使用 SSE2 内在函数进一步优化此卡方函数的建议

Question

我正在尝试将 C 代码中的以下卡方函数转换为 SSE2 内在函数

我得到了这两个函数的正确输出。我使用生成的一些随机 4KB 数据测量了这两个函数运行所需的时间。平均而言，我发现性能提高了约 70-90 毫秒

我只是想知道是否有任何我缺少的进一步优化可以进一步提高性能。任何有关这方面的线索都会有帮助

普通 C 代码：

int observed[256] = {0};
        double chiSquare = 0.0;
        double expected = (double)size / 256; // Constant expected value
        // Calculate frequency of each byte value
        for (int i = 0; i < size; i++) {
            observed[data[i]]++;
        }
        // Calculate the chi-square statistic
        for (int i = 0; i < 256; i++) {
                double diff = observed[i] - expected;
                chiSquare += (diff * diff) / expected;
        }
        return chiSquare;

SSE2 内在函数：

int observed[256] = {0};
        const double expected = (double)size / 256;  // Make 'expected' a constant
        double chiSquare = 0.0;
        // Process data in 16-byte (128-bit) chunks
        for (int i = 0; i < size; i += 16) {
            __m128i dataChunk = _mm_loadu_si128((__m128i*)(data + i));
            // Unpack 8-bit values into 16-bit values for counting
            __m128i dataUnpacked = _mm_unpacklo_epi8(dataChunk, _mm_setzero_si128());
            // Extract and process 8 values in parallel
            for (int j = 0; j <= 1; j++) {
                uint16_t values[8];
                _mm_storeu_si128((__m128i*)values, dataUnpacked);
                for (int k = 0; k < 8; k++) {
                    observed[values[k]]++;
                }
                dataUnpacked = _mm_unpackhi_epi8(dataChunk, _mm_setzero_si128());
            }
        }
        // Calculate the chi-square statistic using SSE2 intrinsics
        __m128d sum = _mm_setzero_pd();
        for (int i = 0; i < 256; i += 2) {
            __m128d observedVec = _mm_set_pd(observed[i + 1], observed[i]);
            __m128d diff = _mm_sub_pd(observedVec, _mm_set1_pd(expected));
            __m128d squaredDiff = _mm_mul_pd(diff, diff);
            __m128d result = _mm_div_pd(squaredDiff, _mm_set1_pd(expected));
            sum = _mm_add_pd(sum, result);
        }
        // Sum up the results in the sum
        double sumArray[2];
        _mm_storeu_pd(sumArray, sum);
        for (int i = 0; i < 2; i++) {
            chiSquare += sumArray[i];
        }
        return chiSquare;
        }**

Answer 1

在我的 Westmere i5 笔记本电脑上，您的 SSE2 版本函数基准测试速度比您的标量函数慢（约 25%）。我对我的机器上的标量函数的性能做了轻微的改进（4KB 数据约提高了 20%）。另外，SSE2 函数并不适用于所有“大小”值，我相信您已经知道这一点。无论如何，我的功能如下。

double getchisquared(int size, uint8_t *data) {
        double diff, chiSquare = 0.0;
        double expected = (double)size / 256; // Constant expected value
        int i, iterations = (size >> 2) << 2;
        // Calculate frequency of each byte value
        for (i = 0; i < iterations;) {
            observed[data[i++]]++;
            observed[data[i++]]++;
            observed[data[i++]]++;
            observed[data[i++]]++;
        }
        for (i = iterations; i < size; i++) {
            observed[data[i]]++;
        }
        // Calculate the chi-square statistic        
        for (i = 0; i < 256; i++) {
                diff = observed[i] - expected;
                chiSquare += (diff * diff) ;
        }
        return chiSquare / expected;        
}     

我认为 SSE2 并没有像 chtz 指出的那样对直方图阶段的优化带来太大希望。你可能会更幸运地使用 AVX2，但我还没有调查过。