How CPU Registers Are Allocated While Creating Machine Code

When a compiler creates machine code, it must decide which CPU physical registers hold each program value at each point in the instruction stream. This is the job of register allocation, typically implemented as one or more compiler passes between intermediate representation (IR) generation and final instruction emission. The key idea is that the compiler works with many “temporaries” (often represented as virtual registers) but the target machine has only a limited set of physical registers, so the compiler must map temporaries to physical registers while respecting correctness constraints such as:

• Liveness (a register’s value must remain intact until it is no longer needed)
• Calling conventions (some registers are caller-saved, some callee-saved; some are reserved for arguments/return values)
• Instruction constraints (some instructions require specific operand registers or forbid others)
• Memory spill (if there aren’t enough registers, values are spilled to the stack and reloaded)

Conceptually, the pipeline is: generate a low-level form with unlimited temporaries → build an allocation model (liveness/interference) → run a register allocator (e.g., graph coloring or linear scan) → rewrite the instruction stream with loads/stores for spills → emit final machine instructions.

Below is a visual overview of the typical flow and where register allocation sits.

keywordRegister Allocation
keywordVirtual Register
keywordInterference (conflict)
keywordSpilling
keywordReload

Note: Exact details vary across compilers (GCC vs. LLVM) and target architectures (x86-64, ARM64, RISC-V), but the correctness constraints and allocation logic are broadly shared.

1) Where register allocation happens in the compilation pipeline

Most optimizing compilers use an internal representation where values are not yet tied to hardware registers. After instruction selection, the compiler typically has:

1. A control-flow graph (CFG) of basic blocks.
2. Instructions in a low-level form that use virtual registers (or “pseudo-registers”).
3. Metadata to compute liveness of temporaries across program points.

Then register allocation proceeds. The allocator uses:

• Liveness analysis to know where each temporary is needed.
• Interference construction (implicitly or explicitly) to determine which temporaries overlap in live ranges.
• A strategy (graph coloring or linear scan) to choose physical registers.

Finally, the compiler performs a rewrite step:

• If two values can’t share a physical register, it inserts moves (or resolves constraints).
• If a value can’t fit, it generates spill code (store to stack) and later reload code.

2) The calling convention constrains which registers can be used

Even before allocation chooses registers for temporaries, the compiler must honor the application binary interface (ABI) and calling convention rules. For example, on x86-64 System V, specific registers are used for passing function arguments and receiving return values, and sets of registers are designated as caller-saved vs. callee-saved. These rules effectively reduce the available pool of registers for allocation across call boundaries.

keywordCalling Convention
keywordCallee-saved register
keywordCaller-saved register
keywordAllocatable Register Set

3) Modeling the problem: interference and live ranges

A register allocator must ensure that at any program point, each physical register holds at most one value that is simultaneously live.

A common model:

• For each temporary $t$, compute its live range (set of instruction positions where $t$ holds a value that may be read later).
• Two temporaries $t_i$ and $t_j$ interfere if their live ranges overlap.
• If $t_i$ and $t_j$ interfere, they must be assigned different physical registers (or one must be spilled).

This can be represented as an interference graph, where vertices are temporaries and edges indicate interference. The allocation problem becomes similar to graph coloring: assign colors (registers) to vertices so that adjacent vertices get different colors.

keywordInterference Graph
keywordLive Range
keywordRegister Coloring

4) Allocation strategies: graph coloring vs. linear scan

Compilers differ in how they solve the allocation problem.

Graph coloring approach (often for SSA-form backends)

• Build an interference graph.
• Simplify it by removing low-degree nodes, pushing them on a stack.
• Color nodes in reverse order (assign the smallest available color).
• If not enough colors exist, spill chosen nodes and retry.

Linear scan approach (common in JITs / simpler backends)

• Process instructions in linear order.
• Track active live ranges currently occupying registers.
• When a new range starts, assign a free register or spill the range with the latest end.

keywordGraph Coloring Register Allocation
keywordLinear Scan Register Allocation
keywordSpill Selection

5) Why spilling works (and what it costs)

Spilling is correctness-preserving but performance-affecting. When a temporary can’t get a register:

• It is stored to a stack slot at some point where it is still valid.
• Later, just before its next use, it is reloaded into a register.
• The allocator must also account for the fact that the register holding the reloaded value becomes live only for the remainder of its needed region.

In performance terms, spills increase:

• Memory traffic (loads/stores)
• Instruction count
• Pressure on caches and memory subsystem

So allocators try to choose spill candidates that minimize the number (and cost) of added loads/stores.

keywordStack Slot
keywordSpill/Reload Code

Callout: The allocator’s goal is not only to “fit” values, but to minimize spill frequency and the number of inserted move/reload instructions.

6) A concrete mental example (register pressure)

Suppose an instruction sequence needs 6 simultaneously live temporaries but the architecture provides only 4 allocatable general-purpose registers for that region. Then at least 2 temporaries must be spilled (or handled with copies and constrained instructions).

This is often summarized as register pressure: the maximum number of live values at once in a region.

keywordRegister Pressure

A typical outcome:

• The allocator keeps 4 temporaries in registers.
• The 2 others become stack-resident.
• Each use of a spilled temporary requires a load, and each definition requires a store.

7) How this becomes actual machine code fields

Once allocation is done, each virtual register is replaced by a concrete physical register number. The final machine encoding includes:

• Register operands in instruction fields (e.g., $rX indices in x86-64-like encodings)
• Possibly stack frame offsets for spill slots (e.g., base register + displacement)

Thus, “register allocation while creating machine code” is the step that bridges:

• abstract temporaries in IR to
• architecture-specific register identifiers and addressing modes in encoded instructions.

keywordPhysical Register Assignment
keywordInstruction Encoding