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Alternatively, we could have done two checks: one outside of the lock and one inside of the lock (before performing the pop) Sometimes the motivation for breaking an operation into multiple lock acquires is to avoid blocking other threads while a compute or I / O inten sive operation executes If this is the case, it's better to refactor code so that the operation occurs outside of the lock This can sometimes be a challenge If it's not possible, optimistic concurrency can sometimes be used In the original code sample, say we had to do some lengthy operation at SO that was based on the shared data we read from inside the lock If we associate a version number with the list, which is incremented each time a thread modifies the list and if we validate it didn' t change once we reacquire the lock, we can know whether atomicity has been preserved If the number has changed, we must throw away any calculations and start back at the beginning

Not all access to shared data needs to happen with heavyweight synchro nization While unsynchronized access to shared data is always a data race,

.

Unemployment Insurance / 189

When r = 1 we wait for the rst success and the probability distribution becomes P(X = x) = pqx 1 , x = 1, 2, 3, as we saw above; if r = 2,the probability distribution becomes P(X = x) = (x 1)p2 qx 2 , x = 2, 3, 4, again as we found above

some races are benign: that is, the program has been written to tolerate the race condition, and so these races are completely harmless The reason for this was already reviewed in 1 0, Memory Models and Lock Free dom: individual reads and writes of word sized memory locations are always atomic (As an aside, benign races aren't always completely harmless: unsyn chronized access to shared data is often an indication of premature clever ness and should be cause for concern when you run across it Developers who inherit and must maintain this code might be tempted to add addi tional (unsafe) accesses surrounding it because they may assume some higher level synchronization has been established Benign races can be used but only when done carefully) As a very simple illustration of where a benign race might be used, imag ine that we have code that spawns N threads to do some work in parallel Each task will search for some item in a collection The collection's contents aren't sorted, so we can't use a binary search The first thread to find a matching item can return, and then all other threads can stop searching One solution is to have all threads synchronize with one another to check whether any of the other tasks have finished, but this would be costly We might amortize the cost of synchronization by doing it only every so often, reducing the responsiveness once the item has been found, but improving the performance of the algorithm But this is heavier weight than necessary We can take a completely different approach Instead of using synchro nization, we can use a single shared variable: any thread can atomically write the value t r u e to it Multiple threads may write it more than once, but this is OK because they write the same value All other threads read from it continuously to notice approximately when the value changes to t r u e The variable changing t o t r u e i s the cue t o quit the search There's no need for a critical region; the threads will remain correct without it and will perform significantly better.

some code e l s ewhere c a l l s F i nd on d i s j Oint data a c ro s s N t h r e a d s i nt F i n d < T > ( T [ ] d at a , T v a l u e , int mySt a rt I d x , int myE n d I d x ) {

I I E a c h o f t h e N t h re a d s do t h i s : for ( i nt i mySt a rt l d x j i < my End l d x j i++ )

OMB No 1545-1110

E[X] =