1 /* Copyright (C) 1991-2021 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 #ifndef _LIBC 24 # include <config.h> 25 #endif 26 27 #include <limits.h> 28 #include <stdlib.h> 29 #include <string.h> 30 31 #ifndef _LIBC 32 # define _quicksort qsort_r 33 # define __compar_d_fn_t compar_d_fn_t 34 typedef int (*compar_d_fn_t) (const void *, const void *, void *); 35 #endif 36 37 /* Byte-wise swap two items of size SIZE. */ 38 #define SWAP(a, b, size) \ 39 do \ 40 { \ 41 size_t __size = (size); \ 42 char *__a = (a), *__b = (b); \ 43 do \ 44 { \ 45 char __tmp = *__a; \ 46 *__a++ = *__b; \ 47 *__b++ = __tmp; \ 48 } while (--__size > 0); \ 49 } while (0) 50 51 /* Discontinue quicksort algorithm when partition gets below this size. 52 This particular magic number was chosen to work best on a Sun 4/260. */ 53 #define MAX_THRESH 4 54 55 /* Stack node declarations used to store unfulfilled partition obligations. */ 56 typedef struct 57 { 58 char *lo; 59 char *hi; 60 } stack_node; 61 62 /* The next 4 #defines implement a very fast in-line stack abstraction. */ 63 /* The stack needs log (total_elements) entries (we could even subtract 64 log(MAX_THRESH)). Since total_elements has type size_t, we get as 65 upper bound for log (total_elements): 66 bits per byte (CHAR_BIT) * sizeof(size_t). */ 67 #define STACK_SIZE (CHAR_BIT * sizeof(size_t)) 68 #define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top)) 69 #define POP(low, high) ((void) (--top, (low = top->lo), (high = top->hi))) 70 #define STACK_NOT_EMPTY (stack < top) 71 72 73 /* Order size using quicksort. This implementation incorporates 74 four optimizations discussed in Sedgewick: 75 76 1. Non-recursive, using an explicit stack of pointer that store the 77 next array partition to sort. To save time, this maximum amount 78 of space required to store an array of SIZE_MAX is allocated on the 79 stack. Assuming a 32-bit (64 bit) integer for size_t, this needs 80 only 32 * sizeof(stack_node) == 256 bytes (for 64 bit: 1024 bytes). 81 Pretty cheap, actually. 82 83 2. Chose the pivot element using a median-of-three decision tree. 84 This reduces the probability of selecting a bad pivot value and 85 eliminates certain extraneous comparisons. 86 87 3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving 88 insertion sort to order the MAX_THRESH items within each partition. 89 This is a big win, since insertion sort is faster for small, mostly 90 sorted array segments. 91 92 4. The larger of the two sub-partitions is always pushed onto the 93 stack first, with the algorithm then concentrating on the 94 smaller partition. This *guarantees* no more than log (total_elems) 95 stack size is needed (actually O(1) in this case)! */ 96 97 void 98 _quicksort (void *const pbase, size_t total_elems, size_t size, /* */ 99 __compar_d_fn_t cmp, void *arg) 100 { 101 char *base_ptr = (char *) pbase; 102 103 const size_t max_thresh = MAX_THRESH * size; 104 105 if (total_elems == 0) 106 /* Avoid lossage with unsigned arithmetic below. */ 107 return; 108 109 if (total_elems > MAX_THRESH) 110 { 111 char *lo = base_ptr; 112 char *hi = &lo[size * (total_elems - 1)]; 113 stack_node stack[STACK_SIZE]; 114 stack_node *top = stack; 115 116 PUSH (NULL, NULL); 117 118 while (STACK_NOT_EMPTY) 119 { 120 char *left_ptr; 121 char *right_ptr; 122 123 /* Select median value from among LO, MID, and HI. Rearrange 124 LO and HI so the three values are sorted. This lowers the 125 probability of picking a pathological pivot value and 126 skips a comparison for both the LEFT_PTR and RIGHT_PTR in 127 the while loops. */ 128 129 char *mid = lo + size * ((hi - lo) / size >> 1); 130 131 if ((*cmp) ((void *) mid, (void *) lo, arg) < 0) 132 SWAP (mid, lo, size); 133 if ((*cmp) ((void *) hi, (void *) mid, arg) < 0) 134 SWAP (mid, hi, size); 135 else 136 goto jump_over; 137 if ((*cmp) ((void *) mid, (void *) lo, arg) < 0) 138 SWAP (mid, lo, size); 139 jump_over:; 140 141 left_ptr = lo + size; 142 right_ptr = hi - size; 143 144 /* Here's the famous ``collapse the walls'' section of quicksort. 145 Gotta like those tight inner loops! They are the main reason 146 that this algorithm runs much faster than others. */ 147 do 148 { 149 while ((*cmp) ((void *) left_ptr, (void *) mid, arg) < 0) 150 left_ptr += size; 151 152 while ((*cmp) ((void *) mid, (void *) right_ptr, arg) < 0) 153 right_ptr -= size; 154 155 if (left_ptr < right_ptr) 156 { 157 SWAP (left_ptr, right_ptr, size); 158 if (mid == left_ptr) 159 mid = right_ptr; 160 else if (mid == right_ptr) 161 mid = left_ptr; 162 left_ptr += size; 163 right_ptr -= size; 164 } 165 else if (left_ptr == right_ptr) 166 { 167 left_ptr += size; 168 right_ptr -= size; 169 break; 170 } 171 } 172 while (left_ptr <= right_ptr); 173 174 /* Set up pointers for next iteration. First determine whether 175 left and right partitions are below the threshold size. If so, 176 ignore one or both. Otherwise, push the larger partition's 177 bounds on the stack and continue sorting the smaller one. */ 178 179 if ((size_t) (right_ptr - lo) <= max_thresh) 180 { 181 if ((size_t) (hi - left_ptr) <= max_thresh) 182 /* Ignore both small partitions. */ 183 POP (lo, hi); 184 else 185 /* Ignore small left partition. */ 186 lo = left_ptr; 187 } 188 else if ((size_t) (hi - left_ptr) <= max_thresh) 189 /* Ignore small right partition. */ 190 hi = right_ptr; 191 else if ((right_ptr - lo) > (hi - left_ptr)) 192 { 193 /* Push larger left partition indices. */ 194 PUSH (lo, right_ptr); 195 lo = left_ptr; 196 } 197 else 198 { 199 /* Push larger right partition indices. */ 200 PUSH (left_ptr, hi); 201 hi = right_ptr; 202 } 203 } 204 } 205 206 /* Once the BASE_PTR array is partially sorted by quicksort the rest 207 is completely sorted using insertion sort, since this is efficient 208 for partitions below MAX_THRESH size. BASE_PTR points to the beginning 209 of the array to sort, and END_PTR points at the very last element in 210 the array (*not* one beyond it!). */ 211 212 #define min(x, y) ((x) < (y) ? (x) : (y)) 213 214 { 215 char *const end_ptr = &base_ptr[size * (total_elems - 1)]; 216 char *tmp_ptr = base_ptr; 217 char *thresh = min(end_ptr, base_ptr + max_thresh); 218 char *run_ptr; 219 220 /* Find smallest element in first threshold and place it at the 221 array's beginning. This is the smallest array element, 222 and the operation speeds up insertion sort's inner loop. */ 223 224 for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size) 225 if ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0) 226 tmp_ptr = run_ptr; 227 228 if (tmp_ptr != base_ptr) 229 SWAP (tmp_ptr, base_ptr, size); 230 231 /* Insertion sort, running from left-hand-side up to right-hand-side. */ 232 233 run_ptr = base_ptr + size; 234 while ((run_ptr += size) <= end_ptr) 235 { 236 tmp_ptr = run_ptr - size; 237 while ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0) 238 tmp_ptr -= size; 239 240 tmp_ptr += size; 241 if (tmp_ptr != run_ptr) 242 { 243 char *trav; 244 245 trav = run_ptr + size; 246 while (--trav >= run_ptr) 247 { 248 char c = *trav; 249 char *hi, *lo; 250 251 for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo) 252 *hi = *lo; 253 *hi = c; 254 } 255 } 256 } 257 } 258 }