1/* Copyright (C) 1991-2023 Free Software Foundation, Inc.
2 This file is part of the GNU C Library.
3
4 The GNU C Library is free software; you can redistribute it and/or
5 modify it under the terms of the GNU Lesser General Public
6 License as published by the Free Software Foundation; either
7 version 2.1 of the License, or (at your option) any later version.
8
9 The GNU C Library is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12 Lesser General Public License for more details.
13
14 You should have received a copy of the GNU Lesser General Public
15 License along with the GNU C Library; if not, see
16 <https://www.gnu.org/licenses/>. */
17
18/* If you consider tuning this algorithm, you should consult first:
19 Engineering a sort function; Jon Bentley and M. Douglas McIlroy;
20 Software - Practice and Experience; Vol. 23 (11), 1249-1265, 1993. */
21
22#include <alloca.h>
23#include <limits.h>
24#include <stdlib.h>
25#include <string.h>
26
27/* Byte-wise swap two items of size SIZE. */
28#define SWAP(a, b, size) \
29 do \
30 { \
31 size_t __size = (size); \
32 char *__a = (a), *__b = (b); \
33 do \
34 { \
35 char __tmp = *__a; \
36 *__a++ = *__b; \
37 *__b++ = __tmp; \
38 } while (--__size > 0); \
39 } while (0)
40
41/* Discontinue quicksort algorithm when partition gets below this size.
42 This particular magic number was chosen to work best on a Sun 4/260. */
43#define MAX_THRESH 4
44
45/* Stack node declarations used to store unfulfilled partition obligations. */
46typedef struct
47 {
48 char *lo;
49 char *hi;
50 } stack_node;
51
52/* The next 4 #defines implement a very fast in-line stack abstraction. */
53/* The stack needs log (total_elements) entries (we could even subtract
54 log(MAX_THRESH)). Since total_elements has type size_t, we get as
55 upper bound for log (total_elements):
56 bits per byte (CHAR_BIT) * sizeof(size_t). */
57#define STACK_SIZE (CHAR_BIT * sizeof (size_t))
58#define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top))
59#define POP(low, high) ((void) (--top, (low = top->lo), (high = top->hi)))
60#define STACK_NOT_EMPTY (stack < top)
61
62
63/* Order size using quicksort. This implementation incorporates
64 four optimizations discussed in Sedgewick:
65
66 1. Non-recursive, using an explicit stack of pointer that store the
67 next array partition to sort. To save time, this maximum amount
68 of space required to store an array of SIZE_MAX is allocated on the
69 stack. Assuming a 32-bit (64 bit) integer for size_t, this needs
70 only 32 * sizeof(stack_node) == 256 bytes (for 64 bit: 1024 bytes).
71 Pretty cheap, actually.
72
73 2. Chose the pivot element using a median-of-three decision tree.
74 This reduces the probability of selecting a bad pivot value and
75 eliminates certain extraneous comparisons.
76
77 3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
78 insertion sort to order the MAX_THRESH items within each partition.
79 This is a big win, since insertion sort is faster for small, mostly
80 sorted array segments.
81
82 4. The larger of the two sub-partitions is always pushed onto the
83 stack first, with the algorithm then concentrating on the
84 smaller partition. This *guarantees* no more than log (total_elems)
85 stack size is needed (actually O(1) in this case)! */
86
87void
88_quicksort (void *const pbase, size_t total_elems, size_t size,
89 __compar_d_fn_t cmp, void *arg)
90{
91 char *base_ptr = (char *) pbase;
92
93 const size_t max_thresh = MAX_THRESH * size;
94
95 if (total_elems == 0)
96 /* Avoid lossage with unsigned arithmetic below. */
97 return;
98
99 if (total_elems > MAX_THRESH)
100 {
101 char *lo = base_ptr;
102 char *hi = &lo[size * (total_elems - 1)];
103 stack_node stack[STACK_SIZE];
104 stack_node *top = stack;
105
106 PUSH (NULL, NULL);
107
108 while (STACK_NOT_EMPTY)
109 {
110 char *left_ptr;
111 char *right_ptr;
112
113 /* Select median value from among LO, MID, and HI. Rearrange
114 LO and HI so the three values are sorted. This lowers the
115 probability of picking a pathological pivot value and
116 skips a comparison for both the LEFT_PTR and RIGHT_PTR in
117 the while loops. */
118
119 char *mid = lo + size * ((hi - lo) / size >> 1);
120
121 if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
122 SWAP (mid, lo, size);
123 if ((*cmp) ((void *) hi, (void *) mid, arg) < 0)
124 SWAP (mid, hi, size);
125 else
126 goto jump_over;
127 if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
128 SWAP (mid, lo, size);
129 jump_over:;
130
131 left_ptr = lo + size;
132 right_ptr = hi - size;
133
134 /* Here's the famous ``collapse the walls'' section of quicksort.
135 Gotta like those tight inner loops! They are the main reason
136 that this algorithm runs much faster than others. */
137 do
138 {
139 while ((*cmp) ((void *) left_ptr, (void *) mid, arg) < 0)
140 left_ptr += size;
141
142 while ((*cmp) ((void *) mid, (void *) right_ptr, arg) < 0)
143 right_ptr -= size;
144
145 if (left_ptr < right_ptr)
146 {
147 SWAP (left_ptr, right_ptr, size);
148 if (mid == left_ptr)
149 mid = right_ptr;
150 else if (mid == right_ptr)
151 mid = left_ptr;
152 left_ptr += size;
153 right_ptr -= size;
154 }
155 else if (left_ptr == right_ptr)
156 {
157 left_ptr += size;
158 right_ptr -= size;
159 break;
160 }
161 }
162 while (left_ptr <= right_ptr);
163
164 /* Set up pointers for next iteration. First determine whether
165 left and right partitions are below the threshold size. If so,
166 ignore one or both. Otherwise, push the larger partition's
167 bounds on the stack and continue sorting the smaller one. */
168
169 if ((size_t) (right_ptr - lo) <= max_thresh)
170 {
171 if ((size_t) (hi - left_ptr) <= max_thresh)
172 /* Ignore both small partitions. */
173 POP (lo, hi);
174 else
175 /* Ignore small left partition. */
176 lo = left_ptr;
177 }
178 else if ((size_t) (hi - left_ptr) <= max_thresh)
179 /* Ignore small right partition. */
180 hi = right_ptr;
181 else if ((right_ptr - lo) > (hi - left_ptr))
182 {
183 /* Push larger left partition indices. */
184 PUSH (lo, right_ptr);
185 lo = left_ptr;
186 }
187 else
188 {
189 /* Push larger right partition indices. */
190 PUSH (left_ptr, hi);
191 hi = right_ptr;
192 }
193 }
194 }
195
196 /* Once the BASE_PTR array is partially sorted by quicksort the rest
197 is completely sorted using insertion sort, since this is efficient
198 for partitions below MAX_THRESH size. BASE_PTR points to the beginning
199 of the array to sort, and END_PTR points at the very last element in
200 the array (*not* one beyond it!). */
201
202#define min(x, y) ((x) < (y) ? (x) : (y))
203
204 {
205 char *const end_ptr = &base_ptr[size * (total_elems - 1)];
206 char *tmp_ptr = base_ptr;
207 char *thresh = min(end_ptr, base_ptr + max_thresh);
208 char *run_ptr;
209
210 /* Find smallest element in first threshold and place it at the
211 array's beginning. This is the smallest array element,
212 and the operation speeds up insertion sort's inner loop. */
213
214 for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
215 if ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0)
216 tmp_ptr = run_ptr;
217
218 if (tmp_ptr != base_ptr)
219 SWAP (tmp_ptr, base_ptr, size);
220
221 /* Insertion sort, running from left-hand-side up to right-hand-side. */
222
223 run_ptr = base_ptr + size;
224 while ((run_ptr += size) <= end_ptr)
225 {
226 tmp_ptr = run_ptr - size;
227 while ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0)
228 tmp_ptr -= size;
229
230 tmp_ptr += size;
231 if (tmp_ptr != run_ptr)
232 {
233 char *trav;
234
235 trav = run_ptr + size;
236 while (--trav >= run_ptr)
237 {
238 char c = *trav;
239 char *hi, *lo;
240
241 for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
242 *hi = *lo;
243 *hi = c;
244 }
245 }
246 }
247 }
248}
249