2)
 355                (loop (if (= ,i ,length-1) (return))
 356                      (setf (,access ,result-vector ,result-i)
 357                            (,access ,vector-1 ,i))
 358                      (incf ,result-i)
 359                      (incf ,i))
 360                (return ,result-vector))
 361               ((funcall2-using-key ,pred ,key
 362                                    (,access ,vector-2 ,j) (,access ,vector-1 ,i))
 363                (setf (,access ,result-vector ,result-i)
 364                      (,access ,vector-2 ,j))
 365                (incf ,j))
 366               (t (setf (,access ,result-vector ,result-i)
 367                        (,access ,vector-1 ,i))
 368                  (incf ,i)))
 369         (incf ,result-i)))))
 370
 371 ) ; EVAL-WHEN
 372
 373 (defun merge (result-type sequence1 sequence2 predicate &key key)
 374   #!+sb-doc
 375   "Merge the sequences SEQUENCE1 and SEQUENCE2 destructively into a
 376    sequence of type RESULT-TYPE using PREDICATE to order the elements."
 377   ;; FIXME: This implementation is remarkably inefficient in various
 378   ;; ways. In decreasing order of estimated user astonishment, I note:
 379   ;; full calls to SPECIFIER-TYPE at runtime; copying input vectors
 380   ;; to lists before doing MERGE-LISTS -- WHN 2003-01-05
 381   (let ((type (specifier-type result-type))
 382         (pred-fun (%coerce-callable-to-fun predicate))
 383         ;; Avoid coercing NIL to a function since 2 out of 3 branches of the
 384         ;; COND below optimize for NIL as the key function. Additionally
 385         ;; recognize the reverse - when you said #'IDENTITY which can be
 386         ;; turned into NIL. Also, in the generic case, don't defer a
 387         ;; type error to the method (even though it also coerces to fun).
 388         (key-fun (when (and key (neq key #'identity))
 389                    (%coerce-callable-to-fun key))))
 390     (cond
 391       ((csubtypep type (specifier-type 'list))
 392        ;; the VECTOR clause, below, goes through MAKE-SEQUENCE, so
 393        ;; benefits from the error checking there. Short of
 394        ;; reimplementing everything, we can't do the same for the LIST
 395        ;; case, so do relevant length checking here:
 396        (let ((s1 (coerce sequence1 'list))
 397              (s2 (coerce sequence2 'list))
 398              ;; MERGE-LISTS* does not contain special code for KEY = NIL.
 399              (key-fun (or key-fun #'identity)))
 400          (when (type= type (specifier-type 'list))
 401            (return-from merge (merge-lists s1 s2 pred-fun key-fun)))
 402          (when (eq type *empty-type*)
 403            (bad-sequence-type-error nil))
 404          (when (type= type (specifier-type 'null))
 405            (if (and (null s1) (null s2))
 406                (return-from merge 'nil)
 407                ;; FIXME: This will break on circular lists (as,
 408                ;; indeed, will the whole MERGE function).
 409                (sequence-type-length-mismatch-error type
 410                                                     (+ (length s1)
 411                                                        (length s2)))))
 412          (if (cons-type-p type)
 413              (multiple-value-bind (min exactp)
 414                  (sb!kernel::cons-type-length-info type)
 415                (let ((length (+ (length s1) (length s2))))
 416                  (if exactp
 417                      (unless (= length min)
 418                        (sequence-type-length-mismatch-error type length))
 419                      (unless (>= length min)
 420                        (sequence-type-length-mismatch-error type length)))
 421                  (merge-lists s1 s2 pred-fun key-fun)))
 422              (sequence-type-too-hairy result-type))))
 423       ((csubtypep type (specifier-type 'vector))
 424        (let* ((vector-1 (coerce sequence1 'vector))
 425               (vector-2 (coerce sequence2 'vector))
 426               (length-1 (length vector-1))
 427               (length-2 (length vector-2))
 428               (result (make-sequence result-type (+ length-1 length-2))))
 429          (declare (vector vector-1 vector-2) ; FIXME: this looks redundant,
 430                   (fixnum length-1 length-2)) ; as does this.
 431          (if (and (simple-vector-p result)
 432                   (simple-vector-p vector-1)
 433                   (simple-vector-p vector-2))
 434              (merge-vectors vector-1 length-1 vector-2 length-2
 435                             result pred-fun key-fun svref)
 436              ;; Some things that could improve the fancy vector case:
 437              ;; - recognize when the only fancy aspect of both inputs
 438              ;;   is that they have fill pointers.
 439              ;; - use the specialized reffer for inputs + output
 440              (merge-vectors vector-1 length-1 vector-2 length-2
 441                             result pred-fun key-fun aref))))
 442       ((and (csubtypep type (specifier-type 'sequence))
 443             (awhen (find-class result-type nil)
 444               (sb!sequence:merge
 445                (sb!mop:class-prototype (sb!pcl:ensure-class-finalized it))
 446                ;; GF dispatch deals with the erroneous situation wherein
 447                ;; either of SEQUENCE1 or SEQUENCE2 is not a sequence.
 448                ;; Note that the one builtin method optimizes for NIL as
 449                ;; the key fun, and we correctly preserve a NIL here.
 450                sequence1 sequence2 pred-fun :key key-fun))))
 451       (t (bad-sequence-type-error result-type)))))