Data dependency

A data dependency in computer science is a situation in which a program statement (instruction) refers to the data of a preceding statement. In compiler theory, the technique used to discover data dependencies among statements (or instructions) is called dependence analysis.

There are three types of dependencies: data, name, and control.

Data dependencies

Assuming statement $S_{1}$ and $S_{2}$, $S_{2}$ depends on $S_{1}$ if:

$\left[I(S_{1})\cap O(S_{2})\right]\cup \left[O(S_{1})\cap I(S_{2})\right]\cup \left[O(S_{1})\cap O(S_{2})\right]\neq \varnothing$

where:

• $I(S_{i})$ is the set of memory locations read by $S_{i}$,
• $O(S_{j})$ is the set of memory locations written by $S_{j}$, and
• there is a feasible run-time execution path from $S_{1}$ to $S_{2}$.

This Condition is called Bernstein Condition, named by A. J. Bernstein.

Three cases exist:

• Anti-dependence: $I(S_{1})\cap O(S_{2})\neq \varnothing$, $S_{1}\rightarrow S_{2}$ and $S_{1}$ reads something before $S_{2}$ overwrites it
• Flow (data) dependence: $O(S_{1})\cap I(S_{2})\neq \varnothing$, $S_{1}\rightarrow S_{2}$ and $S_{1}$ writes before something read by $S_{2}$
• Output dependence: $O(S_{1})\cap O(S_{2})\neq \varnothing$, $S_{1}\rightarrow S_{2}$ and both write the same memory location.

Flow dependency (True dependency)

A Flow dependency, also known as a data dependency or true dependency or read-after-write (RAW), occurs when an instruction depends on the result of a previous instruction.

1. A = 3
2. B = A
3. C = B

Instruction 3 is truly dependent on instruction 2, as the final value of C depends on the instruction updating B. Instruction 2 is truly dependent on instruction 1, as the final value of B depends on the instruction updating A. Since instruction 3 is truly dependent upon instruction 2 and instruction 2 is truly dependent on instruction 1, instruction 3 is also truly dependent on instruction 1. Instruction level parallelism is therefore not an option in this example.

Anti-dependency

An anti-dependency, also known as write-after-read (WAR), occurs when an instruction requires a value that is later updated. In the following example, instruction 2 anti-depends on instruction 3 — the ordering of these instructions cannot be changed, nor can they be executed in parallel (possibly changing the instruction ordering), as this would affect the final value of A.

1. B = 3
2. A = B + 1
3. B = 7

Example :

 MUL R3,R1,R2
 ADD R2,R5,R6

It is clear that there is anti-dependence between these 2 instructions. At first we read R2 then in second instruction we are Writing a new value for it.

An anti-dependency is an example of a name dependency. That is, renaming of variables could remove the dependency, as in the next example:

1. B = 3
N. B2 = B
2. A = B2 + 1
3. B = 7

A new variable, B2, has been declared as a copy of B in a new instruction, instruction N. The anti-dependency between 2 and 3 has been removed, meaning that these instructions may now be executed in parallel. However, the modification has introduced a new dependency: instruction 2 is now truly dependent on instruction N, which is truly dependent upon instruction 1. As flow dependencies, these new dependencies are impossible to safely remove.

Output dependency

An output dependency, also known as write-after-write (WAW), occurs when the ordering of instructions will affect the final output value of a variable. In the example below, there is an output dependency between instructions 3 and 1 — changing the ordering of instructions in this example will change the final value of A, thus these instructions cannot be executed in parallel.

1. B = 3
2. A = B + 1
3. B = 7

As with anti-dependencies, output dependencies are name dependencies. That is, they may be removed through renaming of variables, as in the below modification of the above example:

1. B2 = 3
2. A = B2 + 1
3. B = 7

A commonly used naming convention for data dependencies is the following: Read-after-Write or RAW (flow dependency), Write-After-Read or WAR (anti-dependency), or Write-after-Write or WAW (output dependency).

Implications

Conventional programs are written assuming the sequential execution model. Under this model, instructions execute one after the other, atomically (i.e., at any given point in time, only one instruction is executed) and in the order specified by the program.

However, dependencies among statements or instructions may hinder parallelism — parallel execution of multiple instructions, either by a parallelizing compiler or by a processor exploiting instruction-level parallelism. Recklessly executing multiple instructions without considering related dependences may cause danger of getting wrong results, namely hazards.

See also

• Dependency analysis
• Control dependency