Why Does Changing a Loop Counter's Bit Width Impact _mm_popcnt_u64 Performance on Intel CPUs?

Replacing a 32-bit loop counter with 64-bit can lead to significant performance deviations with _mm_popcnt_u64 on Intel CPUs

This problem arises due to a false data dependency, specifically, the
_mm_popcnt_u64 instruction has a false dependency on its destination register, causing it to wait until the destination register is ready before executing. This dependency can carry across loop iterations, making it difficult for the processor to parallelize different loop iterations.

The choice of loop variable type (unsigned vs. uint64_t) influences the register allocator

which assigns registers to variables, leading to differences in the register allocation and false dependency chains for the _mm_popcnt_u64 instructions.

Inserting the static keyword in front of the size variable

can alter the register allocation and break the false dependency chains. In some cases, this can lead to improved performance by eliminating the cross-iteration dependency on the destination register.

To mitigate this issue and achieve consistent performance:

• Consider using inline assembly to control register allocation and break the false dependency chain.
• Avoid using the same register for multiple _mm_popcnt_u64 instructions within a loop iteration.
• When possible, use a loop variable type (e.g., unsigned vs. uint64_t) that breaks the false dependency chain.
• Use static variables or other techniques to ensure that variables are allocated to specific registers.
• Test various alternatives on different compilers to identify the best performing code for a specific platform and compiler combination.
• Leverage advanced compiler optimization techniques such as loop unrolling and vectorization to further improve performance.

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