How can SSE instructions and assembly optimization improve the performance of a population count algorithm with a two-level loop?

Understanding the Issue

In your code, you handle population counts within a two-level loop and try to optimize the inner loop with assembly. The loop iterates through a byte slice and uses the __mm_add_epi32_inplace_purego function to add positional popcounts to an array.

Optimization via Assembly

To optimize the inner loop, you can implement __mm_add_epi32_inplace_purego in assembly. Below is the suggested optimized version of the function:

<code class="assembly">.text
.globl __mm_add_epi32_inplace_purego
__mm_add_epi32_inplace_purego:
    movq rdi, [rsi]
    movq rsi, [rdi+8]
    addq rsi, rdi
    movups (%rsi, %rax, 8), %xmm0
    addq , %rsi
    movups (%rsi, %rax, 8), %xmm1
    paddusbd %xmm0, %xmm0
    paddusbd %xmm1, %xmm1
    vextracti128 <pre class="brush:php;toolbar:false"><code class="assembly">.text
.globl __optimized_population_count_loop
__optimized_population_count_loop:
    movq rdi, [rsi]
    leaq (0, %rdi, 4), %rdx  # multiple rdi by 4, rdx = counts
    movq rsp, r11
    and rsp, -16
    subq r15, r11
    movq r15, r9
    mov rdi, (%rsi)
    movq r15, rsi
    mov %rsi, rsi
    pxor %eax, %eax
    dec %rsi

.loop:
    inc %rsi
    addq , rsi
    cmp rsi, rdi
    cmovge %rsi, rsi
    movsw (%rdi, %rax, 2), %ax
    movsw (%rsi, %rax, 2), %dx
    movw %ax, (%rdx)
    movw %dx, 2(%rdx)

.end_loop:</code>

, %xmm0, %eax vextracti128 , %xmm1, %edx addl %eax, (%rdi) addl %edx, 4(%rdi) addl %r8d, (%rdi) ret

Explanation:

This assembly code optimizes the function using packed SSE instructions. It:

• Computes popcounts in 16-bit blocks using paddusbd.
• Extracts the low 128-bit portion using vextracti128.
• Adds the results to the [8]int32 array at the address given by %rdi.

Enhanced Whole Loop with Assembly

Explanation:

The complete loop is now optimized in assembly. It uses:

• A loop to process 2-byte chunks.
• Streaming loads via consecutive addq $32, rsi to avoid cache misses.
• A fast and compact way to save the results using movw.

Conclusion

This optimized version should significantly improve the performance of your algorithm for computing positional population counts.

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