Bit arrays

Data Structures in the Linux Kernel

Bit arrays and bit operations in the Linux kernel

Besides different linked and tree based data structures, the Linux kernel provides API for bit arrays or bitmap. Bit arrays are heavily used in the Linux kernel and following source code files contain common API for work with such structures:

Besides these two files, there is also architecture-specific header file which provides optimized bit operations for certain architecture. We consider x86_64 architecture, so in our case it will be:

header file. As I just wrote above, the bitmap is heavily used in the Linux kernel. For example a bit array is used to store set of online/offline processors for systems which support hot-plug cpu (more about this you can read in the cpumasks part), a bit array stores set of allocated irqs during initialization of the Linux kernel and etc.

So, the main goal of this part is to see how bit arrays are implemented in the Linux kernel. Let's start.

Declaration of bit array

Before we will look on API for bitmaps manipulation, we must know how to declare it in the Linux kernel. There are two common method to declare own bit array. The first simple way to declare a bit array is to array of unsigned long. For example:

unsigned long my_bitmap[8]

The second way is to use the DECLARE_BITMAP macro which is defined in the include/linux/types.h header file:

#define DECLARE_BITMAP(name,bits) \
unsigned long name[BITS_TO_LONGS(bits)]

We can see that DECLARE_BITMAP macro takes two parameters:

  • name - name of bitmap;

  • bits - amount of bits in bitmap;

and just expands to the definition of unsigned long array with BITS_TO_LONGS(bits) elements, where the BITS_TO_LONGS macro converts a given number of bits to number of longs or in other words it calculates how many 8 byte elements in bits:

#define BITS_PER_BYTE 8
#define DIV_ROUND_UP(n,d) (((n) + (d) - 1) / (d))
#define BITS_TO_LONGS(nr) DIV_ROUND_UP(nr, BITS_PER_BYTE * sizeof(long))

So, for example DECLARE_BITMAP(my_bitmap, 64) will produce:

>>> (((64) + (64) - 1) / (64))
1

and:

unsigned long my_bitmap[1];

After we are able to declare a bit array, we can start to use it.

Architecture-specific bit operations

We already saw above a couple of source code and header files which provide API for manipulation of bit arrays. The most important and widely used API of bit arrays is architecture-specific and located as we already know in the arch/x86/include/asm/bitops.h header file.

First of all let's look at the two most important functions:

  • set_bit;

  • clear_bit.

I think that there is no need to explain what these function do. This is already must be clear from their name. Let's look on their implementation. If you will look into the arch/x86/include/asm/bitops.h header file, you will note that each of these functions represented by two variants: atomic and not. Before we will start to dive into implementations of these functions, first of all we must to know a little about atomic operations.

In simple words atomic operations guarantees that two or more operations will not be performed on the same data concurrently. The x86 architecture provides a set of atomic instructions, for example xchg instruction, cmpxchg instruction and etc. Besides atomic instructions, some of non-atomic instructions can be made atomic with the help of the lock instruction. It is enough to know about atomic operations for now, so we can begin to consider implementation of set_bit and clear_bit functions.

First of all, let's start to consider non-atomic variants of this function. Names of non-atomic set_bit and clear_bit starts from double underscore. As we already know, all of these functions are defined in the arch/x86/include/asm/bitops.h header file and the first function is __set_bit:

static inline void __set_bit(long nr, volatile unsigned long *addr)
{
asm volatile("bts %1,%0" : ADDR : "Ir" (nr) : "memory");
}

As we can see it takes two arguments:

  • nr - number of bit in a bit array.

  • addr - address of a bit array where we need to set bit.

Note that the addr parameter is defined with volatile keyword which tells to compiler that value maybe changed by the given address. The implementation of the __set_bit is pretty easy. As we can see, it just contains one line of inline assembler code. In our case we are using the bts instruction which selects a bit which is specified with the first operand (nr in our case) from the bit array, stores the value of the selected bit in the CF flags register and set this bit.

Note that we can see usage of the nr, but there is addr here. You already might guess that the secret is in ADDR. The ADDR is the macro which is defined in the same header code file and expands to the string which contains value of the given address and +m constraint:

#define ADDR BITOP_ADDR(addr)
#define BITOP_ADDR(x) "+m" (*(volatile long *) (x))

Besides the +m, we can see other constraints in the __set_bit function. Let's look on they and try to understand what do they mean:

  • +m - represents memory operand where + tells that the given operand will be input and output operand;

  • I - represents integer constant;

  • r - represents register operand

Besides these constraint, we also can see - the memory keyword which tells compiler that this code will change value in memory. That's all. Now let's look at the same function but at atomic variant. It looks more complex that its non-atomic variant:

static __always_inline void
set_bit(long nr, volatile unsigned long *addr)
{
if (IS_IMMEDIATE(nr)) {
asm volatile(LOCK_PREFIX "orb %1,%0"
: CONST_MASK_ADDR(nr, addr)
: "iq" ((u8)CONST_MASK(nr))
: "memory");
} else {
asm volatile(LOCK_PREFIX "bts %1,%0"
: BITOP_ADDR(addr) : "Ir" (nr) : "memory");
}
}

First of all note that this function takes the same set of parameters that __set_bit, but additionally marked with the __always_inline attribute. The __always_inline is macro which defined in the include/linux/compiler-gcc.h and just expands to the always_inline attribute:

#define __always_inline inline __attribute__((always_inline))

which means that this function will be always inlined to reduce size of the Linux kernel image. Now let's try to understand implementation of the set_bit function. First of all we check a given number of bit at the beginning of the set_bit function. The IS_IMMEDIATE macro defined in the same header file and expands to the call of the builtin gcc function:

#define IS_IMMEDIATE(nr) (__builtin_constant_p(nr))

The __builtin_constant_p builtin function returns 1 if the given parameter is known to be constant at compile-time and returns 0 in other case. We no need to use slow bts instruction to set bit if the given number of bit is known in compile time constant. We can just apply bitwise or for byte from the give address which contains given bit and masked number of bits where high bit is 1 and other is zero. In other case if the given number of bit is not known constant at compile-time, we do the same as we did in the __set_bit function. The CONST_MASK_ADDR macro:

#define CONST_MASK_ADDR(nr, addr) BITOP_ADDR((void *)(addr) + ((nr)>>3))

expands to the give address with offset to the byte which contains a given bit. For example we have address 0x1000 and the number of bit is 0x9. So, as 0x9 is one byte + one bit our address with be addr + 1:

>>> hex(0x1000 + (0x9 >> 3))
'0x1001'

The CONST_MASK macro represents our given number of bit as byte where high bit is 1 and other bits are 0:

#define CONST_MASK(nr) (1 << ((nr) & 7))
>>> bin(1 << (0x9 & 7))
'0b10'

In the end we just apply bitwise or for these values. So, for example if our address will be 0x4097 and we need to set 0x9 bit:

>>> bin(0x4097)
'0b100000010010111'
>>> bin((0x4097 >> 0x9) | (1 << (0x9 & 7)))
'0b100010'

the ninth bit will be set.

Note that all of these operations are marked with LOCK_PREFIX which is expands to the lock instruction which guarantees atomicity of this operation.

As we already know, besides the set_bit and __set_bit operations, the Linux kernel provides two inverse functions to clear bit in atomic and non-atomic context. They are clear_bit and __clear_bit. Both of these functions are defined in the same header file and takes the same set of arguments. But not only arguments are similar. Generally these functions are very similar on the set_bit and __set_bit. Let's look on the implementation of the non-atomic __clear_bit function:

static inline void __clear_bit(long nr, volatile unsigned long *addr)
{
asm volatile("btr %1,%0" : ADDR : "Ir" (nr));
}

Yes. As we see, it takes the same set of arguments and contains very similar block of inline assembler. It just uses the btr instruction instead of bts. As we can understand form the function's name, it clears a given bit by the given address. The btr instruction acts like bts. This instruction also selects a given bit which is specified in the first operand, stores its value in the CF flag register and clears this bit in the given bit array which is specified with second operand.

The atomic variant of the __clear_bit is clear_bit:

static __always_inline void
clear_bit(long nr, volatile unsigned long *addr)
{
if (IS_IMMEDIATE(nr)) {
asm volatile(LOCK_PREFIX "andb %1,%0"
: CONST_MASK_ADDR(nr, addr)
: "iq" ((u8)~CONST_MASK(nr)));
} else {
asm volatile(LOCK_PREFIX "btr %1,%0"
: BITOP_ADDR(addr)
: "Ir" (nr));
}
}

and as we can see it is very similar on set_bit and just contains two differences. The first difference it uses btr instruction to clear bit when the set_bit uses bts instruction to set bit. The second difference it uses negated mask and and instruction to clear bit in the given byte when the set_bit uses or instruction.

That's all. Now we can set and clear bit in any bit array and and we can go to other operations on bitmasks.

Most widely used operations on a bit arrays are set and clear bit in a bit array in the Linux kernel. But besides this operations it is useful to do additional operations on a bit array. Yet another widely used operation in the Linux kernel - is to know is a given bit set or not in a bit array. We can achieve this with the help of the test_bit macro. This macro is defined in the arch/x86/include/asm/bitops.h header file and expands to the call of the constant_test_bit or variable_test_bit depends on bit number:

#define test_bit(nr, addr) \
(__builtin_constant_p((nr)) \
? constant_test_bit((nr), (addr)) \
: variable_test_bit((nr), (addr)))

So, if the nr is known in compile time constant, the test_bit will be expanded to the call of the constant_test_bit function or variable_test_bit in other case. Now let's look at implementations of these functions. Let's start from the variable_test_bit:

static inline int variable_test_bit(long nr, volatile const unsigned long *addr)
{
int oldbit;
asm volatile("bt %2,%1\n\t"
"sbb %0,%0"
: "=r" (oldbit)
: "m" (*(unsigned long *)addr), "Ir" (nr));
return oldbit;
}

The variable_test_bit function takes similar set of arguments as set_bit and other function take. We also may see inline assembly code here which executes bt and sbb instruction. The bt or bit test instruction selects a given bit which is specified with first operand from the bit array which is specified with the second operand and stores its value in the CF bit of flags register. The second sbb instruction subtracts first operand from second and subtracts value of the CF. So, here write a value of a given bit number from a given bit array to the CF bit of flags register and execute sbb instruction which calculates: 00000000 - CF and writes the result to the oldbit.

The constant_test_bit function does the same as we saw in the set_bit:

static __always_inline int constant_test_bit(long nr, const volatile unsigned long *addr)
{
return ((1UL << (nr & (BITS_PER_LONG-1))) &
(addr[nr >> _BITOPS_LONG_SHIFT])) != 0;
}

It generates a byte where high bit is 1 and other bits are 0 (as we saw in CONST_MASK) and applies bitwise and to the byte which contains a given bit number.

The next widely used bit array related operation is to change bit in a bit array. The Linux kernel provides two helper for this:

  • __change_bit;

  • change_bit.

As you already can guess, these two variants are atomic and non-atomic as for example set_bit and __set_bit. For the start, let's look at the implementation of the __change_bit function:

static inline void __change_bit(long nr, volatile unsigned long *addr)
{
asm volatile("btc %1,%0" : ADDR : "Ir" (nr));
}

Pretty easy, is not it? The implementation of the __change_bit is the same as __set_bit, but instead of bts instruction, we are using btc. This instruction selects a given bit from a given bit array, stores its value in the CF and changes its value by the applying of complement operation. So, a bit with value 1 will be 0 and vice versa:

>>> int(not 1)
0
>>> int(not 0)
1

The atomic version of the __change_bit is the change_bit function:

static inline void change_bit(long nr, volatile unsigned long *addr)
{
if (IS_IMMEDIATE(nr)) {
asm volatile(LOCK_PREFIX "xorb %1,%0"
: CONST_MASK_ADDR(nr, addr)
: "iq" ((u8)CONST_MASK(nr)));
} else {
asm volatile(LOCK_PREFIX "btc %1,%0"
: BITOP_ADDR(addr)
: "Ir" (nr));
}
}

It is similar on set_bit function, but also has two differences. The first difference is xor operation instead of or and the second is btc instead of bts.

For this moment we know the most important architecture-specific operations with bit arrays. Time to look at generic bitmap API.

Common bit operations

Besides the architecture-specific API from the arch/x86/include/asm/bitops.h header file, the Linux kernel provides common API for manipulation of bit arrays. As we know from the beginning of this part, we can find it in the include/linux/bitmap.h header file and additionally in the * lib/bitmap.c source code file. But before these source code files let's look into the include/linux/bitops.h header file which provides a set of useful macro. Let's look on some of they.

First of all let's look at following four macros:

  • for_each_set_bit

  • for_each_set_bit_from

  • for_each_clear_bit

  • for_each_clear_bit_from

All of these macros provide iterator over certain set of bits in a bit array. The first macro iterates over bits which are set, the second does the same, but starts from a certain bits. The last two macros do the same, but iterates over clear bits. Let's look on implementation of the for_each_set_bit macro:

#define for_each_set_bit(bit, addr, size) \
for ((bit) = find_first_bit((addr), (size)); \
(bit) < (size); \
(bit) = find_next_bit((addr), (size), (bit) + 1))

As we may see it takes three arguments and expands to the loop from first set bit which is returned as result of the find_first_bit function and to the last bit number while it is less than given size.

Besides these four macros, the arch/x86/include/asm/bitops.h provides API for rotation of 64-bit or 32-bit values and etc.

The next header file which provides API for manipulation with a bit arrays. For example it provides two functions:

  • bitmap_zero;

  • bitmap_fill.

To clear a bit array and fill it with 1. Let's look on the implementation of the bitmap_zero function:

static inline void bitmap_zero(unsigned long *dst, unsigned int nbits)
{
if (small_const_nbits(nbits))
*dst = 0UL;
else {
unsigned int len = BITS_TO_LONGS(nbits) * sizeof(unsigned long);
memset(dst, 0, len);
}
}

First of all we can see the check for nbits. The small_const_nbits is macro which defined in the same header file and looks:

#define small_const_nbits(nbits) \
(__builtin_constant_p(nbits) && (nbits) <= BITS_PER_LONG)

As we may see it checks that nbits is known constant in compile time and nbits value does not overflow BITS_PER_LONG or 64. If bits number does not overflow amount of bits in a long value we can just set to zero. In other case we need to calculate how many long values do we need to fill our bit array and fill it with memset.

The implementation of the bitmap_fill function is similar on implementation of the biramp_zero function, except we fill a given bit array with 0xff values or 0b11111111:

static inline void bitmap_fill(unsigned long *dst, unsigned int nbits)
{
unsigned int nlongs = BITS_TO_LONGS(nbits);
if (!small_const_nbits(nbits)) {
unsigned int len = (nlongs - 1) * sizeof(unsigned long);
memset(dst, 0xff, len);
}
dst[nlongs - 1] = BITMAP_LAST_WORD_MASK(nbits);
}

Besides the bitmap_fill and bitmap_zero functions, the include/linux/bitmap.h header file provides bitmap_copy which is similar on the bitmap_zero, but just uses memcpy instead of memset. Also it provides bitwise operations for bit array like bitmap_and, bitmap_or, bitamp_xor and etc. We will not consider implementation of these functions because it is easy to understand implementations of these functions if you understood all from this part. Anyway if you are interested how did these function implemented, you may open include/linux/bitmap.h header file and start to research.

That's all.

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