inline static void integral2(const cv::Size2i& size, const uint8_t* srcBase, ptrdiff_t srcStride, uint32_t* sumBase, ptrdiff_t sumStride, double* sqsumBase, ptrdiff_t sqsumStride)
    {
        uint32x4_t v_zero = vmovq_n_u32(0u);
        uint16x8_t v_zero8 = vmovq_n_u16(0u);

        // the first iteration
        const uint8_t* src = internal::getRowPtr(srcBase, srcStride, 0);
        uint32_t* sum = internal::getRowPtr(sumBase, sumStride, 0);
        double* sqsum = internal::getRowPtr(sqsumBase, sqsumStride, 0);

        double prevsq = 0.;

        uint32x4_t prev = v_zero;
        size_t j = 0u;

        for (; j + 7 < size.width; j += 8)
        {
            internal::prefetch(sqsum + j);
            internal::prefetch(sum + j);
            internal::prefetch(src + j);

            uint8x8_t el8shr0 = vld1_u8(src + j);
            uint16x8_t sqel8shr0 = vmull_u8(el8shr0, el8shr0);
            uint8x8_t el8shr1 = vreinterpret_u8_u64(vshl_n_u64(vreinterpret_u64_u8(el8shr0), 8));
            uint8x8_t el8shr2 = vreinterpret_u8_u64(vshl_n_u64(vreinterpret_u64_u8(el8shr0), 16));
            uint8x8_t el8shr3 = vreinterpret_u8_u64(vshl_n_u64(vreinterpret_u64_u8(el8shr0), 24));

            uint16x8_t el8shr12 = vaddl_u8(el8shr1, el8shr2);
            uint16x8_t el8shr03 = vaddl_u8(el8shr0, el8shr3);

            uint16x8_t el8 = vaddq_u16(el8shr12, el8shr03);
            uint16x4_t el4h = vadd_u16(vget_low_u16(el8), vget_high_u16(el8));

            uint32x4_t vsuml = vaddw_u16(prev, vget_low_u16(el8));
            uint32x4_t vsumh = vaddw_u16(prev, el4h);

            vst1q_u32(sum + j, vsuml);
            vst1q_u32(sum + j + 4, vsumh);

            prev = vaddw_u16(prev, vdup_lane_u16(el4h, 3));



            uint16x8_t sqel8shr1 = vextq_u16(v_zero8, sqel8shr0, 7);

            uint32x4_t sqel8shr01l = vaddl_u16(vget_low_u16(sqel8shr0), vget_low_u16(sqel8shr1));
            uint32x4_t sqel8shr01h = vaddl_u16(vget_high_u16(sqel8shr0), vget_high_u16(sqel8shr1));

            uint32x4_t sqel4h = vaddq_u32(sqel8shr01l, sqel8shr01h);

            uint32x2_t sqel2l = vadd_u32(vget_low_u32(sqel8shr01l), vget_high_u32(sqel8shr01l));
            uint32x2_t sqel2hl = vadd_u32(vget_low_u32(sqel4h), vget_high_u32(sqel8shr01l));
            uint32x2_t sqel2hh = vadd_u32(vget_low_u32(sqel4h), vget_high_u32(sqel4h));

            uint32_t buf[8];
            vst1_u32(buf, vget_low_u32(sqel8shr01l));
            vst1_u32(buf + 2, sqel2l);
            vst1_u32(buf + 4, sqel2hl);
            vst1_u32(buf + 6, sqel2hh);
            for (uint32_t k = 0; k < 8; k++)
                sqsum[j + k] = prevsq + buf[k];
            prevsq += buf[7];

        }

        for (uint32_t v = vgetq_lane_u32(prev, 3); j < size.width; ++j)
        {
            sum[j] = (v += src[j]);
            sqsum[j] = (prevsq += src[j] * src[j]);
        }

        // the others
        for (size_t i = 1; i < size.height; ++i)
        {
            src = internal::getRowPtr(srcBase, srcStride, i);
            uint32_t* prevSum = internal::getRowPtr(sumBase, sumStride, i - 1);
            sum = internal::getRowPtr(sumBase, sumStride, i);

            double* prevSqSum = internal::getRowPtr(sqsumBase, sqsumStride, i - 1);
            sqsum = internal::getRowPtr(sqsumBase, sqsumStride, i);

            prev = v_zero;
            prevsq = 0.;
            j = 0u;

            for (; j + 7 < size.width; j += 8)
            {
                internal::prefetch(sqsum + j);
                internal::prefetch(sum + j);
                internal::prefetch(src + j);

                uint32x4_t vsuml = vld1q_u32(prevSum + j);
                uint32x4_t vsumh = vld1q_u32(prevSum + j + 4);

                uint8x8_t el8shr0 = vld1_u8(src + j);
                uint16x8_t sqel8shr0 = vmull_u8(el8shr0, el8shr0);
                uint8x8_t el8shr1 = vreinterpret_u8_u64(vshl_n_u64(vreinterpret_u64_u8(el8shr0), 8));
                uint8x8_t el8shr2 = vreinterpret_u8_u64(vshl_n_u64(vreinterpret_u64_u8(el8shr0), 16));
                uint8x8_t el8shr3 = vreinterpret_u8_u64(vshl_n_u64(vreinterpret_u64_u8(el8shr0), 24));

                vsuml = vaddq_u32(vsuml, prev);
                vsumh = vaddq_u32(vsumh, prev);

                uint16x8_t el8shr12 = vaddl_u8(el8shr1, el8shr2);
                uint16x8_t el8shr03 = vaddl_u8(el8shr0, el8shr3);

                uint16x8_t el8 = vaddq_u16(el8shr12, el8shr03);
                uint16x4_t el4h = vadd_u16(vget_low_u16(el8), vget_high_u16(el8));

                vsuml = vaddw_u16(vsuml, vget_low_u16(el8));
                vsumh = vaddw_u16(vsumh, el4h);

                vst1q_u32(sum + j, vsuml);
                vst1q_u32(sum + j + 4, vsumh);

                prev = vaddw_u16(prev, vdup_lane_u16(el4h, 3));


                uint16x8_t sqel8shr1 = vextq_u16(v_zero8, sqel8shr0, 7);

                uint32x4_t sqel8shr01l = vaddl_u16(vget_low_u16(sqel8shr0), vget_low_u16(sqel8shr1));
                uint32x4_t sqel8shr01h = vaddl_u16(vget_high_u16(sqel8shr0), vget_high_u16(sqel8shr1));

                uint32x4_t sqel4h = vaddq_u32(sqel8shr01l, sqel8shr01h);

                uint32x2_t sqel2l = vadd_u32(vget_low_u32(sqel8shr01l), vget_high_u32(sqel8shr01l));
                uint32x2_t sqel2hl = vadd_u32(vget_low_u32(sqel4h), vget_high_u32(sqel8shr01l));
                uint32x2_t sqel2hh = vadd_u32(vget_low_u32(sqel4h), vget_high_u32(sqel4h));

                uint32_t buf[8];
                vst1_u32(buf, vget_low_u32(sqel8shr01l));
                vst1_u32(buf + 2, sqel2l);
                vst1_u32(buf + 4, sqel2hl);
                vst1_u32(buf + 6, sqel2hh);
                for (uint32_t k = 0; k < 8; k++)
                    sqsum[j + k] = prevsq + prevSqSum[j + k] + buf[k];
                prevsq += buf[7];

            }

            for (uint32_t v = vgetq_lane_u32(prev, 3); j < size.width; ++j)
            {
                sum[j] = (v += src[j]) + prevSum[j];
                sqsum[j] = (prevsq += src[j] * src[j]) + prevSqSum[j];
            }
        }
    }