Static Single Assignment (SSA)

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1️⃣ What is SSA?

SSA is a way of representing code where:

  • Each variable is assigned exactly once.
  • If a variable is reassigned → the compiler creates a new “version” of that variable (x1, x2, x3 …).
  • When there are multiple control-flow branches (if/else), the compiler uses a φ-function to “merge” values back together.

🔎 Note: SSA is not a new kind of IR on its own, but rather a specialized form of IR. Compilers convert their Intermediate Representation (IR) into SSA form to make analysis and optimization easier.

2️⃣ Example

Normal

Original code: 

x = 1;
x = x + 2;
y = x * 3;

After converting to SSA: 

x1 = 1;
x2 = x1 + 2;
y1 = x2 * 3;

Branching (if/else)

Original code: 

if (cond) {
    x = 1;
} else {
    x = 2;
}
y = x + 3;

After converting to SSA: 

if (cond) {
    x1 = 1;
} else {
    x2 = 2;
}
x3 = φ(x1, x2);
y1 = x3 + 3;

Loop (while)

Original code: 

let sum = 0;
let i = 0;

while (i < 3) {
  sum = sum + i;
  i = i + 1;
}

After converting to SSA: 

let sum0 = 0;
let i0 = 0;

while (i0 < 3) {
  let sum1 = sum0 + i0;
  let i1 = i0 + 1;

  // φ-functions to bring values back into the loop
  sum0 = φ(sum1);
  i0 = φ(i1);
}

3️⃣ What is the φ-function?

The φ (phi-function) is a special notation in SSA, not an actual runtime function.

  • It only exists during compiler analysis of control flow.
  • Its role is to select the correct value depending on which branch was executed:
    • If cond is true → x3 = x1.
    • If cond is false → x3 = x2.

In other words: φ acts as a “bridge” that unifies variables from different branches into a single one in SSA.

4️⃣ Why is SSA important?

  • Simplifies analysis: every variable has exactly one definition.

  • Enables stronger optimizations: such as constant propagation, dead code elimination, and register allocation.

5️⃣ Extensions and Variations of SSA

SSA is a flexible and extensible representation, and several variations have been developed to improve its performance and adaptability:

  • Minimal SSA: This extension seeks to insert the minimal number of Φ-functions while ensuring that each variable is assigned exactly once.

  • Pruned SSA: This variant avoids inserting unnecessary Φ-functions by considering live-variable information during the SSA construction process.

  • Semi-pruned SSA: A more efficient variation that omits Φ-functions for variables that are not live when they enter a basic block.

  • Block arguments: An alternative to Φ-functions, where block arguments are used to represent control-flow merges in a way that is more convenient for optimization. Some compilers like LLVM MLIR and Swift SIL use block arguments.

🎯 Conclusion

SSA isn’t just a theoretical concept – it’s the foundation of most modern compilers. It simplifies dataflow analysis and optimization, making compilers more efficient. In short, SSA is the secret sauce that enables compilers to be both smart in analyzing code and powerful in optimizing it.

🔗 References

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