c - 是否可以在 C 中优化并更快地将数组乘以数字？

Question

我有一个 C 代码，它将数组的每个元素乘以一个数字 (0-9)，得到一系列 10 进制数字。

我的问题是这个函数的运行时间比我预期的要长。我需要它更快。 我知道在优化函数时我的问题是进位的依赖性。如何修改这段代码来解决这个问题并使代码更快？ 该解决方案可以使用内在函数或其他专门技术。

到目前为止我最快的版本是这样的:

void ConstMult( uint8_t *V, size_t N, uint8_t digit )
{
  uint8_t CARRY = 0;
  for ( size_t i=0; i< N; ++i )
  {
    V[i] = V[i] * digit + CARRY;
    CARRY = ((uint32_t)V[i] * (uint32_t)0xCCCD) >> 19;
    V[i] -= (CARRY << 3) + (CARRY << 1);
  }
}

但我也尝试了这些速度较慢的方法:

uint8_t ConstMult( uint8_t *V, size_t N, uint8_t digit )
{
  uint8_t CARRY = 0;
  for ( int i=0; i< N; i++ ) 
  {
    char R = V[i] * digit + CARRY;
    CARRY = R / 10;
    R = R - CARRY*10;
    V[i] = R;
  }
  return CARRY; // may be from 0 to 9
}

uint8_t ConstMult(uint8_t *V, size_t N, uint8_t digit)
{
  uint8_t CARRY = 0;
  uint8_t ja = 0;
  for (size_t i = 0; i < N; ++i) {
    uint8_t aux = V[i] * digit;
    uint8_t R = aux + CARRY;
    CARRY = ((u_int32_t)R*(u_int32_t)0xCCCD) >> 19;
    ja = (CARRY << 3) + 2*CARRY;
    R -= ja;
    V[i] = R;
  }
  return CARRY;
}

Answer 1

这是另一个实现(比其他实现快得多):

void ConstMult4(uint8_t *V, size_t N, uint8_t digit)
{
    uint8_t CARRY = 0;

    const uint32_t coef7  = digit * 10000000;
    const uint32_t coef6  = digit * 1000000;
    const uint32_t coef5  = digit * 100000;
    const uint32_t coef4  = digit * 10000;
    const uint32_t coef3  = digit * 1000;
    const uint32_t coef2  = digit * 100;
    const uint32_t coef1  = digit * 10;
    const uint32_t coef0  = digit;

    static uint8_t table[10000][4];
    static int init = 1;

    if(init)
    {
        for(int i=0 ; i<10000 ; ++i)
        {
            table[i][0] = (i / 1) % 10;
            table[i][1] = (i / 10) % 10;
            table[i][2] = (i / 100) % 10;
            table[i][3] = (i / 1000) % 10;
        }

        init = 0;
    }

    for(size_t i=0 ; i<N/8*8 ; i+=8)
    {
        const uint32_t val = V[i+7]*coef7 + V[i+6]*coef6 + V[i+5]*coef5 + V[i+4]*coef4 + V[i+3]*coef3 + V[i+2]*coef2 + V[i+1]*coef1 + V[i+0]*coef0 + CARRY;

        CARRY = val / 100000000;

        const uint32_t loVal = val % 10000;
        const uint32_t hiVal = val / 10000 - CARRY * 10000;
        const uint8_t* loTablePtr = &table[loVal][0];
        const uint8_t* hiTablePtr = &table[hiVal][0];

        // Assume the compiler optimize the 2 following calls
        // (otherwise the performance could be quite bad).
        // memcpy is used to prevent performance issue due to pointer aliasing. 
        memcpy(V+i, loTablePtr, 4);
        memcpy(V+i+4, hiTablePtr, 4);
    }

    for(size_t i=N/8*8 ; i<N ; ++i)
    {
        V[i] = V[i] * digit + CARRY;
        CARRY = V[i] / 10;
        V[i] -= CARRY * 10;
    }
}

此实现假设 V 和 digit 中计算的数字实际上是数字。 它比其他方法要快得多:

• 按照 @phuclv 的建议在内部使用更大的基础(它减少了关键路径并引入了更多并行性)；
• 使用@chqrlieforyellowblockquotes建议的查找表(它可以非常快速地计算除法/模运算)。

甚至可以通过使用 SSE 4.1 内在函数(SIMD 指令)来改进此代码。但代价是代码的可移植性较差(尽管它可以在大多数现代基于 x86_64 的处理器上运行)。这是实现:

void ConstMult5(uint8_t *V, size_t N, uint8_t digit)
{
    uint8_t CARRY = 0;

    static uint8_t table[10000][4];
    static int init = 1;

    if(init)
    {
        for(int i=0 ; i<10000 ; ++i)
        {
            table[i][0] = (i / 1) % 10;
            table[i][1] = (i / 10) % 10;
            table[i][2] = (i / 100) % 10;
            table[i][3] = (i / 1000) % 10;
        }

        init = 0;
    }

    __m128i coefs1 = _mm_set_epi16(1000, 100, 10, 1, 1000, 100, 10, 1);
    __m128i coefs2 = _mm_set_epi32(10000*digit, 10000*digit, digit, digit);

    for(size_t i=0 ; i<N/16*16 ; i+=8)
    {
        // Require SSE 4.1 (thus smmintrin.h need to be included)
        const __m128i vBlock = _mm_loadu_si128((const __m128i*)&V[i]); // load 16 x uint8_t values (only half is used)
        const __m128i v = _mm_cvtepu8_epi16(vBlock); // Convert the block to 8 x int16_t values
        const __m128i tmp1 = _mm_madd_epi16(v, coefs1); // Compute the sum of adjacent pairs of v * coefs1 and put this in 4 x int32_t values
        const __m128i tmp2 = _mm_add_epi32(tmp1, _mm_shuffle_epi32(tmp1, 0b10110001)); // Horizontal partial sum of 4 x int32_t values
        const __m128i tmp3 = _mm_mul_epu32(tmp2, coefs2); // Compute tmp2 * coefs2 and put this in 2 x int64_t values
        const uint32_t val = _mm_extract_epi64(tmp3, 1) + _mm_extract_epi64(tmp3, 0) + CARRY; // Final horizontal sum with CARRY

        CARRY = val / 100000000;

        const uint32_t loVal = val % 10000;
        const uint32_t hiVal = val / 10000 - CARRY * 10000;
        const uint8_t* loTablePtr = &table[loVal][0];
        const uint8_t* hiTablePtr = &table[hiVal][0];

        // See the memcpy remark in the code above (alternative version).
        memcpy(V+i, loTablePtr, 4);
        memcpy(V+i+4, hiTablePtr, 4);
    }

    for(size_t i=N/16*16 ; i<N ; ++i)
    {
        V[i] = V[i] * digit + CARRY;
        CARRY = V[i] / 10;
        V[i] -= CARRY * 10;
    }
}

以下是我的机器(配备 i7-9700KF 处理器)上的性能结果(使用随机输入重复运行 1000 次并取平均值):

ConstMult0(10000): 11.702 us
ConstMult3(10000): 6.768 us (last optimized version)
ConstMult4(10000): 3.569 us
ConstMult5(10000): 2.552 us

基于 SSE 的最终版本比原始实现快 4.6 倍!