1 /* PSPP - computes sample statistics.
2 Copyright (C) 1997-9, 2000 Free Software Foundation, Inc.
3 Written by Ben Pfaff <blp@gnu.org>.
5 This program is free software; you can redistribute it and/or
6 modify it under the terms of the GNU General Public License as
7 published by the Free Software Foundation; either version 2 of the
8 License, or (at your option) any later version.
10 This program is distributed in the hope that it will be useful, but
11 WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 General Public License for more details.
15 You should have received a copy of the GNU General Public License
16 along with this program; if not, write to the Free Software
17 Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
20 /* Copyright (C) 2001 Free Software Foundation, Inc.
22 This file is part of the GNU ISO C++ Library. This library is free
23 software; you can redistribute it and/or modify it under the
24 terms of the GNU General Public License as published by the
25 Free Software Foundation; either version 2, or (at your option)
28 This library is distributed in the hope that it will be useful,
29 but WITHOUT ANY WARRANTY; without even the implied warranty of
30 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
31 GNU General Public License for more details.
33 You should have received a copy of the GNU General Public License along
34 with this library; see the file COPYING. If not, write to the Free
35 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
38 As a special exception, you may use this file as part of a free software
39 library without restriction. Specifically, if other files instantiate
40 templates or use macros or inline functions from this file, or you compile
41 this file and link it with other files to produce an executable, this
42 file does not by itself cause the resulting executable to be covered by
43 the GNU General Public License. This exception does not however
44 invalidate any other reasons why the executable file might be covered by
45 the GNU General Public License. */
50 * Hewlett-Packard Company
52 * Permission to use, copy, modify, distribute and sell this software
53 * and its documentation for any purpose is hereby granted without fee,
54 * provided that the above copyright notice appear in all copies and
55 * that both that copyright notice and this permission notice appear
56 * in supporting documentation. Hewlett-Packard Company makes no
57 * representations about the suitability of this software for any
58 * purpose. It is provided "as is" without express or implied warranty.
62 * Silicon Graphics Computer Systems, Inc.
64 * Permission to use, copy, modify, distribute and sell this software
65 * and its documentation for any purpose is hereby granted without fee,
66 * provided that the above copyright notice appear in all copies and
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70 * purpose. It is provided "as is" without express or implied warranty.
79 #include "algorithm.h"
82 /* Byte-wise swap two items of size SIZE. */
83 #define SWAP(a, b, size) \
86 register size_t __size = (size); \
87 register char *__a = (a), *__b = (b); \
93 } while (--__size > 0); \
96 /* Makes the elements in ARRAY unique, by moving up duplicates,
97 and returns the new number of elements in the array. Sorted
98 arrays only. Arguments same as for sort() above. */
100 unique (void *array, size_t count, size_t size,
101 algo_compare_func *compare, void *aux)
104 char *last = first + size * count;
105 char *result = array;
113 if (compare (result, first, aux))
117 memcpy (result, first, size);
124 /* Helper function that calls sort(), then unique(). */
126 sort_unique (void *array, size_t count, size_t size,
127 algo_compare_func *compare, void *aux)
129 sort (array, count, size, compare, aux);
130 return unique (array, count, size, compare, aux);
137 xmalloc (size_t size)
139 return malloc (size);
143 compare_ints (const void *a_, const void *b_, void *aux)
157 try_unique (const char *title,
158 int *in, size_t in_cnt,
163 in_cnt = unique (in, in_cnt, sizeof *in, compare_ints, NULL);
164 if (in_cnt != out_cnt)
166 fprintf (stderr, "unique_test: %s: in_cnt %d, expected %d\n",
167 title, (int) in_cnt, (int) out_cnt);
171 for (i = 0; i < out_cnt; i++)
174 fprintf (stderr, "unique_test: %s: idx %d = %d, expected %d\n",
175 title, (int) i, in[i], i);
182 int a_in[] = {0, 0, 0, 1, 2, 3, 3, 4, 5, 5};
183 int b_in[] = {0, 1, 2, 2, 2, 3};
187 try_unique ("a", a_in, sizeof a_in / sizeof *a_in, 6);
188 try_unique ("b", b_in, sizeof b_in / sizeof *b_in, 4);
189 try_unique ("c", c_in, sizeof c_in / sizeof *c_in, 1);
190 try_unique ("d", &d_in, 0, 0);
193 #endif /* TEST_UNIQUE */
195 /* Reorders ARRAY, which contains COUNT elements of SIZE bytes
196 each, so that the elements for which PREDICATE returns nonzero
197 precede those for which PREDICATE returns zero. AUX is
198 passed to each predicate as auxiliary data. Returns the
199 number of elements for which PREDICATE returns nonzero. Not
202 partition (void *array, size_t count, size_t size,
203 algo_predicate_func *predicate, void *aux)
206 char *last = first + count * size;
210 /* Move FIRST forward to point to first element that fails
216 else if (!predicate (first, aux))
223 /* Move LAST backward to point to last element that passes
231 else if (predicate (last, aux))
237 /* By swapping FIRST and LAST we extend the starting and
238 ending sequences that pass and fail, respectively,
240 SWAP (first, last, size);
245 /* A algo_random_func that uses random.h. */
247 algo_default_random (unsigned max, void *aux unused)
249 return rng_get_unsigned (pspp_rng ()) % max;
252 /* Randomly reorders ARRAY, which contains COUNT elements of SIZE
253 bytes each. Uses RANDOM as a source of random data, passing
254 AUX as the auxiliary data. RANDOM may be null to use a
255 default random source. */
257 random_shuffle (void *array_, size_t count, size_t size,
258 algo_random_func *random, void *aux)
260 unsigned char *array = array_;
264 random = algo_default_random;
266 for (i = 1; i < count; i++)
267 SWAP (array + i * size, array + random (i + 1, aux) * size, size);
270 /* Copies the COUNT elements of SIZE bytes each from ARRAY to
271 RESULT, except that elements for which PREDICATE is false are
272 not copied. Returns the number of elements copied. AUX is
273 passed to PREDICATE as auxiliary data. */
275 copy_if (const void *array, size_t count, size_t size,
277 algo_predicate_func *predicate, void *aux)
279 const unsigned char *input = array;
280 const unsigned char *last = input + size * count;
281 unsigned char *output = result;
283 while (input <= last)
285 if (predicate (input, aux))
287 memcpy (output, input, size);
299 /* A predicate and its auxiliary data. */
302 algo_predicate_func *predicate;
307 not (const void *data, void *pred_aux_)
309 const struct pred_aux *pred_aux = pred_aux_;
311 return !pred_aux->predicate (data, pred_aux->aux);
314 /* Copies the COUNT elements of SIZE bytes each from ARRAY to
315 RESULT, except that elements for which PREDICATE is true are
316 not copied. Returns the number of elements copied. AUX is
317 passed to PREDICATE as auxiliary data. */
319 remove_copy_if (const void *array, size_t count, size_t size,
321 algo_predicate_func *predicate, void *aux)
323 struct pred_aux pred_aux;
324 pred_aux.predicate = predicate;
326 return copy_if (array, count, size, result, not, &pred_aux);
329 /* Searches ARRAY, which contains COUNT of SIZE bytes each, using
330 a binary search. Returns any element that equals VALUE, if
331 one exists, or a null pointer otherwise. ARRAY must ordered
332 according to COMPARE. AUX is passed to COMPARE as auxiliary
335 binary_search (const void *array, size_t count, size_t size,
337 algo_compare_func *compare, void *aux)
339 assert (array != NULL);
340 assert (count <= INT_MAX);
341 assert (aux != NULL);
345 const unsigned char *first = array;
347 int high = count - 1;
351 int middle = (low + high) / 2;
352 const unsigned char *element = first + middle * size;
353 int cmp = compare (value, element, aux);
360 return (void *) element;
366 /* Copyright (C) 1991, 1992, 1996, 1997, 1999 Free Software Foundation, Inc.
367 This file is part of the GNU C Library.
368 Written by Douglas C. Schmidt (schmidt@ics.uci.edu).
370 The GNU C Library is free software; you can redistribute it and/or
371 modify it under the terms of the GNU Lesser General Public
372 License as published by the Free Software Foundation; either
373 version 2.1 of the License, or (at your option) any later version.
375 The GNU C Library is distributed in the hope that it will be useful,
376 but WITHOUT ANY WARRANTY; without even the implied warranty of
377 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
378 Lesser General Public License for more details.
380 You should have received a copy of the GNU Lesser General Public
381 License along with the GNU C Library; if not, write to the Free
382 Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
385 /* If you consider tuning this algorithm, you should consult first:
386 Engineering a sort function; Jon Bentley and M. Douglas McIlroy;
387 Software - Practice and Experience; Vol. 23 (11), 1249-1265, 1993. */
394 /* Discontinue quicksort algorithm when partition gets below this size.
395 This particular magic number was chosen to work best on a Sun 4/260. */
398 /* Stack node declarations used to store unfulfilled partition obligations. */
405 /* The next 4 #defines implement a very fast in-line stack abstraction. */
406 /* The stack needs log (total_elements) entries (we could even subtract
407 log(MAX_THRESH)). Since total_elements has type size_t, we get as
408 upper bound for log (total_elements):
409 bits per byte (CHAR_BIT) * sizeof(size_t). */
410 #define STACK_SIZE (CHAR_BIT * sizeof(size_t))
411 #define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top))
412 #define POP(low, high) ((void) (--top, (low = top->lo), (high = top->hi)))
413 #define STACK_NOT_EMPTY (stack < top)
416 /* Order size using quicksort. This implementation incorporates
417 four optimizations discussed in Sedgewick:
419 1. Non-recursive, using an explicit stack of pointer that store the
420 next array partition to sort. To save time, this maximum amount
421 of space required to store an array of SIZE_MAX is allocated on the
422 stack. Assuming a 32-bit (64 bit) integer for size_t, this needs
423 only 32 * sizeof(stack_node) == 256 bytes (for 64 bit: 1024 bytes).
424 Pretty cheap, actually.
426 2. Chose the pivot element using a median-of-three decision tree.
427 This reduces the probability of selecting a bad pivot value and
428 eliminates certain extraneous comparisons.
430 3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
431 insertion sort to order the MAX_THRESH items within each partition.
432 This is a big win, since insertion sort is faster for small, mostly
433 sorted array segments.
435 4. The larger of the two sub-partitions is always pushed onto the
436 stack first, with the algorithm then concentrating on the
437 smaller partition. This *guarantees* no more than log (total_elems)
438 stack size is needed (actually O(1) in this case)! */
441 sort (void *const pbase, size_t total_elems, size_t size,
442 algo_compare_func *cmp, void *aux)
444 register char *base_ptr = (char *) pbase;
446 const size_t max_thresh = MAX_THRESH * size;
448 if (total_elems == 0)
449 /* Avoid lossage with unsigned arithmetic below. */
452 if (total_elems > MAX_THRESH)
455 char *hi = &lo[size * (total_elems - 1)];
456 stack_node stack[STACK_SIZE];
457 stack_node *top = stack + 1;
459 while (STACK_NOT_EMPTY)
464 /* Select median value from among LO, MID, and HI. Rearrange
465 LO and HI so the three values are sorted. This lowers the
466 probability of picking a pathological pivot value and
467 skips a comparison for both the LEFT_PTR and RIGHT_PTR in
470 char *mid = lo + size * ((hi - lo) / size >> 1);
472 if ((*cmp) ((void *) mid, (void *) lo, aux) < 0)
473 SWAP (mid, lo, size);
474 if ((*cmp) ((void *) hi, (void *) mid, aux) < 0)
475 SWAP (mid, hi, size);
478 if ((*cmp) ((void *) mid, (void *) lo, aux) < 0)
479 SWAP (mid, lo, size);
482 left_ptr = lo + size;
483 right_ptr = hi - size;
485 /* Here's the famous ``collapse the walls'' section of quicksort.
486 Gotta like those tight inner loops! They are the main reason
487 that this algorithm runs much faster than others. */
490 while ((*cmp) ((void *) left_ptr, (void *) mid, aux) < 0)
493 while ((*cmp) ((void *) mid, (void *) right_ptr, aux) < 0)
496 if (left_ptr < right_ptr)
498 SWAP (left_ptr, right_ptr, size);
501 else if (mid == right_ptr)
506 else if (left_ptr == right_ptr)
513 while (left_ptr <= right_ptr);
515 /* Set up pointers for next iteration. First determine whether
516 left and right partitions are below the threshold size. If so,
517 ignore one or both. Otherwise, push the larger partition's
518 bounds on the stack and continue sorting the smaller one. */
520 if ((size_t) (right_ptr - lo) <= max_thresh)
522 if ((size_t) (hi - left_ptr) <= max_thresh)
523 /* Ignore both small partitions. */
526 /* Ignore small left partition. */
529 else if ((size_t) (hi - left_ptr) <= max_thresh)
530 /* Ignore small right partition. */
532 else if ((right_ptr - lo) > (hi - left_ptr))
534 /* Push larger left partition indices. */
535 PUSH (lo, right_ptr);
540 /* Push larger right partition indices. */
547 /* Once the BASE_PTR array is partially sorted by quicksort the rest
548 is completely sorted using insertion sort, since this is efficient
549 for partitions below MAX_THRESH size. BASE_PTR points to the beginning
550 of the array to sort, and END_PTR points at the very last element in
551 the array (*not* one beyond it!). */
553 #define min(x, y) ((x) < (y) ? (x) : (y))
556 char *const end_ptr = &base_ptr[size * (total_elems - 1)];
557 char *tmp_ptr = base_ptr;
558 char *thresh = min(end_ptr, base_ptr + max_thresh);
559 register char *run_ptr;
561 /* Find smallest element in first threshold and place it at the
562 array's beginning. This is the smallest array element,
563 and the operation speeds up insertion sort's inner loop. */
565 for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
566 if ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, aux) < 0)
569 if (tmp_ptr != base_ptr)
570 SWAP (tmp_ptr, base_ptr, size);
572 /* Insertion sort, running from left-hand-side up to right-hand-side. */
574 run_ptr = base_ptr + size;
575 while ((run_ptr += size) <= end_ptr)
577 tmp_ptr = run_ptr - size;
578 while ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, aux) < 0)
582 if (tmp_ptr != run_ptr)
586 trav = run_ptr + size;
587 while (--trav >= run_ptr)
592 for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)