lib: add find_nth{,_and,_andnot}_bit()

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 <[e-mail]>

include/linux/bitops.h

···
 }
 
 /**
+ * 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
  * @addr: the address to start counting from

include/linux/find.h

···
 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);
···
 	return _find_first_bit(addr, 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
 /**

lib/find_bit.c

···
 	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.
···
 }
 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,