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  * Quicksort 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 #include <linux/types.h>
  14 #include <linux/export.h>
  15 #include <linux/sort.h>
  16
  17 /**
  18  * is_aligned - is this pointer & size okay for word-wide copying?
  19  * @base: pointer to data
  20  * @size: size of each element
  21  * @align: required alignment (typically 4 or 8)
  22  *
  23  * Returns true if elements can be copied using word loads and stores.
  24  * The size must be a multiple of the alignment, and the base address must
  25  * be if we do not have CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS.
  26  *
  27  * For some reason, gcc doesn't know to optimize "if (a & mask || b & mask)"
  28  * to "if ((a | b) & mask)", so we do that by hand.
  29  */
  30 __attribute_const__ __always_inline
  31 static bool is_aligned(const void *base, size_t size, unsigned char align)
  32 {
  33         unsigned char lsbits = (unsigned char)size;
  34
  35         (void)base;
  36 #ifndef CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS
  37         lsbits |= (unsigned char)(uintptr_t)base;
  38 #endif
  39         return (lsbits & (align - 1)) == 0;
  40 }
  41
  42 /**
  43  * swap_words_32 - swap two elements in 32-bit chunks
  44  * @a: pointer to the first element to swap
  45  * @b: pointer to the second element to swap
  46  * @n: element size (must be a multiple of 4)
  47  *
  48  * Exchange the two objects in memory.  This exploits base+index addressing,
  49  * which basically all CPUs have, to minimize loop overhead computations.
  50  *
  51  * For some reason, on x86 gcc 7.3.0 adds a redundant test of n at the
  52  * bottom of the loop, even though the zero flag is still valid from the
  53  * subtract (since the intervening mov instructions don't alter the flags).
  54  * Gcc 8.1.0 doesn't have that problem.
  55  */
  56 static void swap_words_32(void *a, void *b, size_t n)
  57 {
  58         do {
  59                 u32 t = *(u32 *)(a + (n -= 4));
  60                 *(u32 *)(a + n) = *(u32 *)(b + n);
  61                 *(u32 *)(b + n) = t;
  62         } while (n);
  63 }
  64
  65 /**
  66  * swap_words_64 - swap two elements in 64-bit chunks
  67  * @a: pointer to the first element to swap
  68  * @b: pointer to the second element to swap
  69  * @n: 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: pointer to the first element to swap
 104  * @b: pointer to the second element to swap
 105  * @n: element size
 106  *
 107  * This is the fallback if alignment doesn't allow using larger chunks.
 108  */
 109 static void swap_bytes(void *a, void *b, size_t n)
 110 {
 111         do {
 112                 char t = ((char *)a)[--n];
 113                 ((char *)a)[n] = ((char *)b)[n];
 114                 ((char *)b)[n] = t;
 115         } while (n);
 116 }
 117
 118 /*
 119  * The values are arbitrary as long as they can't be confused with
 120  * a pointer, but small integers make for the smallest compare
 121  * instructions.
 122  */
 123 #define SWAP_WORDS_64 (swap_r_func_t)0
 124 #define SWAP_WORDS_32 (swap_r_func_t)1
 125 #define SWAP_BYTES    (swap_r_func_t)2
 126 #define SWAP_WRAPPER  (swap_r_func_t)3
 127
 128 struct wrapper {
 129         cmp_func_t cmp;
 130         swap_func_t swap;
 131 };
 132
 133 /*
 134  * The function pointer is last to make tail calls most efficient if the
 135  * compiler decides not to inline this function.
 136  */
 137 static void do_swap(void *a, void *b, size_t size, swap_r_func_t swap_func, const void *priv)
 138 {
 139         if (swap_func == SWAP_WRAPPER) {
 140                 ((const struct wrapper *)priv)->swap(a, b, (int)size);
 141                 return;
 142         }
 143
 144         if (swap_func == SWAP_WORDS_64)
 145                 swap_words_64(a, b, size);
 146         else if (swap_func == SWAP_WORDS_32)
 147                 swap_words_32(a, b, size);
 148         else if (swap_func == SWAP_BYTES)
 149                 swap_bytes(a, b, size);
 150         else
 151                 swap_func(a, b, (int)size, priv);
 152 }
 153
 154 #define _CMP_WRAPPER ((cmp_r_func_t)0L)
 155
 156 static int do_cmp(const void *a, const void *b, cmp_r_func_t cmp, const void *priv)
 157 {
 158         if (cmp == _CMP_WRAPPER)
 159                 return ((const struct wrapper *)priv)->cmp(a, b);
 160         return cmp(a, b, priv);
 161 }
 162
 163 /**
 164  * parent - given the offset of the child, find the offset of the parent.
 165  * @i: the offset of the heap element whose parent is sought.  Non-zero.
 166  * @lsbit: a precomputed 1-bit mask, equal to "size & -size"
 167  * @size: size of each element
 168  *
 169  * In terms of array indexes, the parent of element j = @i/@size is simply
 170  * (j-1)/2.  But when working in byte offsets, we can't use implicit
 171  * truncation of integer divides.
 172  *
 173  * Fortunately, we only need one bit of the quotient, not the full divide.
 174  * @size has a least significant bit.  That bit will be clear if @i is
 175  * an even multiple of @size, and set if it's an odd multiple.
 176  *
 177  * Logically, we're doing "if (i & lsbit) i -= size;", but since the
 178  * branch is unpredictable, it's done with a bit of clever branch-free
 179  * code instead.
 180  */
 181 __attribute_const__ __always_inline
 182 static size_t parent(size_t i, unsigned int lsbit, size_t size)
 183 {
 184         i -= size;
 185         i -= size & -(i & lsbit);
 186         return i / 2;
 187 }
 188
 189 /**
 190  * sort_r - sort an array of elements
 191  * @base: pointer to data to sort
 192  * @num: number of elements
 193  * @size: size of each element
 194  * @cmp_func: pointer to comparison function
 195  * @swap_func: pointer to swap function or NULL
 196  * @priv: third argument passed to comparison function
 197  *
 198  * This function does a heapsort on the given array.  You may provide
 199  * a swap_func function if you need to do something more than a memory
 200  * copy (e.g. fix up pointers or auxiliary data), but the built-in swap
 201  * avoids a slow retpoline and so is significantly faster.
 202  *
 203  * Sorting time is O(n log n) both on average and worst-case. While
 204  * quicksort is slightly faster on average, it suffers from exploitable
 205  * O(n*n) worst-case behavior and extra memory requirements that make
 206  * it less suitable for kernel use.
 207  */
 208 void sort_r(void *base, size_t num, size_t size,
 209             cmp_r_func_t cmp_func,
 210             swap_r_func_t swap_func,
 211             const void *priv)
 212 {
 213         /* pre-scale counters for performance */
 214         size_t n = num * size, a = (num/2) * size;
 215         const unsigned int lsbit = size & -size;  /* Used to find parent */
 216         size_t shift = 0;
 217
 218         if (!a)         /* num < 2 || size == 0 */
 219                 return;
 220
 221         /* called from 'sort' without swap function, let's pick the default */
 222         if (swap_func == SWAP_WRAPPER && !((struct wrapper *)priv)->swap)
 223                 swap_func = NULL;
 224
 225         if (!swap_func) {
 226                 if (is_aligned(base, size, 8))
 227                         swap_func = SWAP_WORDS_64;
 228                 else if (is_aligned(base, size, 4))
 229                         swap_func = SWAP_WORDS_32;
 230                 else
 231                         swap_func = SWAP_BYTES;
 232         }
 233
 234         /*
 235          * Loop invariants:
 236          * 1. elements [a,n) satisfy the heap property (compare greater than
 237          *    all of their children),
 238          * 2. elements [n,num*size) are sorted, and
 239          * 3. a <= b <= c <= d <= n (whenever they are valid).
 240          */
 241         for (;;) {
 242                 size_t b, c, d;
 243
 244                 if (a)                  /* Building heap: sift down a */
 245                         a -= size << shift;
 246                 else if (n > 3 * size) { /* Sorting: Extract two largest elements */
 247                         n -= size;
 248                         do_swap(base, base + n, size, swap_func, priv);
 249                         shift = do_cmp(base + size, base + 2 * size, cmp_func, priv) <= 0;
 250                         a = size << shift;
 251                         n -= size;
 252                         do_swap(base + a, base + n, size, swap_func, priv);
 253                 } else {                /* Sort complete */
 254                         break;
 255                 }
 256
 257                 /*
 258                  * Sift element at "a" down into heap.  This is the
 259                  * "bottom-up" variant, which significantly reduces
 260                  * calls to cmp_func(): we find the sift-down path all
 261                  * the way to the leaves (one compare per level), then
 262                  * backtrack to find where to insert the target element.
 263                  *
 264                  * Because elements tend to sift down close to the leaves,
 265                  * this uses fewer compares than doing two per level
 266                  * on the way down.  (A bit more than half as many on
 267                  * average, 3/4 worst-case.)
 268                  */
 269                 for (b = a; c = 2*b + size, (d = c + size) < n;)
 270                         b = do_cmp(base + c, base + d, cmp_func, priv) > 0 ? c : d;
 271                 if (d == n)     /* Special case last leaf with no sibling */
 272                         b = c;
 273
 274                 /* Now backtrack from "b" to the correct location for "a" */
 275                 while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0)
 276                         b = parent(b, lsbit, size);
 277                 c = b;                  /* Where "a" belongs */
 278                 while (b != a) {        /* Shift it into place */
 279                         b = parent(b, lsbit, size);
 280                         do_swap(base + b, base + c, size, swap_func, priv);
 281                 }
 282         }
 283
 284         n -= size;
 285         do_swap(base, base + n, size, swap_func, priv);
 286         if (n == size * 2 && do_cmp(base, base + size, cmp_func, priv) > 0)
 287                 do_swap(base, base + size, size, swap_func, priv);
 288 }
 289 EXPORT_SYMBOL(sort_r);
 290
 291 void sort(void *base, size_t num, size_t size,
 292           cmp_func_t cmp_func,
 293           swap_func_t swap_func)
 294 {
 295         struct wrapper w = {
 296                 .cmp  = cmp_func,
 297                 .swap = swap_func,
 298         };
 299
 300         return sort_r(base, num, size, _CMP_WRAPPER, SWAP_WRAPPER, &w);
 301 }
 302 EXPORT_SYMBOL(sort);