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Live Variable Analysis

(Related issue https://github.com/numba/numba/pull/1611)

Numba uses reference-counting for garbage collection, a technique that requires cooperation by the compiler. The Numba IR encodes the location where a decref must be inserted. These locations are determined by live variable analysis. The corresponding source code is the _insert_var_dels() method in https://github.com/numba/numba/blob/master/numba/interpreter.py.

In Python semantic, once a variable is defined inside a function, it is alive until the variable is explicitly deleted or the function scope is ended. However, Numba analyzes the code to determine the minimum bound of the lifetime of each variable by its definition and usages during compilation. As soon as a variable is unreachable, a del instruction is inserted at the closest basic-block (either at the start of the next block(s) or at the end of the current block). This means variables can be released earlier than in regular Python code.

The behavior of the live variable analysis affects memory usage of the compiled code. Internally, Numba does not differentiate temporary variables and user variables. Since each operation generates at least one temporary variable, a function can accumulate a high number of temporary variables if they are not released as soon as possible. Our generator implementation can benefit from early releasing of variables, which reduces the size of the state to suspend at each yield point.

Notes on behavior of the live variable analysis

Variable deleted before definition

(Related issue: https://github.com/numba/numba/pull/1738)

When a variable lifetime is confined within the loop body (its definition and usage does not escape the loop body), like:

def f(arr):
  # BB 0
  res = 0
  # BB 1
  for i in (0, 1):
      # BB 2
      t = arr[i]
      if t[i] > 1:
          # BB 3
          res += t[i]
  # BB 4
  return res

Variable t is never referenced outside of the loop. A del instruction is emitted for t at the head of the loop (BB 1) before a variable is defined. The reason is obvious once we know the control flow graph:

         +------------------------------> BB4
BB 0 --> BB 1  -->  BB 2 ---> BB 3
         ^          |          |
         |          V          V

Variable t is defined in BB 1. In BB 2, the evaluation of t[i] > 1 uses t, which is the last use if execution takes the false branch and goto BB 1. In BB 3, t is only used in res += t[i], which is the last use if execution takes the true branch. Because BB 3, an outgoing branch of BB 2 uses t, t must be deleted at the common predecessor. The closest point is BB 1, which does not have t defined from the incoming edge of BB 0.

Alternatively, if t is deleted at BB 4, we will still have to delete the variable before its definition because BB4 can be executed without executing the loop body (BB 2 and BB 3), where the variable is defined.