Iterative algorithm for a forward data-flow problem
The purpose of this article is to tell you about an iterative algorithm for forward data-flow problem. Before starting, you should know some terminology related to data flow analysis.
Terminologies for Iterative algorithm :
Here, we will discuss terminologies for iterative algorithm as follows.
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- Data flow analysis –
It is defined as a technique in which set of values calculated at various points in a computer program for collecting information.
- Control Flow Graph (CFG) –
It is used to determine those parts of a program to which a particular value assigned to a variable might propagate.
- Naive approach (Kildall’s method) –
The easiest way to perform data-flow analysis of programs is to set up data-flow equations for each node of the control-flow graph and in this approach until the whole system stabilizes such that it reaches a fix point so, solve them by repeatedly calculating the output from the input locally at each node.
- An iterative algorithm –
An iterative algorithm is the most common way to solve the data flow analysis equations. In this algorithm, we particularly have two states first one is in-state and the other one is out-state. The algorithm starts with an approximation of the in-state of each block and then computed by applying the transfer functions on the in-states. The in-states is updated by applying the join operations. The latter two steps are repeated until we reach the fix point: the situation in which the in-states do not change.
- The efficiency of the above algorithm –
The efficiency of this algorithm for solving the data-flow equations is influenced by the order in which local nodes are visited, and also it depends on whether the data-flow equations are used for forwarding or backward data-flow analysis over the Control Flow Graph.
Iteration orders for solving data flow equations :
A few iteration orders for solving data-flow equations are discussed below as follows.
- Random order –
In this iteration, order is not aware whether the data-flow equations solve a forward or backward data-flow problem. And hence, the performance is relatively poor compared to specialized iteration orders.
- Post order –
This iteration order for backward data-flow problems. A node is visited after all its successor nodes have been visited, and implemented with the depth-first strategy.
- Reverse post order –
This iteration order for forwarding data-flow problems. The node is visited before any of its successor nodes has been visited, except when the successor is reached by a back edge.
- Forward data analysis –
Consider an arbitrary point ‘p’ In a forward analysis, we are reasoning about facts up to ‘p’, considering only the predecessors of the node at ‘p’. In a backward analysis, we are reasoning about facts from ‘p’ onward, considering only the successors.
line 1: if b==4 then line 2: a = 5; line 3: else line 4: a = 3; line 5: endif line 6: line 7: if a < 4 then ...// rest of the code
Example descriptions :
From the above example, we can observe that the reaching definition of variable at line 7 is the set of assignments a = 5 at line 2 and a = 3 at line 4.