// SPDX-License-Identifier: GPL-2.0 | |

/* | |

* A fast, small, non-recursive O(n log n) sort for the Linux kernel | |

* | |

* This performs n*log2(n) + 0.37*n + o(n) comparisons on average, | |

* and 1.5*n*log2(n) + O(n) in the (very contrived) worst case. | |

* | |

* Glibc qsort() manages n*log2(n) - 1.26*n for random inputs (1.63*n | |

* better) at the expense of stack usage and much larger code to avoid | |

* quicksort's O(n^2) worst case. | |

*/ | |

#define pr_fmt(fmt) KBUILD_MODNAME ": " fmt | |

#include <linux/types.h> | |

#include <linux/export.h> | |

#include <linux/sort.h> | |

/** | |

* is_aligned - is this pointer & size okay for word-wide copying? | |

* @base: pointer to data | |

* @size: size of each element | |

* @align: required alignment (typically 4 or 8) | |

* | |

* Returns true if elements can be copied using word loads and stores. | |

* The size must be a multiple of the alignment, and the base address must | |

* be if we do not have CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS. | |

* | |

* For some reason, gcc doesn't know to optimize "if (a & mask || b & mask)" | |

* to "if ((a | b) & mask)", so we do that by hand. | |

*/ | |

__attribute_const__ __always_inline | |

static bool is_aligned(const void *base, size_t size, unsigned char align) | |

{ | |

unsigned char lsbits = (unsigned char)size; | |

(void)base; | |

#ifndef CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS | |

lsbits |= (unsigned char)(uintptr_t)base; | |

#endif | |

return (lsbits & (align - 1)) == 0; | |

} | |

/** | |

* swap_words_32 - swap two elements in 32-bit chunks | |

* @a: pointer to the first element to swap | |

* @b: pointer to the second element to swap | |

* @n: element size (must be a multiple of 4) | |

* | |

* Exchange the two objects in memory. This exploits base+index addressing, | |

* which basically all CPUs have, to minimize loop overhead computations. | |

* | |

* For some reason, on x86 gcc 7.3.0 adds a redundant test of n at the | |

* bottom of the loop, even though the zero flag is stil valid from the | |

* subtract (since the intervening mov instructions don't alter the flags). | |

* Gcc 8.1.0 doesn't have that problem. | |

*/ | |

static void swap_words_32(void *a, void *b, size_t n) | |

{ | |

do { | |

u32 t = *(u32 *)(a + (n -= 4)); | |

*(u32 *)(a + n) = *(u32 *)(b + n); | |

*(u32 *)(b + n) = t; | |

} while (n); | |

} | |

/** | |

* swap_words_64 - swap two elements in 64-bit chunks | |

* @a: pointer to the first element to swap | |

* @b: pointer to the second element to swap | |

* @n: element size (must be a multiple of 8) | |

* | |

* Exchange the two objects in memory. This exploits base+index | |

* addressing, which basically all CPUs have, to minimize loop overhead | |

* computations. | |

* | |

* We'd like to use 64-bit loads if possible. If they're not, emulating | |

* one requires base+index+4 addressing which x86 has but most other | |

* processors do not. If CONFIG_64BIT, we definitely have 64-bit loads, | |

* but it's possible to have 64-bit loads without 64-bit pointers (e.g. | |

* x32 ABI). Are there any cases the kernel needs to worry about? | |

*/ | |

static void swap_words_64(void *a, void *b, size_t n) | |

{ | |

do { | |

#ifdef CONFIG_64BIT | |

u64 t = *(u64 *)(a + (n -= 8)); | |

*(u64 *)(a + n) = *(u64 *)(b + n); | |

*(u64 *)(b + n) = t; | |

#else | |

/* Use two 32-bit transfers to avoid base+index+4 addressing */ | |

u32 t = *(u32 *)(a + (n -= 4)); | |

*(u32 *)(a + n) = *(u32 *)(b + n); | |

*(u32 *)(b + n) = t; | |

t = *(u32 *)(a + (n -= 4)); | |

*(u32 *)(a + n) = *(u32 *)(b + n); | |

*(u32 *)(b + n) = t; | |

#endif | |

} while (n); | |

} | |

/** | |

* swap_bytes - swap two elements a byte at a time | |

* @a: pointer to the first element to swap | |

* @b: pointer to the second element to swap | |

* @n: element size | |

* | |

* This is the fallback if alignment doesn't allow using larger chunks. | |

*/ | |

static void swap_bytes(void *a, void *b, size_t n) | |

{ | |

do { | |

char t = ((char *)a)[--n]; | |

((char *)a)[n] = ((char *)b)[n]; | |

((char *)b)[n] = t; | |

} while (n); | |

} | |

typedef void (*swap_func_t)(void *a, void *b, int size); | |

/* | |

* The values are arbitrary as long as they can't be confused with | |

* a pointer, but small integers make for the smallest compare | |

* instructions. | |

*/ | |

#define SWAP_WORDS_64 (swap_func_t)0 | |

#define SWAP_WORDS_32 (swap_func_t)1 | |

#define SWAP_BYTES (swap_func_t)2 | |

/* | |

* The function pointer is last to make tail calls most efficient if the | |

* compiler decides not to inline this function. | |

*/ | |

static void do_swap(void *a, void *b, size_t size, swap_func_t swap_func) | |

{ | |

if (swap_func == SWAP_WORDS_64) | |

swap_words_64(a, b, size); | |

else if (swap_func == SWAP_WORDS_32) | |

swap_words_32(a, b, size); | |

else if (swap_func == SWAP_BYTES) | |

swap_bytes(a, b, size); | |

else | |

swap_func(a, b, (int)size); | |

} | |

/** | |

* parent - given the offset of the child, find the offset of the parent. | |

* @i: the offset of the heap element whose parent is sought. Non-zero. | |

* @lsbit: a precomputed 1-bit mask, equal to "size & -size" | |

* @size: size of each element | |

* | |

* In terms of array indexes, the parent of element j = @i/@size is simply | |

* (j-1)/2. But when working in byte offsets, we can't use implicit | |

* truncation of integer divides. | |

* | |

* Fortunately, we only need one bit of the quotient, not the full divide. | |

* @size has a least significant bit. That bit will be clear if @i is | |

* an even multiple of @size, and set if it's an odd multiple. | |

* | |

* Logically, we're doing "if (i & lsbit) i -= size;", but since the | |

* branch is unpredictable, it's done with a bit of clever branch-free | |

* code instead. | |

*/ | |

__attribute_const__ __always_inline | |

static size_t parent(size_t i, unsigned int lsbit, size_t size) | |

{ | |

i -= size; | |

i -= size & -(i & lsbit); | |

return i / 2; | |

} | |

/** | |

* sort - sort an array of elements | |

* @base: pointer to data to sort | |

* @num: number of elements | |

* @size: size of each element | |

* @cmp_func: pointer to comparison function | |

* @swap_func: pointer to swap function or NULL | |

* | |

* This function does a heapsort on the given array. You may provide | |

* a swap_func function if you need to do something more than a memory | |

* copy (e.g. fix up pointers or auxiliary data), but the built-in swap | |

* avoids a slow retpoline and so is significantly faster. | |

* | |

* Sorting time is O(n log n) both on average and worst-case. While | |

* quicksort is slightly faster on average, it suffers from exploitable | |

* O(n*n) worst-case behavior and extra memory requirements that make | |

* it less suitable for kernel use. | |

*/ | |

void sort(void *base, size_t num, size_t size, | |

int (*cmp_func)(const void *, const void *), | |

void (*swap_func)(void *, void *, int size)) | |

{ | |

/* pre-scale counters for performance */ | |

size_t n = num * size, a = (num/2) * size; | |

const unsigned int lsbit = size & -size; /* Used to find parent */ | |

if (!a) /* num < 2 || size == 0 */ | |

return; | |

if (!swap_func) { | |

if (is_aligned(base, size, 8)) | |

swap_func = SWAP_WORDS_64; | |

else if (is_aligned(base, size, 4)) | |

swap_func = SWAP_WORDS_32; | |

else | |

swap_func = SWAP_BYTES; | |

} | |

/* | |

* Loop invariants: | |

* 1. elements [a,n) satisfy the heap property (compare greater than | |

* all of their children), | |

* 2. elements [n,num*size) are sorted, and | |

* 3. a <= b <= c <= d <= n (whenever they are valid). | |

*/ | |

for (;;) { | |

size_t b, c, d; | |

if (a) /* Building heap: sift down --a */ | |

a -= size; | |

else if (n -= size) /* Sorting: Extract root to --n */ | |

do_swap(base, base + n, size, swap_func); | |

else /* Sort complete */ | |

break; | |

/* | |

* Sift element at "a" down into heap. This is the | |

* "bottom-up" variant, which significantly reduces | |

* calls to cmp_func(): we find the sift-down path all | |

* the way to the leaves (one compare per level), then | |

* backtrack to find where to insert the target element. | |

* | |

* Because elements tend to sift down close to the leaves, | |

* this uses fewer compares than doing two per level | |

* on the way down. (A bit more than half as many on | |

* average, 3/4 worst-case.) | |

*/ | |

for (b = a; c = 2*b + size, (d = c + size) < n;) | |

b = cmp_func(base + c, base + d) >= 0 ? c : d; | |

if (d == n) /* Special case last leaf with no sibling */ | |

b = c; | |

/* Now backtrack from "b" to the correct location for "a" */ | |

while (b != a && cmp_func(base + a, base + b) >= 0) | |

b = parent(b, lsbit, size); | |

c = b; /* Where "a" belongs */ | |

while (b != a) { /* Shift it into place */ | |

b = parent(b, lsbit, size); | |

do_swap(base + b, base + c, size, swap_func); | |

} | |

} | |

} | |

EXPORT_SYMBOL(sort); |