lib/sort.c

   1 // SPDX-License-Identifier: GPL-2.0
   2 /*
   3  * A fast, small, non-recursive O(n log n) sort for the Linux kernel
   4  *
   5  * This performs n*log2(n) + 0.37*n + o(n) comparisons on average,
   6  * and 1.5*n*log2(n) + O(n) in the (very contrived) worst case.
   7  *
   8  * Glibc qsort() manages n*log2(n) - 1.26*n for random inputs (1.63*n
   9  * better) at the expense of stack usage and much larger code to avoid
  10  * quicksort's O(n^2) worst case.
  11  */
  12
  13 #define pr_fmt(fmt) KBUILD_MODNAME ": " fmt
  14
  15 #include <linux/types.h>
  16 #include <linux/export.h>
  17 #include <linux/sort.h>
  18
  19 /**
  20  * is_aligned - is this pointer & size okay for word-wide copying?
  21  * @base: pointer to data
  22  * @size: size of each element
  23  * @align: required alignment (typically 4 or 8)
  24  *
  25  * Returns true if elements can be copied using word loads and stores.
  26  * The size must be a multiple of the alignment, and the base address must
  27  * be if we do not have CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS.
  28  *
  29  * For some reason, gcc doesn't know to optimize "if (a & mask || b & mask)"
  30  * to "if ((a | b) & mask)", so we do that by hand.
  31  */
  32 __attribute_const__ __always_inline
  33 static bool is_aligned(const void *base, size_t size, unsigned char align)
  34 {
  35         unsigned char lsbits = (unsigned char)size;
  36
  37         (void)base;
  38 #ifndef CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS
  39         lsbits |= (unsigned char)(uintptr_t)base;
  40 #endif
  41         return (lsbits & (align - 1)) == 0;
  42 }
  43
  44 /**
  45  * swap_words_32 - swap two elements in 32-bit chunks
  46  * @a, @b: pointers to the elements
  47  * @size: element size (must be a multiple of 4)
  48  *
  49  * Exchange the two objects in memory.  This exploits base+index addressing,
  50  * which basically all CPUs have, to minimize loop overhead computations.
  51  *
  52  * For some reason, on x86 gcc 7.3.0 adds a redundant test of n at the
  53  * bottom of the loop, even though the zero flag is stil valid from the
  54  * subtract (since the intervening mov instructions don't alter the flags).
  55  * Gcc 8.1.0 doesn't have that problem.
  56  */
  57 static void swap_words_32(void *a, void *b, size_t n)
  58 {
  59         do {
  60                 u32 t = *(u32 *)(a + (n -= 4));
  61                 *(u32 *)(a + n) = *(u32 *)(b + n);
  62                 *(u32 *)(b + n) = t;
  63         } while (n);
  64 }
  65
  66 /**
  67  * swap_words_64 - swap two elements in 64-bit chunks
  68  * @a, @b: pointers to the elements
  69  * @size: element size (must be a multiple of 8)
  70  *
  71  * Exchange the two objects in memory.  This exploits base+index
  72  * addressing, which basically all CPUs have, to minimize loop overhead
  73  * computations.
  74  *
  75  * We'd like to use 64-bit loads if possible.  If they're not, emulating
  76  * one requires base+index+4 addressing which x86 has but most other
  77  * processors do not.  If CONFIG_64BIT, we definitely have 64-bit loads,
  78  * but it's possible to have 64-bit loads without 64-bit pointers (e.g.
  79  * x32 ABI).  Are there any cases the kernel needs to worry about?
  80  */
  81 static void swap_words_64(void *a, void *b, size_t n)
  82 {
  83         do {
  84 #ifdef CONFIG_64BIT
  85                 u64 t = *(u64 *)(a + (n -= 8));
  86                 *(u64 *)(a + n) = *(u64 *)(b + n);
  87                 *(u64 *)(b + n) = t;
  88 #else
  89                 /* Use two 32-bit transfers to avoid base+index+4 addressing */
  90                 u32 t = *(u32 *)(a + (n -= 4));
  91                 *(u32 *)(a + n) = *(u32 *)(b + n);
  92                 *(u32 *)(b + n) = t;
  93
  94                 t = *(u32 *)(a + (n -= 4));
  95                 *(u32 *)(a + n) = *(u32 *)(b + n);
  96                 *(u32 *)(b + n) = t;
  97 #endif
  98         } while (n);
  99 }
 100
 101 /**
 102  * swap_bytes - swap two elements a byte at a time
 103  * @a, @b: pointers to the elements
 104  * @size: element size
 105  *
 106  * This is the fallback if alignment doesn't allow using larger chunks.
 107  */
 108 static void swap_bytes(void *a, void *b, size_t n)
 109 {
 110         do {
 111                 char t = ((char *)a)[--n];
 112                 ((char *)a)[n] = ((char *)b)[n];
 113                 ((char *)b)[n] = t;
 114         } while (n);
 115 }
 116
 117 typedef void (*swap_func_t)(void *a, void *b, int size);
 118
 119 /*
 120  * The values are arbitrary as long as they can't be confused with
 121  * a pointer, but small integers make for the smallest compare
 122  * instructions.
 123  */
 124 #define SWAP_WORDS_64 (swap_func_t)0
 125 #define SWAP_WORDS_32 (swap_func_t)1
 126 #define SWAP_BYTES    (swap_func_t)2
 127
 128 /*
 129  * The function pointer is last to make tail calls most efficient if the
 130  * compiler decides not to inline this function.
 131  */
 132 static void do_swap(void *a, void *b, size_t size, swap_func_t swap_func)
 133 {
 134         if (swap_func == SWAP_WORDS_64)
 135                 swap_words_64(a, b, size);
 136         else if (swap_func == SWAP_WORDS_32)
 137                 swap_words_32(a, b, size);
 138         else if (swap_func == SWAP_BYTES)
 139                 swap_bytes(a, b, size);
 140         else
 141                 swap_func(a, b, (int)size);
 142 }
 143
 144 /**
 145  * parent - given the offset of the child, find the offset of the parent.
 146  * @i: the offset of the heap element whose parent is sought.  Non-zero.
 147  * @lsbit: a precomputed 1-bit mask, equal to "size & -size"
 148  * @size: size of each element
 149  *
 150  * In terms of array indexes, the parent of element j = @i/@size is simply
 151  * (j-1)/2.  But when working in byte offsets, we can't use implicit
 152  * truncation of integer divides.
 153  *
 154  * Fortunately, we only need one bit of the quotient, not the full divide.
 155  * @size has a least significant bit.  That bit will be clear if @i is
 156  * an even multiple of @size, and set if it's an odd multiple.
 157  *
 158  * Logically, we're doing "if (i & lsbit) i -= size;", but since the
 159  * branch is unpredictable, it's done with a bit of clever branch-free
 160  * code instead.
 161  */
 162 __attribute_const__ __always_inline
 163 static size_t parent(size_t i, unsigned int lsbit, size_t size)
 164 {
 165         i -= size;
 166         i -= size & -(i & lsbit);
 167         return i / 2;
 168 }
 169
 170 /**
 171  * sort - sort an array of elements
 172  * @base: pointer to data to sort
 173  * @num: number of elements
 174  * @size: size of each element
 175  * @cmp_func: pointer to comparison function
 176  * @swap_func: pointer to swap function or NULL
 177  *
 178  * This function does a heapsort on the given array.  You may provide
 179  * a swap_func function if you need to do something more than a memory
 180  * copy (e.g. fix up pointers or auxiliary data), but the built-in swap
 181  * avoids a slow retpoline and so is significantly faster.
 182  *
 183  * Sorting time is O(n log n) both on average and worst-case. While
 184  * quicksort is slightly faster on average, it suffers from exploitable
 185  * O(n*n) worst-case behavior and extra memory requirements that make
 186  * it less suitable for kernel use.
 187  */
 188 void sort(void *base, size_t num, size_t size,
 189           int (*cmp_func)(const void *, const void *),
 190           void (*swap_func)(void *, void *, int size))
 191 {
 192         /* pre-scale counters for performance */
 193         size_t n = num * size, a = (num/2) * size;
 194         const unsigned int lsbit = size & -size;  /* Used to find parent */
 195
 196         if (!a)         /* num < 2 || size == 0 */
 197                 return;
 198
 199         if (!swap_func) {
 200                 if (is_aligned(base, size, 8))
 201                         swap_func = SWAP_WORDS_64;
 202                 else if (is_aligned(base, size, 4))
 203                         swap_func = SWAP_WORDS_32;
 204                 else
 205                         swap_func = SWAP_BYTES;
 206         }
 207
 208         /*
 209          * Loop invariants:
 210          * 1. elements [a,n) satisfy the heap property (compare greater than
 211          *    all of their children),
 212          * 2. elements [n,num*size) are sorted, and
 213          * 3. a <= b <= c <= d <= n (whenever they are valid).
 214          */
 215         for (;;) {
 216                 size_t b, c, d;
 217
 218                 if (a)                  /* Building heap: sift down --a */
 219                         a -= size;
 220                 else if (n -= size)     /* Sorting: Extract root to --n */
 221                         do_swap(base, base + n, size, swap_func);
 222                 else                    /* Sort complete */
 223                         break;
 224
 225                 /*
 226                  * Sift element at "a" down into heap.  This is the
 227                  * "bottom-up" variant, which significantly reduces
 228                  * calls to cmp_func(): we find the sift-down path all
 229                  * the way to the leaves (one compare per level), then
 230                  * backtrack to find where to insert the target element.
 231                  *
 232                  * Because elements tend to sift down close to the leaves,
 233                  * this uses fewer compares than doing two per level
 234                  * on the way down.  (A bit more than half as many on
 235                  * average, 3/4 worst-case.)
 236                  */
 237                 for (b = a; c = 2*b + size, (d = c + size) < n;)
 238                         b = cmp_func(base + c, base + d) >= 0 ? c : d;
 239                 if (d == n)     /* Special case last leaf with no sibling */
 240                         b = c;
 241
 242                 /* Now backtrack from "b" to the correct location for "a" */
 243                 while (b != a && cmp_func(base + a, base + b) >= 0)
 244                         b = parent(b, lsbit, size);
 245                 c = b;                  /* Where "a" belongs */
 246                 while (b != a) {        /* Shift it into place */
 247                         b = parent(b, lsbit, size);
 248                         do_swap(base + b, base + c, size, swap_func);
 249                 }
 250         }
 251 }
 252 EXPORT_SYMBOL(sort);