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Memory access pattern

Memory access pattern represents the pattern in which a piece of code or a loop accesses its data. In most modern computer systems the bottleneck is the memory subsystem, and the memory access pattern can have a significant impact on loop performance.

It was noticed that programs often exhibit locality of reference when accessing data, and the memory subsystem is built to exploit this fact. However, not all programs are equally efficient regarding the way they use the memory subsystem, and there are code transformations that can help improve the memory access pattern for better performance.

There are four principal memory access patterns in programs:

  • Constant - happens when a loop is accessing the same memory location over and over.

  • Sequential (sometimes called consecutive or linear) - happens when a loop is accessing data sequentially in memory

  • Strided - happens when a loop is accessing data sequentially in memory, but the difference between the two neighboring memory accesses is greater than 1.

  • Random - happens when a loop is accessing data without any observable pattern.

In the case of nested loops, the memory access pattern is always analyzed in the context of the innermost loop. The statements in the innermost loop execute most often and they have the largest impact on performance. We observe how the memory is accessed when the iterator of the innermost loop changes its value.

To illustrate the memory access patterns, consider the following loop nest:

for (int i = 0; i < n; i++) {
  d[i] = 0.0;
  for (int j = 0; j < n; j++) {
    d[i] += a[j] + b[j * n] + c[index[j]];
  }
}

This loop is accessing data from the five arrays: a, b, c, index and d. The innermost loop iterates over j, so the memory access patterns are as follows:

  • Access to d[i] is constant. It doesn't depend on the value of j and it has the same value inside the innermost loop.

  • Access to a[j] is sequential. Everytime the iterator variable j increases by 1, the loop is accessing the next neighboring element. The same applies to the access to index[j].

  • Access to b[j * n] is strided. Everytime the iterator variable j increases by 1, the loop is accessing the element of the array b increased by n.

  • Access to c[index[j]] is random. The value accessed when the iterator variable j increases its value is not known and it is considered random.

Performance Implication of Memory Access Pattern

As already mentioned, the memory access pattern is very important for the loop's speed. Here is the list of memory access pattern with regards to performance:

  • Constant memory access pattern is the fastest. Typically, the compiler can allocate a register to replace reads and writes to memory.

  • Sequential memory access pattern is the next best. It uses the memory subsystem in the most optimal way compared to other memory access patterns.

  • Strided memory access pattern is somewhere in the middle performance-wise. It doesn't use the memory subsystem optimally, but the CPU can figure out the memory access pattern and prefetch data before it is needed.

  • Random memory access pattern is the worst.

There are transformations, such as loop interchange, loop tiling, loop sectioning, etc. where most of the benefit comes from improving the memory access pattern or converting from the more expensive memory access pattern to a cheaper one.

When it comes to vectorization, the compilers typically vectorize loops with constant and sequential memory access patterns.

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