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Time-space tradeoff

As explained in Fast Python: High performance techniques for large datasets

A time-space tradeoff is a design choice that exchanges computational time for storage or memory, or storage or memory for computational time.

A time-space tradeoff exchanges memory for computation. An extended board stores copied boundary cells so the core loop avoids boundary-condition tests and can run faster. section 5.6.1

Evaluate the tradeoff against the whole implementation:

  • Allocate an extended board when removing repeated boundary tests simplifies or accelerates the core algorithm. section 5.6.1
  • Account for the cost of copying the original board and storing the larger array; available memory and algorithmic costs determine whether the exchange pays off. section 5.6.1
  • Treat disabled wraparound and bounds checks as related performance choices: they remove CPython or verification overhead but restrict convenient indexing idioms. section 5.6.1
def live(cnp.ndarray[cnp.uint8_t, ndim=2] old_world):
    cdef int size_y = old_world.shape[0]
    cdef int size_x = old_world.shape[1]
    cdef cnp.ndarray[cnp.uint8_t, ndim=2] extended_world =
      np.empty((size_y + 2, size_x + 2), dtype=np.uint8)   # empty
    cdef cnp.ndarray[cnp.uint8_t, ndim=2] new_world =
      np.empty((size_y, size_x), np.uint8)
    cdef cnp.ndarray[cnp.uint8_t, ndim=1] states = np.empty((5,), np.uint8)
 
    live_core(old_world, extended_world, new_world, states)
    return new_world

Inspect the Cython function that allocates the extended and output boards before delegating to the optimized core loop. section 5.6.1

How Fast Python: High performance techniques for large datasets covers it

How deep it goes
Explains allocation, boundary copying, and indexing costs, but gives no generalized decision rule beyond workload and resource dependence.
Examples
Uses a cellular-automaton board, an extended wraparound array, and a Cython live-core loop.
What it assumes
Assumes familiarity with arrays, boundary handling, Cython, and the performance effects of CPython machinery.
What you can do after
Apply it via Cython by allocating copied boundary storage and simplifying the main computation loop.
How it connects
Connects memory allocation with Cython, boundary conditions, wraparound, bounds checking, and CPython execution overhead.
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