Register Allocation in Compiler Design

During the intermediate code generation phase in compilers, several techniques must be followed to ensure that the generated code can execute on any system. When a program runs, variables and temporary values need to be stored efficiently. While primary memory (RAM) is available, accessing it is significantly slower compared to CPU registers, which provide the fastest storage. However, registers are limited in both size and number, making their efficient use crucial for performance optimization.

This process, known as register allocation, plays a vital role in optimizing compiled code. The compiler determines which variables should be stored in registers and when to spill (move) them to memory if registers run out. In this chapter, we will explore register allocation in detail, discuss its challenges, examine different strategies, and analyze examples for a better understanding.

What is Register Allocation?

Register Allocation is the process of assigning variables, temporary values, and computations to CPU registers during code generation. There are a set of goals −

• Minimize Memory Access − Keep frequently used values in registers.
• Reduce Register Spills − Avoid excessive movement between registers and memory.
• Optimize Execution Speed − Ensure efficient use of registers to speed up program execution.

Steps in Register Allocation

Register Allocation generally consists of the following steps:

• Liveness Analysis − This determines which variables are "alive" at a given point in the program. Now a variable is alive if it is needed later and should not be overwritten.
• Interference Graph Construction − This creates a graph where nodes represent variables. And the edges of the graph connect variables that cannot share the same register.
• Register Assignment − Next it assigns registers to variables while ensuring that variables interfering with each other get different registers.
• Spilling (if necessary) − This is an optional stage. If there are more variables than available registers, some variables are spilled to memory.

Register Allocation for Arithmetic Operations

Let us see the thing in action. Consider the following arithmetic expression in C −

z = (a + b) * (c - d);

The intermediate representation (IR) using atoms −

(ADD, a, b, T1)    # T1 = a + b  
(SUB, c, d, T2)    # T2 = c - d  
(MUL, T1, T2, z)   # z = T1 * T2 

Register Allocation Using Three Registers (R1, R2, R3)

Allocate R1 for a, R2 for b

MOV a, R1  
MOV b, R2  
ADD R1, R2   # T1 = a + b

Reassign R1 for c, R2 for d (Here we can see a and b are no longer needed).

MOV c, R1  
MOV d, R2  
SUB R1, R2   # T2 = c - d  

Reassign R3 for T1, R1 for T2 and multiply –

MOV T1, R3  
MOV T2, R1  
MUL R3, R1   # z = T1 * T2  

Here, we can see how it efficiently reused the registers, instead of using a new register for each operation.

Strategies for Register Allocation

Compilers use different strategies to allocate registers as given below:

Graph Coloring Algorithm

Graph Coloring Algorithm is the most widely used technique for register allocation. It constructs an interference graph where −

• Nodes represent variables.
• Edges represent conflicts (Like variables that cannot share the same register).
• Uses graph coloring to assign registers. This gives that no two connected nodes get the same register.

Example: Graph Coloring for Three Variables

Consider the following variables and their conflicts −

T1 interferes with T2 and T3  
T2 interferes with T1  
T3 interferes with T1  

The interference graph −

If we have two registers (R1, R2), we color the graph as follows −

T1 → R1  
T2 → R2  
T3 → R2  

Since T2 and T3 do not interfere, they can share R2.

The color of T2 and T3 can be same, since they are not connected.

Linear Scan Allocation

Linear Scan Allocation is faster but less optimal than graph coloring. It used in Just-in-Time (JIT) compilers. Here variables are assigned registers based on their lifetime intervals. Here spilling is applied when necessary.

Example: Linear Scan with Two Registers

Take a look at the following example −

Here, T3 reuses R1 after T1 is no longer needed.

Register Spilling

When there are more variables than available registers, the compiler must spill some variables to memory.

Example: Spilling When Registers Are Full

If we need three registers, but only have two, we spill −

MOV a, R1  
MOV b, R2  
ADD R1, R2   # T1 = a + b  

STORE T1, MEM[100]  # Spill T1 to memory  

MOV c, R1  
MOV d, R2  
SUB R1, R2   # T2 = c - d  

LOAD T1, MEM[100]  # Load T1 back from memory  
MUL T1, R1   # z = T1 * T2  

Here we can see T1 was stored in memory and reloaded due to register shortage.

Register Allocation: Real-World Applications

Register allocation plays a crucial role in several real-world applications where performance optimization is essential −

• Compilers (GCC, LLVM) − Optimizes register usage to speed up execution.
• JIT Compilers (Java, JavaScript V8 Engine) − Uses linear scan allocation for fast runtime allocation.
• Embedded Systems − Minimizes register spills due to limited memory availability.

Advantages and Limitations of Register Allocation

The following table highlights the advantages and limitations of Register Allocation −

Conclusion

In this chapter, we explored the concept of register allocation and its importance in compiler design. We examined two popular strategies for assigning registers: graph coloring and linear scan allocation. Through examples, we saw how arithmetic operations, memory spills, and register reuse are managed to enhance execution speed.

Effective register allocation ensures that compiled code runs efficiently by reducing memory accesses and maximizing CPU register usage. Without proper allocation, programs would execute significantly slower due to frequent memory loads and stores.