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/* SPDX-License-Identifier: GPL-2.0 */
#ifndef _EYTZINGER_H
#define _EYTZINGER_H
#include <linux/bitops.h>
#include <linux/log2.h>
#ifdef EYTZINGER_DEBUG
#define EYTZINGER_BUG_ON(cond) BUG_ON(cond)
#else
#define EYTZINGER_BUG_ON(cond)
#endif
/*
* Traversal for trees in eytzinger layout - a full binary tree layed out in an
* array.
*
* Consider using an eytzinger tree any time you would otherwise be doing binary
* search over an array. Binary search is a worst case scenario for branch
* prediction and prefetching, but in an eytzinger tree every node's children
* are adjacent in memory, thus we can prefetch children before knowing the
* result of the comparison, assuming multiple nodes fit on a cacheline.
*
* Two variants are provided, for one based indexing and zero based indexing.
*
* Zero based indexing is more convenient, but one based indexing has better
* alignment and thus better performance because each new level of the tree
* starts at a power of two, and thus if element 0 was cacheline aligned, each
* new level will be as well.
*/
static inline unsigned eytzinger1_child(unsigned i, unsigned child)
{
EYTZINGER_BUG_ON(child > 1);
return (i << 1) + child;
}
static inline unsigned eytzinger1_left_child(unsigned i)
{
return eytzinger1_child(i, 0);
}
static inline unsigned eytzinger1_right_child(unsigned i)
{
return eytzinger1_child(i, 1);
}
static inline unsigned eytzinger1_first(unsigned size)
{
return size ? rounddown_pow_of_two(size) : 0;
}
static inline unsigned eytzinger1_last(unsigned size)
{
return rounddown_pow_of_two(size + 1) - 1;
}
/*
* eytzinger1_next() and eytzinger1_prev() have the nice properties that
*
* eytzinger1_next(0) == eytzinger1_first())
* eytzinger1_prev(0) == eytzinger1_last())
*
* eytzinger1_prev(eytzinger1_first()) == 0
* eytzinger1_next(eytzinger1_last()) == 0
*/
static inline unsigned eytzinger1_next(unsigned i, unsigned size)
{
EYTZINGER_BUG_ON(i > size);
if (eytzinger1_right_child(i) <= size) {
i = eytzinger1_right_child(i);
i <<= __fls(size + 1) - __fls(i);
i >>= i > size;
} else {
i >>= ffz(i) + 1;
}
return i;
}
static inline unsigned eytzinger1_prev(unsigned i, unsigned size)
{
EYTZINGER_BUG_ON(i > size);
if (eytzinger1_left_child(i) <= size) {
i = eytzinger1_left_child(i) + 1;
i <<= __fls(size + 1) - __fls(i);
i -= 1;
i >>= i > size;
} else {
i >>= __ffs(i) + 1;
}
return i;
}
static inline unsigned eytzinger1_extra(unsigned size)
{
return size
? (size + 1 - rounddown_pow_of_two(size)) << 1
: 0;
}
static inline unsigned __eytzinger1_to_inorder(unsigned i, unsigned size,
unsigned extra)
{
unsigned b = __fls(i);
unsigned shift = __fls(size) - b;
int s;
EYTZINGER_BUG_ON(!i || i > size);
i ^= 1U << b;
i <<= 1;
i |= 1;
i <<= shift;
/*
* sign bit trick:
*
* if (i > extra)
* i -= (i - extra) >> 1;
*/
s = extra - i;
i += (s >> 1) & (s >> 31);
return i;
}
static inline unsigned __inorder_to_eytzinger1(unsigned i, unsigned size,
unsigned extra)
{
unsigned shift;
int s;
EYTZINGER_BUG_ON(!i || i > size);
/*
* sign bit trick:
*
* if (i > extra)
* i += i - extra;
*/
s = extra - i;
i -= s & (s >> 31);
shift = __ffs(i);
i >>= shift + 1;
i |= 1U << (__fls(size) - shift);
return i;
}
static inline unsigned eytzinger1_to_inorder(unsigned i, unsigned size)
{
return __eytzinger1_to_inorder(i, size, eytzinger1_extra(size));
}
static inline unsigned inorder_to_eytzinger1(unsigned i, unsigned size)
{
return __inorder_to_eytzinger1(i, size, eytzinger1_extra(size));
}
#define eytzinger1_for_each(_i, _size) \
for (unsigned (_i) = eytzinger1_first((_size)); \
(_i) != 0; \
(_i) = eytzinger1_next((_i), (_size)))
/* Zero based indexing version: */
static inline unsigned eytzinger0_child(unsigned i, unsigned child)
{
EYTZINGER_BUG_ON(child > 1);
return (i << 1) + 1 + child;
}
static inline unsigned eytzinger0_left_child(unsigned i)
{
return eytzinger0_child(i, 0);
}
static inline unsigned eytzinger0_right_child(unsigned i)
{
return eytzinger0_child(i, 1);
}
static inline unsigned eytzinger0_first(unsigned size)
{
return eytzinger1_first(size) - 1;
}
static inline unsigned eytzinger0_last(unsigned size)
{
return eytzinger1_last(size) - 1;
}
static inline unsigned eytzinger0_next(unsigned i, unsigned size)
{
return eytzinger1_next(i + 1, size) - 1;
}
static inline unsigned eytzinger0_prev(unsigned i, unsigned size)
{
return eytzinger1_prev(i + 1, size) - 1;
}
static inline unsigned eytzinger0_extra(unsigned size)
{
return eytzinger1_extra(size);
}
static inline unsigned __eytzinger0_to_inorder(unsigned i, unsigned size,
unsigned extra)
{
return __eytzinger1_to_inorder(i + 1, size, extra) - 1;
}
static inline unsigned __inorder_to_eytzinger0(unsigned i, unsigned size,
unsigned extra)
{
return __inorder_to_eytzinger1(i + 1, size, extra) - 1;
}
static inline unsigned eytzinger0_to_inorder(unsigned i, unsigned size)
{
return __eytzinger0_to_inorder(i, size, eytzinger0_extra(size));
}
static inline unsigned inorder_to_eytzinger0(unsigned i, unsigned size)
{
return __inorder_to_eytzinger0(i, size, eytzinger0_extra(size));
}
#define eytzinger0_for_each(_i, _size) \
for (unsigned (_i) = eytzinger0_first((_size)); \
(_i) != -1; \
(_i) = eytzinger0_next((_i), (_size)))
/* return greatest node <= @search, or -1 if not found */
static inline int eytzinger0_find_le(void *base, size_t nr, size_t size,
cmp_func_t cmp, const void *search)
{
unsigned i, n = 0;
if (!nr)
return -1;
do {
i = n;
n = eytzinger0_child(i, cmp(base + i * size, search) <= 0);
} while (n < nr);
if (n & 1) {
/*
* @i was greater than @search, return previous node:
*
* if @i was leftmost/smallest element,
* eytzinger0_prev(eytzinger0_first())) returns -1, as expected
*/
return eytzinger0_prev(i, nr);
} else {
return i;
}
}
static inline int eytzinger0_find_gt(void *base, size_t nr, size_t size,
cmp_func_t cmp, const void *search)
{
ssize_t idx = eytzinger0_find_le(base, nr, size, cmp, search);
/*
* if eytitzinger0_find_le() returned -1 - no element was <= search - we
* want to return the first element; next/prev identities mean this work
* as expected
*
* similarly if find_le() returns last element, we should return -1;
* identities mean this all works out:
*/
return eytzinger0_next(idx, nr);
}
static inline int eytzinger0_find_ge(void *base, size_t nr, size_t size,
cmp_func_t cmp, const void *search)
{
ssize_t idx = eytzinger0_find_le(base, nr, size, cmp, search);
if (idx < nr && !cmp(base + idx * size, search))
return idx;
return eytzinger0_next(idx, nr);
}
#define eytzinger0_find(base, nr, size, _cmp, search) \
({ \
void *_base = (base); \
const void *_search = (search); \
size_t _nr = (nr); \
size_t _size = (size); \
size_t _i = 0; \
int _res; \
\
while (_i < _nr && \
(_res = _cmp(_search, _base + _i * _size))) \
_i = eytzinger0_child(_i, _res > 0); \
_i; \
})
void eytzinger0_sort_r(void *, size_t, size_t,
cmp_r_func_t, swap_r_func_t, const void *);
void eytzinger0_sort(void *, size_t, size_t, cmp_func_t, swap_func_t);
#endif /* _EYTZINGER_H */