Intermediate code formulas

Intermediate code generation. 5 formulas for GATE CS Compiler Design, each with when to use it. Each is explained in the topic notes.

All 5 Intermediate code formulas

INSTRUCTION AND TEMPORARY COUNT FOR AN ASSIGNMENT

temporaries = n, instructions = n + 1

For $x = E$ where $E$ has $n$ operator occurrences and nothing is shared. The scheme gives each operator a new temporary (temporaries are never reused) and then copies the last one to $x$ . With a DAG, replace $n$ by the number of operator nodes in the DAG.

ONE-DIMENSIONAL ARRAY ADDRESS

addr (A [i]) = base + (i - low) \times w

$w$ is the width of one element in bytes and $low$ is the lower bound of the index. For a 0-based array the term is just $i \times w$ .

TWO-DIMENSIONAL ARRAY ADDRESS, ROW-MAJOR

addr (A [i] [j]) = base + ((i - l_{1}) n_{2} + (j - l_{2})) \times w

$n_{2} = u_{2} - l_{2} + 1$ is the number of columns, and $l_{1}, l_{2}$ are the lower bounds. Row-major is the default for C-style arrays unless stated otherwise.

TWO-DIMENSIONAL ARRAY ADDRESS, COLUMN-MAJOR

addr (A [i] [j]) = base + ((j - l_{2}) n_{1} + (i - l_{1})) \times w

$n_{1} = u_{1} - l_{1} + 1$ is the number of rows. Use this only when the question says the layout is column-major.

ASSIGNMENTS IN SSA FORM

# assignments in SSA = # assignments in the code + # ϕ -functions

Each original assignment gets exactly one new name, and each $ϕ$ is one more assignment. Since each SSA name is assigned once, this is also the number of names created by assignments and $ϕ$ -functions. Variables that are only read and never assigned (inputs) keep their names and are not counted.

Where this was asked: 2024 (1), 2025 (1). See the 2 previous-year questions on Intermediate code. This shows what was asked, not what will be asked.

KEEP GOING

Intermediate code: the notes and 2 solved previous-year questions