How can you optimize an 8-bit positional popcount algorithm using assembly, specifically by focusing on the inner loop and utilizing techniques like prefetching and scalar population counting?

How to optimise this 8-bit positional popcount using assembly?

In the provided code, the function __mm_add_epi32_inplace_purego can be optimized using assembly to improve its performance. The inner loop in particular can be optimized for faster execution.

The provided algorithm for counting positional population is called a "positional population count." This algorithm is used in machine learning and involves counting the number of set bits in a series of bytes. In the given code, _mm_add_epi32_inplace_purego is called in two levels of loop, and the goal is to optimize the inner loop.

The provided code primarily works on an array of 8-bit integers called counts. The inner loop iterates over a byte slice, and for each byte, it adds the corresponding bit positions from an array of bit patterns (_expand_byte) to the counts array. The _expand_byte array contains bit patterns that expand each byte into its individual bits.

To optimize the inner loop using assembly, you need to keep the counters in general-purpose registers for better performance and prefetch memory well in advance to improve streaming behavior. You can also implement scalar population counting using a simple shift and add combination (SHRL/ADCL).

An example of optimized assembly code is provided below. This code is written for a specific processor architecture and may need to be modified to run on other systems.

<code class="assembly">#include "textflag.h"

// func PospopcntReg(counts *[8]int32, buf []byte)
TEXT ·PospopcntReg(SB),NOSPLIT,-32
    MOVQ counts+0(FP), DI
    MOVQ buf_base+8(FP), SI     // SI = &buf[0]
    MOVQ buf_len+16(FP), CX     // CX = len(buf)

    // load counts into register R8--R15
    MOVL 4*0(DI), R8
    MOVL 4*1(DI), R9
    MOVL 4*2(DI), R10
    MOVL 4*3(DI), R11
    MOVL 4*4(DI), R12
    MOVL 4*5(DI), R13
    MOVL 4*6(DI), R14
    MOVL 4*7(DI), R15

    SUBQ , CX            // pre-subtract 32 bit from CX
    JL scalar

vector: VMOVDQU (SI), Y0        // load 32 bytes from buf
    PREFETCHT0 384(SI)      // prefetch some data
    ADDQ , SI            // advance SI past them

    VPMOVMSKB Y0, AX        // move MSB of Y0 bytes to AX
    POPCNTL AX, AX          // count population of AX
    ADDL AX, R15            // add to counter
    VPADDD Y0, Y0, Y0       // shift Y0 left by one place

    VPMOVMSKB Y0, AX        // move MSB of Y0 bytes to AX
    POPCNTL AX, AX          // count population of AX
    ADDL AX, R14            // add to counter
    VPADDD Y0, Y0, Y0       // shift Y0 left by one place

    VPMOVMSKB Y0, AX        // move MSB of Y0 bytes to AX
    POPCNTL AX, AX          // count population of AX
    ADDL AX, R13            // add to counter
    VPADDD Y0, Y0, Y0       // shift Y0 left by one place

    VPMOVMSKB Y0, AX        // move MSB of Y0 bytes to AX
    POPCNTL AX, AX          // count population of AX
    ADDL AX, R12            // add to counter
    VPADDD Y0, Y0, Y0       // shift Y0 left by one place

    VPMOVMSKB Y0, AX        // move MSB of Y0 bytes to AX
    POPCNTL AX, AX          // count population of AX
    ADDL AX, R11            // add to counter
    VPADDD Y0, Y0, Y0       // shift Y0 left by one place

    VPMOVMSKB Y0, AX        // move MSB of Y0 bytes to AX
    POPCNTL AX, AX          // count population of AX
    ADDL AX, R10            // add to counter
    VPADDD Y0, Y0, Y0       // shift Y0 left by one place

    VPMOVMSKB Y0, AX        // move MSB of Y0 bytes to AX
    POPCNTL AX, AX          // count population of AX
    ADDL AX, R9         // add to counter
    VPADDD Y0, Y0, Y0       // shift Y0 left by one place

    VPMOVMSKB Y0, AX        // move MSB of Y0 bytes to AX
    POPCNTL AX, AX          // count population of AX
    ADDL AX, R8         // add to counter

    SUBQ , CX
    JGE vector          // repeat as long as bytes are left

scalar: ADDQ , CX            // undo last subtraction
    JE done             // if CX=0, there's nothing left

loop:   MOVBLZX (SI), AX        // load a byte from buf
    INCQ SI             // advance past it

    SHRL , AX         // CF=LSB, shift byte to the right
    ADCL , R8         // add CF to R8

    SHRL , AX
    ADCL , R9         // add CF to R9

    SHRL , AX
    ADCL , R10            // add CF to R10

    SHRL , AX
    ADCL , R11            // add CF to R11

    SHRL , AX
    ADCL , R12            // add CF to R12

    SHRL , AX
    ADCL , R13            // add CF to R13

    SHRL , AX
    ADCL , R14            // add CF to R14

    SHRL , AX
    ADCL , R15            // add CF to R15

    DECQ CX             // mark this byte as done
    JNE loop            // and proceed if any bytes are left

    // write R8--R15 back to counts
done:   MOVL R8, 4*0(DI)
    MOVL R9, 4*1(DI)
    MOVL R10, 4*2(DI)
    MOVL R11, 4*3(DI)
    MOVL R12, 4*4(DI)
    MOVL R13, 4*5(DI)
    MOVL R14, 4*6(DI)
    MOVL R15, 4*7(DI)

    VZEROUPPER          // restore SSE-compatibility
    RET</code>

In summary, the optimization involves using general-purpose registers for counters, prefetching memory in advance, and implementing scalar population counting using SHRL/ADCL. This approach can significantly improve the performance of the positional population count algorithm.

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