Fetch-and-add

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In computer science, the fetch-and-add CPU instruction is a special instruction that atomically modifies the contents of a memory location. It is used to implement mutual exclusion and concurrent algorithms in multiprocessor systems, a generalization of semaphores.

In uniprocessor systems, it is sufficient to disable interrupts before accessing a critical section. However, in multiprocessor systems (even with interrupts disabled) two or more processors could be attempting to access the same memory at the same time. The fetch-and-add instruction allows any processor to atomically increment a value in memory, preventing such multiple processor collisions.

Maurice Herlihy (1991) proved that fetch-and-add has a finite consensus number, in contrast to the compare-and-swap operation. The fetch-and-add operation can solve the wait-free consensus problem for no more than two concurrent processes.[1]

Implementation[edit]

The fetch-and-add instruction behaves like the following function. Crucially, the entire function is executed atomically: no process can interrupt the function mid-execution and hence see a state that only exists during the execution of the function. This code only serves to help explain the behaviour of fetch-and-add; atomicity requires explicit hardware support and hence can not be implemented as a simple high level function.

<< atomic >>
function FetchAndAdd(address location, int l) {
    int value := *location
    *location := value + l
    return value
}

Note that the operation Fetch-and-Increment act as Fetch-and-Add with l=1. With fetch-and-add primitive a mutual exclusion lock can be implemented as:

 record locktype {
    int ticketnumber
    int turn
 }
 procedure LockInit( locktype* lock ) {
    lock.ticketnumber := 0
    lock.turn  := 0
 }
 procedure Lock( locktype* lock ) {
    int myturn := FetchAndAdd( &lock.ticketnumber )
    while lock.turn ≠ myturn 
        skip // spin until lock is acquired
 }
 procedure UnLock( locktype* lock) {
    FetchAndAdd( &lock.turn )
 }

These routines provide a mutual-exclusion lock when following conditions are met:

  • Locktype data structure is initialized with function LockInit before use
  • Number of tasks waiting for the lock does not exceed INT_MAX at any time
  • Integer datatype used in lock values can 'wrap around' when continuously incremented

x86 implementation[edit]

In the x86 architecture, the instruction ADD with the destination operand specifying a memory location is a fetch-and-add instruction that has been there since the 8086 (it just wasn't called that then), and with the LOCK prefix, is atomic across multiple processors. However, it could not return the original value of the memory location (though it returned some flags) until the 486 introduced the XADD instruction.

The following is a C implementation for the GCC compiler, for both 32 and 64 bit x86 Intel platforms, based on extended asm syntax:

 inline int fetch_and_add( int * variable, int value ) {
     asm volatile("lock; xaddl %%eax, %2;"
                  :"=a" (value)                  //Output
                  :"a" (value), "m" (*variable)  //Input
                  :"memory");
     return value;
 }

See also[edit]

References[edit]

  1. ^ Herlihy, Maurice (January 1991). "Wait-free synchronization". ACM Trans. Program. Lang. Syst. 13 (1): 124–149. doi:10.1145/114005.102808. Retrieved 2007-05-20.