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326 lines
10 KiB
C
326 lines
10 KiB
C
/* Copyright (C) 1991-2023 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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/* If you consider tuning this algorithm, you should consult first:
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Engineering a sort function; Jon Bentley and M. Douglas McIlroy;
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Software - Practice and Experience; Vol. 23 (11), 1249-1265, 1993. */
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#include <alloca.h>
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#include <limits.h>
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#include <memswap.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdbool.h>
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/* Swap SIZE bytes between addresses A and B. These helpers are provided
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along the generic one as an optimization. */
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enum swap_type_t
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{
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SWAP_WORDS_64,
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SWAP_WORDS_32,
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SWAP_BYTES
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};
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/* If this function returns true, elements can be safely copied using word
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loads and stores. Otherwise, it might not be safe. BASE (as an integer)
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must be a multiple of the word alignment. SIZE must be a multiple of
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WORDSIZE. Since WORDSIZE must be a multiple of the word alignment, and
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WORDSIZE is a power of two on all supported platforms, this function for
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speed merely checks that BASE and SIZE are both multiples of the word
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size. */
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static inline bool
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is_aligned (const void *base, size_t size, size_t wordsize)
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{
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return (((uintptr_t) base | size) & (wordsize - 1)) == 0;
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}
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static inline void
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swap_words_64 (void * restrict a, void * restrict b, size_t n)
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{
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typedef uint64_t __attribute__ ((__may_alias__)) u64_alias_t;
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do
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{
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n -= 8;
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u64_alias_t t = *(u64_alias_t *)(a + n);
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*(u64_alias_t *)(a + n) = *(u64_alias_t *)(b + n);
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*(u64_alias_t *)(b + n) = t;
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} while (n);
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}
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static inline void
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swap_words_32 (void * restrict a, void * restrict b, size_t n)
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{
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typedef uint32_t __attribute__ ((__may_alias__)) u32_alias_t;
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do
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{
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n -= 4;
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u32_alias_t t = *(u32_alias_t *)(a + n);
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*(u32_alias_t *)(a + n) = *(u32_alias_t *)(b + n);
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*(u32_alias_t *)(b + n) = t;
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} while (n);
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}
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/* Replace the indirect call with a serie of if statements. It should help
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the branch predictor. */
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static void
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do_swap (void * restrict a, void * restrict b, size_t size,
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enum swap_type_t swap_type)
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{
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if (swap_type == SWAP_WORDS_64)
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swap_words_64 (a, b, size);
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else if (swap_type == SWAP_WORDS_32)
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swap_words_32 (a, b, size);
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else
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__memswap (a, b, size);
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}
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/* Discontinue quicksort algorithm when partition gets below this size.
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This particular magic number was chosen to work best on a Sun 4/260. */
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#define MAX_THRESH 4
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/* Stack node declarations used to store unfulfilled partition obligations. */
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typedef struct
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{
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char *lo;
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char *hi;
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} stack_node;
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/* The stack needs log (total_elements) entries (we could even subtract
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log(MAX_THRESH)). Since total_elements has type size_t, we get as
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upper bound for log (total_elements):
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bits per byte (CHAR_BIT) * sizeof(size_t). */
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enum { STACK_SIZE = CHAR_BIT * sizeof (size_t) };
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static inline stack_node *
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push (stack_node *top, char *lo, char *hi)
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{
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top->lo = lo;
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top->hi = hi;
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return ++top;
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}
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static inline stack_node *
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pop (stack_node *top, char **lo, char **hi)
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{
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--top;
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*lo = top->lo;
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*hi = top->hi;
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return top;
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}
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static inline void
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insertion_sort_qsort_partitions (void *const pbase, size_t total_elems,
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size_t size, enum swap_type_t swap_type,
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__compar_d_fn_t cmp, void *arg)
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{
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char *base_ptr = (char *) pbase;
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char *const end_ptr = &base_ptr[size * (total_elems - 1)];
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char *tmp_ptr = base_ptr;
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#define min(x, y) ((x) < (y) ? (x) : (y))
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const size_t max_thresh = MAX_THRESH * size;
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char *thresh = min(end_ptr, base_ptr + max_thresh);
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char *run_ptr;
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/* Find smallest element in first threshold and place it at the
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array's beginning. This is the smallest array element,
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and the operation speeds up insertion sort's inner loop. */
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for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
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if (cmp (run_ptr, tmp_ptr, arg) < 0)
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tmp_ptr = run_ptr;
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if (tmp_ptr != base_ptr)
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do_swap (tmp_ptr, base_ptr, size, swap_type);
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/* Insertion sort, running from left-hand-side up to right-hand-side. */
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run_ptr = base_ptr + size;
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while ((run_ptr += size) <= end_ptr)
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{
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tmp_ptr = run_ptr - size;
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while (cmp (run_ptr, tmp_ptr, arg) < 0)
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tmp_ptr -= size;
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tmp_ptr += size;
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if (tmp_ptr != run_ptr)
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{
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char *trav;
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trav = run_ptr + size;
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while (--trav >= run_ptr)
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{
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char c = *trav;
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char *hi, *lo;
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for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
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*hi = *lo;
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*hi = c;
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}
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}
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}
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}
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/* Order size using quicksort. This implementation incorporates
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four optimizations discussed in Sedgewick:
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1. Non-recursive, using an explicit stack of pointer that store the
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next array partition to sort. To save time, this maximum amount
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of space required to store an array of SIZE_MAX is allocated on the
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stack. Assuming a 32-bit (64 bit) integer for size_t, this needs
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only 32 * sizeof(stack_node) == 256 bytes (for 64 bit: 1024 bytes).
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Pretty cheap, actually.
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2. Chose the pivot element using a median-of-three decision tree.
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This reduces the probability of selecting a bad pivot value and
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eliminates certain extraneous comparisons.
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3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
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insertion sort to order the MAX_THRESH items within each partition.
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This is a big win, since insertion sort is faster for small, mostly
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sorted array segments.
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4. The larger of the two sub-partitions is always pushed onto the
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stack first, with the algorithm then concentrating on the
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smaller partition. This *guarantees* no more than log (total_elems)
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stack size is needed (actually O(1) in this case)! */
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void
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_quicksort (void *const pbase, size_t total_elems, size_t size,
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__compar_d_fn_t cmp, void *arg)
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{
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char *base_ptr = (char *) pbase;
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const size_t max_thresh = MAX_THRESH * size;
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if (total_elems == 0)
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/* Avoid lossage with unsigned arithmetic below. */
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return;
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enum swap_type_t swap_type;
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if (is_aligned (pbase, size, 8))
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swap_type = SWAP_WORDS_64;
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else if (is_aligned (pbase, size, 4))
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swap_type = SWAP_WORDS_32;
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else
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swap_type = SWAP_BYTES;
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if (total_elems > MAX_THRESH)
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{
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char *lo = base_ptr;
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char *hi = &lo[size * (total_elems - 1)];
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stack_node stack[STACK_SIZE];
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stack_node *top = stack + 1;
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while (stack < top)
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{
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char *left_ptr;
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char *right_ptr;
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/* Select median value from among LO, MID, and HI. Rearrange
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LO and HI so the three values are sorted. This lowers the
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probability of picking a pathological pivot value and
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skips a comparison for both the LEFT_PTR and RIGHT_PTR in
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the while loops. */
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char *mid = lo + size * ((hi - lo) / size >> 1);
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if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
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do_swap (mid, lo, size, swap_type);
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if ((*cmp) ((void *) hi, (void *) mid, arg) < 0)
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do_swap (mid, hi, size, swap_type);
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else
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goto jump_over;
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if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
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do_swap (mid, lo, size, swap_type);
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jump_over:;
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left_ptr = lo + size;
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right_ptr = hi - size;
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/* Here's the famous ``collapse the walls'' section of quicksort.
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Gotta like those tight inner loops! They are the main reason
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that this algorithm runs much faster than others. */
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do
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{
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while ((*cmp) ((void *) left_ptr, (void *) mid, arg) < 0)
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left_ptr += size;
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while ((*cmp) ((void *) mid, (void *) right_ptr, arg) < 0)
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right_ptr -= size;
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if (left_ptr < right_ptr)
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{
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do_swap (left_ptr, right_ptr, size, swap_type);
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if (mid == left_ptr)
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mid = right_ptr;
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else if (mid == right_ptr)
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mid = left_ptr;
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left_ptr += size;
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right_ptr -= size;
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}
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else if (left_ptr == right_ptr)
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{
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left_ptr += size;
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right_ptr -= size;
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break;
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}
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}
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while (left_ptr <= right_ptr);
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/* Set up pointers for next iteration. First determine whether
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left and right partitions are below the threshold size. If so,
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ignore one or both. Otherwise, push the larger partition's
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bounds on the stack and continue sorting the smaller one. */
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if ((size_t) (right_ptr - lo) <= max_thresh)
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{
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if ((size_t) (hi - left_ptr) <= max_thresh)
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/* Ignore both small partitions. */
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top = pop (top, &lo, &hi);
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else
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/* Ignore small left partition. */
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lo = left_ptr;
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}
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else if ((size_t) (hi - left_ptr) <= max_thresh)
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/* Ignore small right partition. */
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hi = right_ptr;
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else if ((right_ptr - lo) > (hi - left_ptr))
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{
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/* Push larger left partition indices. */
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top = push (top, lo, right_ptr);
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lo = left_ptr;
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}
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else
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{
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/* Push larger right partition indices. */
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top = push (top, left_ptr, hi);
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hi = right_ptr;
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}
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}
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}
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/* Once the BASE_PTR array is partially sorted by quicksort the rest
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is completely sorted using insertion sort, since this is efficient
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for partitions below MAX_THRESH size. BASE_PTR points to the beginning
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of the array to sort, and END_PTR points at the very last element in
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the array (*not* one beyond it!). */
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insertion_sort_qsort_partitions (pbase, total_elems, size, swap_type, cmp,
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arg);
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}
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