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       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                 :          3 :         return (lsbits & (align - 1)) == 0;
      42                 :            : }
      43                 :            : 
      44                 :            : /**
      45                 :            :  * swap_words_32 - swap two elements in 32-bit chunks
      46                 :            :  * @a: pointer to the first element to swap
      47                 :            :  * @b: pointer to the second element to swap
      48                 :            :  * @n: element size (must be a multiple of 4)
      49                 :            :  *
      50                 :            :  * Exchange the two objects in memory.  This exploits base+index addressing,
      51                 :            :  * which basically all CPUs have, to minimize loop overhead computations.
      52                 :            :  *
      53                 :            :  * For some reason, on x86 gcc 7.3.0 adds a redundant test of n at the
      54                 :            :  * bottom of the loop, even though the zero flag is stil valid from the
      55                 :            :  * subtract (since the intervening mov instructions don't alter the flags).
      56                 :            :  * Gcc 8.1.0 doesn't have that problem.
      57                 :            :  */
      58                 :            : static void swap_words_32(void *a, void *b, size_t n)
      59                 :            : {
      60                 :            :         do {
      61                 :          3 :                 u32 t = *(u32 *)(a + (n -= 4));
      62                 :          3 :                 *(u32 *)(a + n) = *(u32 *)(b + n);
      63                 :          3 :                 *(u32 *)(b + n) = t;
      64                 :          3 :         } while (n);
      65                 :            : }
      66                 :            : 
      67                 :            : /**
      68                 :            :  * swap_words_64 - swap two elements in 64-bit chunks
      69                 :            :  * @a: pointer to the first element to swap
      70                 :            :  * @b: pointer to the second element to swap
      71                 :            :  * @n: element size (must be a multiple of 8)
      72                 :            :  *
      73                 :            :  * Exchange the two objects in memory.  This exploits base+index
      74                 :            :  * addressing, which basically all CPUs have, to minimize loop overhead
      75                 :            :  * computations.
      76                 :            :  *
      77                 :            :  * We'd like to use 64-bit loads if possible.  If they're not, emulating
      78                 :            :  * one requires base+index+4 addressing which x86 has but most other
      79                 :            :  * processors do not.  If CONFIG_64BIT, we definitely have 64-bit loads,
      80                 :            :  * but it's possible to have 64-bit loads without 64-bit pointers (e.g.
      81                 :            :  * x32 ABI).  Are there any cases the kernel needs to worry about?
      82                 :            :  */
      83                 :          3 : static void swap_words_64(void *a, void *b, size_t n)
      84                 :            : {
      85                 :            :         do {
      86                 :            : #ifdef CONFIG_64BIT
      87                 :            :                 u64 t = *(u64 *)(a + (n -= 8));
      88                 :            :                 *(u64 *)(a + n) = *(u64 *)(b + n);
      89                 :            :                 *(u64 *)(b + n) = t;
      90                 :            : #else
      91                 :            :                 /* Use two 32-bit transfers to avoid base+index+4 addressing */
      92                 :          3 :                 u32 t = *(u32 *)(a + (n -= 4));
      93                 :          3 :                 *(u32 *)(a + n) = *(u32 *)(b + n);
      94                 :          3 :                 *(u32 *)(b + n) = t;
      95                 :            : 
      96                 :          3 :                 t = *(u32 *)(a + (n -= 4));
      97                 :          3 :                 *(u32 *)(a + n) = *(u32 *)(b + n);
      98                 :          3 :                 *(u32 *)(b + n) = t;
      99                 :            : #endif
     100                 :          3 :         } while (n);
     101                 :          3 : }
     102                 :            : 
     103                 :            : /**
     104                 :            :  * swap_bytes - swap two elements a byte at a time
     105                 :            :  * @a: pointer to the first element to swap
     106                 :            :  * @b: pointer to the second element to swap
     107                 :            :  * @n: element size
     108                 :            :  *
     109                 :            :  * This is the fallback if alignment doesn't allow using larger chunks.
     110                 :            :  */
     111                 :            : static void swap_bytes(void *a, void *b, size_t n)
     112                 :            : {
     113                 :            :         do {
     114                 :          0 :                 char t = ((char *)a)[--n];
     115                 :          0 :                 ((char *)a)[n] = ((char *)b)[n];
     116                 :          0 :                 ((char *)b)[n] = t;
     117                 :          0 :         } while (n);
     118                 :            : }
     119                 :            : 
     120                 :            : typedef void (*swap_func_t)(void *a, void *b, int size);
     121                 :            : 
     122                 :            : /*
     123                 :            :  * The values are arbitrary as long as they can't be confused with
     124                 :            :  * a pointer, but small integers make for the smallest compare
     125                 :            :  * instructions.
     126                 :            :  */
     127                 :            : #define SWAP_WORDS_64 (swap_func_t)0
     128                 :            : #define SWAP_WORDS_32 (swap_func_t)1
     129                 :            : #define SWAP_BYTES    (swap_func_t)2
     130                 :            : 
     131                 :            : /*
     132                 :            :  * The function pointer is last to make tail calls most efficient if the
     133                 :            :  * compiler decides not to inline this function.
     134                 :            :  */
     135                 :          3 : static void do_swap(void *a, void *b, size_t size, swap_func_t swap_func)
     136                 :            : {
     137                 :          3 :         if (swap_func == SWAP_WORDS_64)
     138                 :          3 :                 swap_words_64(a, b, size);
     139                 :          3 :         else if (swap_func == SWAP_WORDS_32)
     140                 :            :                 swap_words_32(a, b, size);
     141                 :          0 :         else if (swap_func == SWAP_BYTES)
     142                 :            :                 swap_bytes(a, b, size);
     143                 :            :         else
     144                 :          0 :                 swap_func(a, b, (int)size);
     145                 :          3 : }
     146                 :            : 
     147                 :            : typedef int (*cmp_func_t)(const void *, const void *);
     148                 :            : typedef int (*cmp_r_func_t)(const void *, const void *, const void *);
     149                 :            : #define _CMP_WRAPPER ((cmp_r_func_t)0L)
     150                 :            : 
     151                 :            : static int do_cmp(const void *a, const void *b,
     152                 :            :                   cmp_r_func_t cmp, const void *priv)
     153                 :            : {
     154                 :          3 :         if (cmp == _CMP_WRAPPER)
     155                 :          3 :                 return ((cmp_func_t)(priv))(a, b);
     156                 :          0 :         return cmp(a, b, priv);
     157                 :            : }
     158                 :            : 
     159                 :            : /**
     160                 :            :  * parent - given the offset of the child, find the offset of the parent.
     161                 :            :  * @i: the offset of the heap element whose parent is sought.  Non-zero.
     162                 :            :  * @lsbit: a precomputed 1-bit mask, equal to "size & -size"
     163                 :            :  * @size: size of each element
     164                 :            :  *
     165                 :            :  * In terms of array indexes, the parent of element j = @i/@size is simply
     166                 :            :  * (j-1)/2.  But when working in byte offsets, we can't use implicit
     167                 :            :  * truncation of integer divides.
     168                 :            :  *
     169                 :            :  * Fortunately, we only need one bit of the quotient, not the full divide.
     170                 :            :  * @size has a least significant bit.  That bit will be clear if @i is
     171                 :            :  * an even multiple of @size, and set if it's an odd multiple.
     172                 :            :  *
     173                 :            :  * Logically, we're doing "if (i & lsbit) i -= size;", but since the
     174                 :            :  * branch is unpredictable, it's done with a bit of clever branch-free
     175                 :            :  * code instead.
     176                 :            :  */
     177                 :            : __attribute_const__ __always_inline
     178                 :            : static size_t parent(size_t i, unsigned int lsbit, size_t size)
     179                 :            : {
     180                 :          3 :         i -= size;
     181                 :          3 :         i -= size & -(i & lsbit);
     182                 :          3 :         return i / 2;
     183                 :            : }
     184                 :            : 
     185                 :            : /**
     186                 :            :  * sort_r - sort an array of elements
     187                 :            :  * @base: pointer to data to sort
     188                 :            :  * @num: number of elements
     189                 :            :  * @size: size of each element
     190                 :            :  * @cmp_func: pointer to comparison function
     191                 :            :  * @swap_func: pointer to swap function or NULL
     192                 :            :  * @priv: third argument passed to comparison function
     193                 :            :  *
     194                 :            :  * This function does a heapsort on the given array.  You may provide
     195                 :            :  * a swap_func function if you need to do something more than a memory
     196                 :            :  * copy (e.g. fix up pointers or auxiliary data), but the built-in swap
     197                 :            :  * avoids a slow retpoline and so is significantly faster.
     198                 :            :  *
     199                 :            :  * Sorting time is O(n log n) both on average and worst-case. While
     200                 :            :  * quicksort is slightly faster on average, it suffers from exploitable
     201                 :            :  * O(n*n) worst-case behavior and extra memory requirements that make
     202                 :            :  * it less suitable for kernel use.
     203                 :            :  */
     204                 :          3 : void sort_r(void *base, size_t num, size_t size,
     205                 :            :             int (*cmp_func)(const void *, const void *, const void *),
     206                 :            :             void (*swap_func)(void *, void *, int size),
     207                 :            :             const void *priv)
     208                 :            : {
     209                 :            :         /* pre-scale counters for performance */
     210                 :          3 :         size_t n = num * size, a = (num/2) * size;
     211                 :          3 :         const unsigned int lsbit = size & -size;  /* Used to find parent */
     212                 :            : 
     213                 :          3 :         if (!a)         /* num < 2 || size == 0 */
     214                 :          3 :                 return;
     215                 :            : 
     216                 :          3 :         if (!swap_func) {
     217                 :          3 :                 if (is_aligned(base, size, 8))
     218                 :            :                         swap_func = SWAP_WORDS_64;
     219                 :          3 :                 else if (is_aligned(base, size, 4))
     220                 :            :                         swap_func = SWAP_WORDS_32;
     221                 :            :                 else
     222                 :            :                         swap_func = SWAP_BYTES;
     223                 :            :         }
     224                 :            : 
     225                 :            :         /*
     226                 :            :          * Loop invariants:
     227                 :            :          * 1. elements [a,n) satisfy the heap property (compare greater than
     228                 :            :          *    all of their children),
     229                 :            :          * 2. elements [n,num*size) are sorted, and
     230                 :            :          * 3. a <= b <= c <= d <= n (whenever they are valid).
     231                 :            :          */
     232                 :            :         for (;;) {
     233                 :            :                 size_t b, c, d;
     234                 :            : 
     235                 :          3 :                 if (a)                  /* Building heap: sift down --a */
     236                 :          3 :                         a -= size;
     237                 :          3 :                 else if (n -= size)     /* Sorting: Extract root to --n */
     238                 :          3 :                         do_swap(base, base + n, size, swap_func);
     239                 :            :                 else                    /* Sort complete */
     240                 :            :                         break;
     241                 :            : 
     242                 :            :                 /*
     243                 :            :                  * Sift element at "a" down into heap.  This is the
     244                 :            :                  * "bottom-up" variant, which significantly reduces
     245                 :            :                  * calls to cmp_func(): we find the sift-down path all
     246                 :            :                  * the way to the leaves (one compare per level), then
     247                 :            :                  * backtrack to find where to insert the target element.
     248                 :            :                  *
     249                 :            :                  * Because elements tend to sift down close to the leaves,
     250                 :            :                  * this uses fewer compares than doing two per level
     251                 :            :                  * on the way down.  (A bit more than half as many on
     252                 :            :                  * average, 3/4 worst-case.)
     253                 :            :                  */
     254                 :          3 :                 for (b = a; c = 2*b + size, (d = c + size) < n;)
     255                 :          3 :                         b = do_cmp(base + c, base + d, cmp_func, priv) >= 0 ? c : d;
     256                 :          3 :                 if (d == n)     /* Special case last leaf with no sibling */
     257                 :          3 :                         b = c;
     258                 :            : 
     259                 :            :                 /* Now backtrack from "b" to the correct location for "a" */
     260                 :          3 :                 while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0)
     261                 :            :                         b = parent(b, lsbit, size);
     262                 :          3 :                 c = b;                  /* Where "a" belongs */
     263                 :          3 :                 while (b != a) {        /* Shift it into place */
     264                 :            :                         b = parent(b, lsbit, size);
     265                 :          3 :                         do_swap(base + b, base + c, size, swap_func);
     266                 :            :                 }
     267                 :            :         }
     268                 :            : }
     269                 :            : EXPORT_SYMBOL(sort_r);
     270                 :            : 
     271                 :          3 : void sort(void *base, size_t num, size_t size,
     272                 :            :           int (*cmp_func)(const void *, const void *),
     273                 :            :           void (*swap_func)(void *, void *, int size))
     274                 :            : {
     275                 :          3 :         return sort_r(base, num, size, _CMP_WRAPPER, swap_func, cmp_func);
     276                 :            : }
     277                 :            : EXPORT_SYMBOL(sort);