b19e86ece1b576616a1ce5784065071c6da0ba22
[glibc.git] / stdlib / qsort.c
1 /* Copyright (C) 1991,1992,1996,1997,1999,2004 Free Software Foundation, Inc.
2 This file is part of the GNU C Library.
3 Written by Douglas C. Schmidt (schmidt@ics.uci.edu).
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, write to the Free
17 Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
18 02111-1307 USA. */
19
20 /* If you consider tuning this algorithm, you should consult first:
21 Engineering a sort function; Jon Bentley and M. Douglas McIlroy;
22 Software - Practice and Experience; Vol. 23 (11), 1249-1265, 1993. */
23
24 #include <alloca.h>
25 #include <limits.h>
26 #include <stdlib.h>
27 #include <string.h>
28
29 /* Byte-wise swap two items of size SIZE. */
30 #define SWAP(a, b, size) \
31 do \
32 { \
33 register size_t __size = (size); \
34 register char *__a = (a), *__b = (b); \
35 do \
36 { \
37 char __tmp = *__a; \
38 *__a++ = *__b; \
39 *__b++ = __tmp; \
40 } while (--__size > 0); \
41 } while (0)
42
43 /* Discontinue quicksort algorithm when partition gets below this size.
44 This particular magic number was chosen to work best on a Sun 4/260. */
45 #define MAX_THRESH 4
46
47 /* Stack node declarations used to store unfulfilled partition obligations. */
48 typedef struct
49 {
50 char *lo;
51 char *hi;
52 } stack_node;
53
54 /* The next 4 #defines implement a very fast in-line stack abstraction. */
55 /* The stack needs log (total_elements) entries (we could even subtract
56 log(MAX_THRESH)). Since total_elements has type size_t, we get as
57 upper bound for log (total_elements):
58 bits per byte (CHAR_BIT) * sizeof(size_t). */
59 #define STACK_SIZE (CHAR_BIT * sizeof(size_t))
60 #define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top))
61 #define POP(low, high) ((void) (--top, (low = top->lo), (high = top->hi)))
62 #define STACK_NOT_EMPTY (stack < top)
63
64
65 /* Order size using quicksort. This implementation incorporates
66 four optimizations discussed in Sedgewick:
67
68 1. Non-recursive, using an explicit stack of pointer that store the
69 next array partition to sort. To save time, this maximum amount
70 of space required to store an array of SIZE_MAX is allocated on the
71 stack. Assuming a 32-bit (64 bit) integer for size_t, this needs
72 only 32 * sizeof(stack_node) == 256 bytes (for 64 bit: 1024 bytes).
73 Pretty cheap, actually.
74
75 2. Chose the pivot element using a median-of-three decision tree.
76 This reduces the probability of selecting a bad pivot value and
77 eliminates certain extraneous comparisons.
78
79 3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
80 insertion sort to order the MAX_THRESH items within each partition.
81 This is a big win, since insertion sort is faster for small, mostly
82 sorted array segments.
83
84 4. The larger of the two sub-partitions is always pushed onto the
85 stack first, with the algorithm then concentrating on the
86 smaller partition. This *guarantees* no more than log (total_elems)
87 stack size is needed (actually O(1) in this case)! */
88
89 void
90 _quicksort (void *const pbase, size_t total_elems, size_t size,
91 __compar_d_fn_t cmp, void *arg)
92 {
93 register char *base_ptr = (char *) pbase;
94
95 const size_t max_thresh = MAX_THRESH * size;
96
97 if (total_elems == 0)
98 /* Avoid lossage with unsigned arithmetic below. */
99 return;
100
101 if (total_elems > MAX_THRESH)
102 {
103 char *lo = base_ptr;
104 char *hi = &lo[size * (total_elems - 1)];
105 stack_node stack[STACK_SIZE];
106 stack_node *top = stack;
107
108 PUSH (NULL, NULL);
109
110 while (STACK_NOT_EMPTY)
111 {
112 char *left_ptr;
113 char *right_ptr;
114
115 /* Select median value from among LO, MID, and HI. Rearrange
116 LO and HI so the three values are sorted. This lowers the
117 probability of picking a pathological pivot value and
118 skips a comparison for both the LEFT_PTR and RIGHT_PTR in
119 the while loops. */
120
121 char *mid = lo + size * ((hi - lo) / size >> 1);
122
123 if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
124 SWAP (mid, lo, size);
125 if ((*cmp) ((void *) hi, (void *) mid, arg) < 0)
126 SWAP (mid, hi, size);
127 else
128 goto jump_over;
129 if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
130 SWAP (mid, lo, size);
131 jump_over:;
132
133 left_ptr = lo + size;
134 right_ptr = hi - size;
135
136 /* Here's the famous ``collapse the walls'' section of quicksort.
137 Gotta like those tight inner loops! They are the main reason
138 that this algorithm runs much faster than others. */
139 do
140 {
141 while ((*cmp) ((void *) left_ptr, (void *) mid, arg) < 0)
142 left_ptr += size;
143
144 while ((*cmp) ((void *) mid, (void *) right_ptr, arg) < 0)
145 right_ptr -= size;
146
147 if (left_ptr < right_ptr)
148 {
149 SWAP (left_ptr, right_ptr, size);
150 if (mid == left_ptr)
151 mid = right_ptr;
152 else if (mid == right_ptr)
153 mid = left_ptr;
154 left_ptr += size;
155 right_ptr -= size;
156 }
157 else if (left_ptr == right_ptr)
158 {
159 left_ptr += size;
160 right_ptr -= size;
161 break;
162 }
163 }
164 while (left_ptr <= right_ptr);
165
166 /* Set up pointers for next iteration. First determine whether
167 left and right partitions are below the threshold size. If so,
168 ignore one or both. Otherwise, push the larger partition's
169 bounds on the stack and continue sorting the smaller one. */
170
171 if ((size_t) (right_ptr - lo) <= max_thresh)
172 {
173 if ((size_t) (hi - left_ptr) <= max_thresh)
174 /* Ignore both small partitions. */
175 POP (lo, hi);
176 else
177 /* Ignore small left partition. */
178 lo = left_ptr;
179 }
180 else if ((size_t) (hi - left_ptr) <= max_thresh)
181 /* Ignore small right partition. */
182 hi = right_ptr;
183 else if ((right_ptr - lo) > (hi - left_ptr))
184 {
185 /* Push larger left partition indices. */
186 PUSH (lo, right_ptr);
187 lo = left_ptr;
188 }
189 else
190 {
191 /* Push larger right partition indices. */
192 PUSH (left_ptr, hi);
193 hi = right_ptr;
194 }
195 }
196 }
197
198 /* Once the BASE_PTR array is partially sorted by quicksort the rest
199 is completely sorted using insertion sort, since this is efficient
200 for partitions below MAX_THRESH size. BASE_PTR points to the beginning
201 of the array to sort, and END_PTR points at the very last element in
202 the array (*not* one beyond it!). */
203
204 #define min(x, y) ((x) < (y) ? (x) : (y))
205
206 {
207 char *const end_ptr = &base_ptr[size * (total_elems - 1)];
208 char *tmp_ptr = base_ptr;
209 char *thresh = min(end_ptr, base_ptr + max_thresh);
210 register char *run_ptr;
211
212 /* Find smallest element in first threshold and place it at the
213 array's beginning. This is the smallest array element,
214 and the operation speeds up insertion sort's inner loop. */
215
216 for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
217 if ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0)
218 tmp_ptr = run_ptr;
219
220 if (tmp_ptr != base_ptr)
221 SWAP (tmp_ptr, base_ptr, size);
222
223 /* Insertion sort, running from left-hand-side up to right-hand-side. */
224
225 run_ptr = base_ptr + size;
226 while ((run_ptr += size) <= end_ptr)
227 {
228 tmp_ptr = run_ptr - size;
229 while ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0)
230 tmp_ptr -= size;
231
232 tmp_ptr += size;
233 if (tmp_ptr != run_ptr)
234 {
235 char *trav;
236
237 trav = run_ptr + size;
238 while (--trav >= run_ptr)
239 {
240 char c = *trav;
241 char *hi, *lo;
242
243 for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
244 *hi = *lo;
245 *hi = c;
246 }
247 }
248 }
249 }
250 }