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In this code, a store to x is made at 50 and then a load of x is made at 5l If the order of instructions were swapped, the result would be wrong Imagine that x originally held the value O Because x would be read before the value 1 had been written to it, then y would erroneously contain 0 (instead of 1 ) after executing this code The second type of data dependence, output dependence, or store after-store, occurs when the same variable is written to multiple times We cannot reorder these instructions, or else earlier stores would pass later ones, and overwrite their values,

Benefits / 165

2 = Var(X) = E(X )2 =

Processors like Alpha are known to perform some suspicious reordering that can violate data dependence Modern versions of Windows need not consider Alpha architectures

If w e were t o swap S O and S1 , the variable x would contain the value a instead of 1 after they were done This is incorrect, and, therefore, this reordering must be disallowed Compilers often combine such writes into one, deleting the first, but this preserves the end value and is not the same as reordering them The third and final type of data dependence is antidependence, aka store-after-Ioad If a value is written to after it has been read, the program author probably expects the load to observe the variable's value as it was before the store happened

If we imagine x originally holds the value a in this particular example, moving the store at S1 before the load at SO would erroneously cause y to equal 1 instead of O Data dependencies are also transitive For example

must report the amount of taxable liability income received by an employee on its W-2 form at year-end

(x )2

= = =

In this particular example, S2 has a true dependence on S1 and S1 has a true dependence on SO Because this dependence is transitive, S2 therefore also has a true dependence on SO

Modern processors provide physical atomicity at a fine-grained level Recall from 2, Synchronization and Time, that the basic purpose of a crit ical region is to provide logical atomicity at a higher level Critical regions are typically implemented through a combination of software and hard ware, taking advantage of the kinds of atomic operations we're about to see These same atomic operations are the building blocks out of which low lock code is written too We'll later use these guarantees and various primitives discussed in this section to build some real examples of low lock code But first: What kinds of atomicity, if any, do ordinary load and store instructions enjoy

.

In our above example, we calculate the mean value, E(X) = = 45 090 = 405 and variance, Var(X) = npq = 45 090 010 = 4 05, meaning that the stan dard deviation is = 405 = 201246 We have seen that the standard deviation is a measure of the variation in the distribution To illustrate this,

.