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Subject[PATCH v3 3/6] lib: add find_nth{,_and,_andnot}_bit()
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Kernel lacks for a function that searches for Nth bit in a bitmap.
Usually people do it like this:
for_each_set_bit(bit, mask, size)
if (n-- == 0)
return bit;

We can do it more efficiently, if we:
1. find a word containing Nth bit, using hweight(); and
2. find the bit, using a helper fns(), that works similarly to
__ffs() and ffz().

fns() is implemented as a simple loop. For x86_64, there's PDEP instruction
to do that: ret = clz(pdep(1 << idx, num)). However, for large bitmaps the
most of improvement comes from using hweight(), so I kept fns() simple.

New find_nth_bit() is ~70 times faster on x86_64/kvm in find_bit benchmark:
find_nth_bit: 7154190 ns, 16411 iterations
for_each_bit: 505493126 ns, 16315 iterations

With all that, a family of 3 new functions is added, and used where
appropriate in the following patches.

Signed-off-by: Yury Norov <yury.norov@gmail.com>
---
Comparing to v2, it adds a path that allows quit earlier if the
condition can't be met:
for (idx = 0; (idx + 1) * BITS_PER_LONG <= sz; idx++) {
+ if (idx * BITS_PER_LONG + nr >= sz)
+ goto out;
...

include/linux/bitops.h | 19 ++++++++++
include/linux/find.h | 86 ++++++++++++++++++++++++++++++++++++++++++
lib/find_bit.c | 44 +++++++++++++++++++++
3 files changed, 149 insertions(+)

diff --git a/include/linux/bitops.h b/include/linux/bitops.h
index 3b89c64bcfd8..d7dd83fafeba 100644
--- a/include/linux/bitops.h
+++ b/include/linux/bitops.h
@@ -247,6 +247,25 @@ static inline unsigned long __ffs64(u64 word)
return __ffs((unsigned long)word);
}

+/**
+ * fns - find N'th set bit in a word
+ * @word: The word to search
+ * @n: Bit to find
+ */
+static inline unsigned long fns(unsigned long word, unsigned int n)
+{
+ unsigned int bit;
+
+ while (word) {
+ bit = __ffs(word);
+ if (n-- == 0)
+ return bit;
+ __clear_bit(bit, &word);
+ }
+
+ return BITS_PER_LONG;
+}
+
/**
* assign_bit - Assign value to a bit in memory
* @nr: the bit to set
diff --git a/include/linux/find.h b/include/linux/find.h
index dead6f53a97b..b100944daba0 100644
--- a/include/linux/find.h
+++ b/include/linux/find.h
@@ -15,6 +15,11 @@ unsigned long _find_next_and_bit(const unsigned long *addr1, const unsigned long
unsigned long _find_next_zero_bit(const unsigned long *addr, unsigned long nbits,
unsigned long start);
extern unsigned long _find_first_bit(const unsigned long *addr, unsigned long size);
+unsigned long __find_nth_bit(const unsigned long *addr, unsigned long size, unsigned long n);
+unsigned long __find_nth_and_bit(const unsigned long *addr1, const unsigned long *addr2,
+ unsigned long size, unsigned long n);
+unsigned long __find_nth_andnot_bit(const unsigned long *addr1, const unsigned long *addr2,
+ unsigned long size, unsigned long n);
extern unsigned long _find_first_and_bit(const unsigned long *addr1,
const unsigned long *addr2, unsigned long size);
extern unsigned long _find_first_zero_bit(const unsigned long *addr, unsigned long size);
@@ -136,6 +141,87 @@ unsigned long find_first_bit(const unsigned long *addr, unsigned long size)
}
#endif

+/**
+ * find_nth_bit - find N'th set bit in a memory region
+ * @addr: The address to start the search at
+ * @size: The maximum number of bits to search
+ * @n: The number of set bit, which position is needed, counting from 0
+ *
+ * The following is semantically equivalent:
+ * idx = find_nth_bit(addr, size, 0);
+ * idx = find_first_bit(addr, size);
+ *
+ * Returns the bit number of the N'th set bit.
+ * If no such, returns @size.
+ */
+static inline
+unsigned long find_nth_bit(const unsigned long *addr, unsigned long size, unsigned long n)
+{
+ if (n >= size)
+ return size;
+
+ if (small_const_nbits(size)) {
+ unsigned long val = *addr & GENMASK(size - 1, 0);
+
+ return val ? fns(val, n) : size;
+ }
+
+ return __find_nth_bit(addr, size, n);
+}
+
+/**
+ * find_nth_and_bit - find N'th set bit in 2 memory regions
+ * @addr1: The 1st address to start the search at
+ * @addr2: The 2nd address to start the search at
+ * @size: The maximum number of bits to search
+ * @n: The number of set bit, which position is needed, counting from 0
+ *
+ * Returns the bit number of the N'th set bit.
+ * If no such, returns @size.
+ */
+static inline
+unsigned long find_nth_and_bit(const unsigned long *addr1, const unsigned long *addr2,
+ unsigned long size, unsigned long n)
+{
+ if (n >= size)
+ return size;
+
+ if (small_const_nbits(size)) {
+ unsigned long val = *addr1 & *addr2 & GENMASK(size - 1, 0);
+
+ return val ? fns(val, n) : size;
+ }
+
+ return __find_nth_and_bit(addr1, addr2, size, n);
+}
+
+/**
+ * find_nth_andnot_bit - find N'th set bit in 2 memory regions,
+ * flipping bits in 2nd region
+ * @addr1: The 1st address to start the search at
+ * @addr2: The 2nd address to start the search at
+ * @size: The maximum number of bits to search
+ * @n: The number of set bit, which position is needed, counting from 0
+ *
+ * Returns the bit number of the N'th set bit.
+ * If no such, returns @size.
+ */
+static inline
+unsigned long find_nth_andnot_bit(const unsigned long *addr1, const unsigned long *addr2,
+ unsigned long size, unsigned long n)
+{
+ if (n >= size)
+ return size;
+
+ if (small_const_nbits(size)) {
+ unsigned long val = *addr1 & (~*addr2) & GENMASK(size - 1, 0);
+
+ return val ? fns(val, n) : size;
+ }
+
+ return __find_nth_andnot_bit(addr1, addr2, size, n);
+}
+
#ifndef find_first_and_bit
/**
* find_first_and_bit - find the first set bit in both memory regions
diff --git a/lib/find_bit.c b/lib/find_bit.c
index 8707b4ef3e5e..ae2a59b59bfe 100644
--- a/lib/find_bit.c
+++ b/lib/find_bit.c
@@ -68,6 +68,30 @@ out: \
sz; \
})

+#define FIND_NTH_BIT(FETCH, size, num) \
+({ \
+ unsigned long sz = (size), nr = (num), idx, w, tmp; \
+ \
+ for (idx = 0; (idx + 1) * BITS_PER_LONG <= sz; idx++) { \
+ if (idx * BITS_PER_LONG + nr >= sz) \
+ goto out; \
+ \
+ tmp = (FETCH); \
+ w = hweight_long(tmp); \
+ if (w > nr) \
+ goto found; \
+ \
+ nr -= w; \
+ } \
+ \
+ if (sz % BITS_PER_LONG) \
+ tmp = (FETCH) & BITMAP_LAST_WORD_MASK(sz); \
+found: \
+ sz = min(idx * BITS_PER_LONG + fns(tmp, nr), sz); \
+out: \
+ sz; \
+})
+
#ifndef find_first_bit
/*
* Find the first set bit in a memory region.
@@ -111,6 +135,26 @@ unsigned long _find_next_bit(const unsigned long *addr, unsigned long nbits, uns
EXPORT_SYMBOL(_find_next_bit);
#endif

+unsigned long __find_nth_bit(const unsigned long *addr, unsigned long size, unsigned long n)
+{
+ return FIND_NTH_BIT(addr[idx], size, n);
+}
+EXPORT_SYMBOL(__find_nth_bit);
+
+unsigned long __find_nth_and_bit(const unsigned long *addr1, const unsigned long *addr2,
+ unsigned long size, unsigned long n)
+{
+ return FIND_NTH_BIT(addr1[idx] & addr2[idx], size, n);
+}
+EXPORT_SYMBOL(__find_nth_and_bit);
+
+unsigned long __find_nth_andnot_bit(const unsigned long *addr1, const unsigned long *addr2,
+ unsigned long size, unsigned long n)
+{
+ return FIND_NTH_BIT(addr1[idx] & ~addr2[idx], size, n);
+}
+EXPORT_SYMBOL(__find_nth_andnot_bit);
+
#ifndef find_next_and_bit
unsigned long _find_next_and_bit(const unsigned long *addr1, const unsigned long *addr2,
unsigned long nbits, unsigned long start)
--
2.34.1
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