NEON vectorize sum of products of unsigned bytes: (a[i]-int1) * (b[i]-int2)

Question

I need to improve a loop, because is called by my application thousands of times. I suppose I need to do it with Neon, but I don´t know where to begin.

Assumptions / pre-conditions:

• w is always 320 (multiple of 16/32).
• pa and pb are 16-byte aligned
• ma and mb are positive.

 int whileInstruction (const unsigned char *pa,const unsigned char *pb,int ma,int mb,int w)
{
    int sum=0;

    do {
        sum += ((*pa++)-ma)*((*pb++)-mb);

    } while(--w);


    return sum;
}

This attempt at vectorizing it is not working well, and isn't safe (missing clobbers), but demonstrates what I'm trying to do:

int whileInstruction (const unsigned char *pa,const unsigned char *pb,int ma,int mb,int w)
{

    asm volatile("lsr          %2, %2, #3      \n"
                 ".loop:                       \n"
                 "# load 8 elements:             \n"
                 "vld4.8      {d0-d3}, [%1]!   \n"
                 "vld4.8      {d4-d7}, [%2]!   \n"
                 "# do the operation:     \n"
                 "vaddl.u8    q7, d0, r7       \n"
                 "vaddl.u8    q8, d1, d8       \n"
                 "vmlal.u8    q7, q7, q8       \n"
                 "# Sum the vector a save in sum (this is wrong):\n"
                 "vaddl.u8    q7, d0, r7       \n"
                 "subs        %2, %2, #1       \n" // Decrement iteration count
                 "bne         .loop            \n" // Repeat unil iteration count is not zero
                 :
                 : "r"(pa), "r"(pb), "r"(w),"r"(ma),"r"(mb),"r"(sum)
                 : "r4", "r5", "r6","r7","r8","r9"
                 );

    return sum;
}

Answer 1

Here is a simple NEON implementation. I have tested this against the scalar code to make sure that it works. Note that for best performance both pa and pb should be 16 byte aligned.

#include <arm_neon.h>

int whileInstruction_neon(const unsigned char *pa, const unsigned char *pb, int ma, int mb, int w)
{
    int sum = 0;

    const int32x4_t vma = { ma, ma, ma, ma };
    const int32x4_t vmb = { mb, mb, mb, mb };

    int32x4_t vsumll = { 0 };
    int32x4_t vsumlh = { 0 };
    int32x4_t vsumhl = { 0 };
    int32x4_t vsumhh = { 0 };
    int32x4_t vsum;

    int i;

    for (i = 0; i <= (w - 16); i += 16)
    {
        uint8x16_t va = vld1q_u8(pa);   // load vector from pa
        uint8x16_t vb = vld1q_u8(pb);   // load vector from pb

        // unpack va into 4 vectors

        int16x8_t val =  (int16x8_t)vmovl_u8(vget_low_u8(va));
        int16x8_t vah =  (int16x8_t)vmovl_u8(vget_high_u8(va));
        int32x4_t vall = vmovl_s16(vget_low_s16(val));
        int32x4_t valh = vmovl_s16(vget_high_s16(val));
        int32x4_t vahl = vmovl_s16(vget_low_s16(vah));
        int32x4_t vahh = vmovl_s16(vget_high_s16(vah));

        // subtract means

        vall = vsubq_s32(vall, vma);
        valh = vsubq_s32(valh, vma);
        vahl = vsubq_s32(vahl, vma);
        vahh = vsubq_s32(vahh, vma);

        // unpack vb into 4 vectors

        int16x8_t vbl =  (int16x8_t)vmovl_u8(vget_low_u8(vb));
        int16x8_t vbh =  (int16x8_t)vmovl_u8(vget_high_u8(vb));
        int32x4_t vbll = vmovl_s16(vget_low_s16(vbl));
        int32x4_t vblh = vmovl_s16(vget_high_s16(vbl));
        int32x4_t vbhl = vmovl_s16(vget_low_s16(vbh));
        int32x4_t vbhh = vmovl_s16(vget_high_s16(vbh));

        // subtract means

        vbll = vsubq_s32(vbll, vmb);
        vblh = vsubq_s32(vblh, vmb);
        vbhl = vsubq_s32(vbhl, vmb);
        vbhh = vsubq_s32(vbhh, vmb);

        // update 4 partial sum of products vectors

        vsumll = vmlaq_s32(vsumll, vall, vbll);
        vsumlh = vmlaq_s32(vsumlh, valh, vblh);
        vsumhl = vmlaq_s32(vsumhl, vahl, vbhl);
        vsumhh = vmlaq_s32(vsumhh, vahh, vbhh);

        pa += 16;
        pb += 16;
    }

    // sum 4 partial sum of product vectors

    vsum = vaddq_s32(vsumll, vsumlh);
    vsum = vaddq_s32(vsum, vsumhl);
    vsum = vaddq_s32(vsum, vsumhh);

    // do scalar horizontal sum across final vector

    sum = vgetq_lane_s32(vsum, 0);
    sum += vgetq_lane_s32(vsum, 1);
    sum += vgetq_lane_s32(vsum, 2);
    sum += vgetq_lane_s32(vsum, 3);

    // handle any residual non-multiple of 16 points

    for ( ; i < w; ++i)
    {
        sum +=  (*pa++ - ma) * (*pb++ - mb);
    }

    return sum;
}