1/* Copyright (C) 1991-2020 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, see
17 <https://www.gnu.org/licenses/>. */
18
19/* If you consider tuning this algorithm, you should consult first:
20 Engineering a sort function; Jon Bentley and M. Douglas McIlroy;
21 Software - Practice and Experience; Vol. 23 (11), 1249-1265, 1993. */
22
23#include <alloca.h>
24#include <limits.h>
25#include <stdlib.h>
26#include <string.h>
27
28/* Byte-wise swap two items of size SIZE. */
29#define SWAP(a, b, size) \
30 do \
31 { \
32 size_t __size = (size); \
33 char *__a = (a), *__b = (b); \
34 do \
35 { \
36 char __tmp = *__a; \
37 *__a++ = *__b; \
38 *__b++ = __tmp; \
39 } while (--__size > 0); \
40 } while (0)
41
42/* Discontinue quicksort algorithm when partition gets below this size.
43 This particular magic number was chosen to work best on a Sun 4/260. */
44#define MAX_THRESH 4
45
46/* Stack node declarations used to store unfulfilled partition obligations. */
47typedef struct
48 {
49 char *lo;
50 char *hi;
51 } stack_node;
52
53/* The next 4 #defines implement a very fast in-line stack abstraction. */
54/* The stack needs log (total_elements) entries (we could even subtract
55 log(MAX_THRESH)). Since total_elements has type size_t, we get as
56 upper bound for log (total_elements):
57 bits per byte (CHAR_BIT) * sizeof(size_t). */
58#define STACK_SIZE (CHAR_BIT * sizeof (size_t))
59#define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top))
60#define POP(low, high) ((void) (--top, (low = top->lo), (high = top->hi)))
61#define STACK_NOT_EMPTY (stack < top)
62
63
64/* Order size using quicksort. This implementation incorporates
65 four optimizations discussed in Sedgewick:
66
67 1. Non-recursive, using an explicit stack of pointer that store the
68 next array partition to sort. To save time, this maximum amount
69 of space required to store an array of SIZE_MAX is allocated on the
70 stack. Assuming a 32-bit (64 bit) integer for size_t, this needs
71 only 32 * sizeof(stack_node) == 256 bytes (for 64 bit: 1024 bytes).
72 Pretty cheap, actually.
73
74 2. Chose the pivot element using a median-of-three decision tree.
75 This reduces the probability of selecting a bad pivot value and
76 eliminates certain extraneous comparisons.
77
78 3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
79 insertion sort to order the MAX_THRESH items within each partition.
80 This is a big win, since insertion sort is faster for small, mostly
81 sorted array segments.
82
83 4. The larger of the two sub-partitions is always pushed onto the
84 stack first, with the algorithm then concentrating on the
85 smaller partition. This *guarantees* no more than log (total_elems)
86 stack size is needed (actually O(1) in this case)! */
87
88void
89_quicksort (void *const pbase, size_t total_elems, size_t size,
90 __compar_d_fn_t cmp, void *arg)
91{
92 char *base_ptr = (char *) pbase;
93
94 const size_t max_thresh = MAX_THRESH * size;
95
96 if (total_elems == 0)
97 /* Avoid lossage with unsigned arithmetic below. */
98 return;
99
100 if (total_elems > MAX_THRESH)
101 {
102 char *lo = base_ptr;
103 char *hi = &lo[size * (total_elems - 1)];
104 stack_node stack[STACK_SIZE];
105 stack_node *top = stack;
106
107 PUSH (NULL, NULL);
108
109 while (STACK_NOT_EMPTY)
110 {
111 char *left_ptr;
112 char *right_ptr;
113
114 /* Select median value from among LO, MID, and HI. Rearrange
115 LO and HI so the three values are sorted. This lowers the
116 probability of picking a pathological pivot value and
117 skips a comparison for both the LEFT_PTR and RIGHT_PTR in
118 the while loops. */
119
120 char *mid = lo + size * ((hi - lo) / size >> 1);
121
122 if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
123 SWAP (mid, lo, size);
124 if ((*cmp) ((void *) hi, (void *) mid, arg) < 0)
125 SWAP (mid, hi, size);
126 else
127 goto jump_over;
128 if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
129 SWAP (mid, lo, size);
130 jump_over:;
131
132 left_ptr = lo + size;
133 right_ptr = hi - size;
134
135 /* Here's the famous ``collapse the walls'' section of quicksort.
136 Gotta like those tight inner loops! They are the main reason
137 that this algorithm runs much faster than others. */
138 do
139 {
140 while ((*cmp) ((void *) left_ptr, (void *) mid, arg) < 0)
141 left_ptr += size;
142
143 while ((*cmp) ((void *) mid, (void *) right_ptr, arg) < 0)
144 right_ptr -= size;
145
146 if (left_ptr < right_ptr)
147 {
148 SWAP (left_ptr, right_ptr, size);
149 if (mid == left_ptr)
150 mid = right_ptr;
151 else if (mid == right_ptr)
152 mid = left_ptr;
153 left_ptr += size;
154 right_ptr -= size;
155 }
156 else if (left_ptr == right_ptr)
157 {
158 left_ptr += size;
159 right_ptr -= size;
160 break;
161 }
162 }
163 while (left_ptr <= right_ptr);
164
165 /* Set up pointers for next iteration. First determine whether
166 left and right partitions are below the threshold size. If so,
167 ignore one or both. Otherwise, push the larger partition's
168 bounds on the stack and continue sorting the smaller one. */
169
170 if ((size_t) (right_ptr - lo) <= max_thresh)
171 {
172 if ((size_t) (hi - left_ptr) <= max_thresh)
173 /* Ignore both small partitions. */
174 POP (lo, hi);
175 else
176 /* Ignore small left partition. */
177 lo = left_ptr;
178 }
179 else if ((size_t) (hi - left_ptr) <= max_thresh)
180 /* Ignore small right partition. */
181 hi = right_ptr;
182 else if ((right_ptr - lo) > (hi - left_ptr))
183 {
184 /* Push larger left partition indices. */
185 PUSH (lo, right_ptr);
186 lo = left_ptr;
187 }
188 else
189 {
190 /* Push larger right partition indices. */
191 PUSH (left_ptr, hi);
192 hi = right_ptr;
193 }
194 }
195 }
196
197 /* Once the BASE_PTR array is partially sorted by quicksort the rest
198 is completely sorted using insertion sort, since this is efficient
199 for partitions below MAX_THRESH size. BASE_PTR points to the beginning
200 of the array to sort, and END_PTR points at the very last element in
201 the array (*not* one beyond it!). */
202
203#define min(x, y) ((x) < (y) ? (x) : (y))
204
205 {
206 char *const end_ptr = &base_ptr[size * (total_elems - 1)];
207 char *tmp_ptr = base_ptr;
208 char *thresh = min(end_ptr, base_ptr + max_thresh);
209 char *run_ptr;
210
211 /* Find smallest element in first threshold and place it at the
212 array's beginning. This is the smallest array element,
213 and the operation speeds up insertion sort's inner loop. */
214
215 for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
216 if ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0)
217 tmp_ptr = run_ptr;
218
219 if (tmp_ptr != base_ptr)
220 SWAP (tmp_ptr, base_ptr, size);
221
222 /* Insertion sort, running from left-hand-side up to right-hand-side. */
223
224 run_ptr = base_ptr + size;
225 while ((run_ptr += size) <= end_ptr)
226 {
227 tmp_ptr = run_ptr - size;
228 while ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0)
229 tmp_ptr -= size;
230
231 tmp_ptr += size;
232 if (tmp_ptr != run_ptr)
233 {
234 char *trav;
235
236 trav = run_ptr + size;
237 while (--trav >= run_ptr)
238 {
239 char c = *trav;
240 char *hi, *lo;
241
242 for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
243 *hi = *lo;
244 *hi = c;
245 }
246 }
247 }
248 }
249}
250