例如,乘法和除法可以使用位运算符来实现

i*2 = i<<1
i*3 = (i<<1) + i;
i*10 = (i<<3) + (i<<1)

等等。

用say (i<<3)+(i<<1)乘10是否比直接用i*10更快?有没有什么输入是不能用这种方法乘或除的?


当前回答

这取决于处理器和编译器。一些编译器已经通过这种方式优化代码了,其他的还没有。 因此,每次需要以这种方式优化代码时,您都需要检查。

除非您迫切需要优化,否则我不会为了节省汇编指令或处理器周期而打乱源代码。

其他回答

不要这样做,除非你绝对需要这样做,并且你的代码意图是移位而不是乘法/除法。

在典型的日子里,你可能会节省一些机器周期(或松弛,因为编译器更知道优化什么),但成本并不值得——你把时间花在小细节上而不是实际的工作上,维护代码变得更加困难,你的同事会诅咒你。

对于高负载计算,您可能需要这样做,其中每个节省的周期意味着几分钟的运行时。但是,您应该一次优化一个地方,并每次都进行性能测试,看看您是否真的使它更快了,还是破坏了编译器逻辑。

如果在gcc编译器上比较x+x, x*2和x<<1语法的输出,那么在x86汇编中会得到相同的结果:https://godbolt.org/z/JLpp0j

        push    rbp
        mov     rbp, rsp
        mov     DWORD PTR [rbp-4], edi
        mov     eax, DWORD PTR [rbp-4]
        add     eax, eax
        pop     rbp
        ret

因此,您可以认为gcc足够聪明,可以独立于您输入的内容确定自己的最佳解决方案。

有些优化编译器无法做到,因为它们只适用于减少的输入集。

下面是c++示例代码,可以执行更快的除法,执行64位“乘倒数”。分子和分母都必须低于某个阈值。注意,它必须被编译为使用64位指令才能比普通除法更快。

#include <stdio.h>
#include <chrono>

static const unsigned s_bc = 32;
static const unsigned long long s_p = 1ULL << s_bc;
static const unsigned long long s_hp = s_p / 2;

static unsigned long long s_f;
static unsigned long long s_fr;

static void fastDivInitialize(const unsigned d)
{
    s_f = s_p / d;
    s_fr = s_f * (s_p - (s_f * d));
}

static unsigned fastDiv(const unsigned n)
{
    return (s_f * n + ((s_fr * n + s_hp) >> s_bc)) >> s_bc;
}

static bool fastDivCheck(const unsigned n, const unsigned d)
{
    // 32 to 64 cycles latency on modern cpus
    const unsigned expected = n / d;

    // At least 10 cycles latency on modern cpus
    const unsigned result = fastDiv(n);

    if (result != expected)
    {
        printf("Failed for: %u/%u != %u\n", n, d, expected);
        return false;
    }

    return true;
}

int main()
{
    unsigned result = 0;

    // Make sure to verify it works for your expected set of inputs
    const unsigned MAX_N = 65535;
    const unsigned MAX_D = 40000;

    const double ONE_SECOND_COUNT = 1000000000.0;

    auto t0 = std::chrono::steady_clock::now();
    unsigned count = 0;
    printf("Verifying...\n");
    for (unsigned d = 1; d <= MAX_D; ++d)
    {
        fastDivInitialize(d);
        for (unsigned n = 0; n <= MAX_N; ++n)
        {
            count += !fastDivCheck(n, d);
        }
    }
    auto t1 = std::chrono::steady_clock::now();
    printf("Errors: %u / %u (%.4fs)\n", count, MAX_D * (MAX_N + 1), (t1 - t0).count() / ONE_SECOND_COUNT);

    t0 = t1;
    for (unsigned d = 1; d <= MAX_D; ++d)
    {
        fastDivInitialize(d);
        for (unsigned n = 0; n <= MAX_N; ++n)
        {
            result += fastDiv(n);
        }
    }
    t1 = std::chrono::steady_clock::now();
    printf("Fast division time: %.4fs\n", (t1 - t0).count() / ONE_SECOND_COUNT);

    t0 = t1;
    count = 0;
    for (unsigned d = 1; d <= MAX_D; ++d)
    {
        for (unsigned n = 0; n <= MAX_N; ++n)
        {
            result += n / d;
        }
    }
    t1 = std::chrono::steady_clock::now();
    printf("Normal division time: %.4fs\n", (t1 - t0).count() / ONE_SECOND_COUNT);

    getchar();
    return result;
}

我同意德鲁·霍尔的明确回答。不过,答案可能需要一些额外的注释。

对于绝大多数软件开发人员来说,处理器和编译器已经不再与问题相关。我们大多数人远远超出了8088和MS-DOS。它可能只与那些仍在开发嵌入式处理器的人有关……

在我的软件公司,Math (add/sub/mul/div)应该用于所有数学。 当数据类型之间转换时应该使用Shift。字节长度为n>>8,而不是n/256。

I think in the one case that you want to multiply or divide by a power of two, you can't go wrong with using bitshift operators, even if the compiler converts them to a MUL/DIV, because some processors microcode (really, a macro) them anyway, so for those cases you will achieve an improvement, especially if the shift is more than 1. Or more explicitly, if the CPU has no bitshift operators, it will be a MUL/DIV anyway, but if the CPU has bitshift operators, you avoid a microcode branch and this is a few instructions less.

I am writing some code right now that requires a lot of doubling/halving operations because it is working on a dense binary tree, and there is one more operation that I suspect might be more optimal than an addition - a left (power of two multiply) shift with an addition. This can be replaced with a left shift and an xor if the shift is wider than the number of bits you want to add, easy example is (i<<1)^1, which adds one to a doubled value. This does not of course apply to a right shift (power of two divide) because only a left (little endian) shift fills the gap with zeros.

在我的代码中,这些乘/除2和2的幂运算被大量使用,因为公式已经很短了,每条可以消除的指令都可以获得很大的收益。如果处理器不支持这些位移操作符,就不会有增益,也不会有损失。

Also, in the algorithms I am writing, they visually represent the movements that occur so in that sense they are in fact more clear. The left hand side of a binary tree is bigger, and the right is smaller. As well as that, in my code, odd and even numbers have a special significance, and all left-hand children in the tree are odd and all right hand children, and the root, are even. In some cases, which I haven't encountered yet, but may, oh, actually, I didn't even think of this, x&1 may be a more optimal operation compared to x%2. x&1 on an even number will produce zero, but will produce 1 for an odd number.

再深入一点,如果x和3是0,我就知道4是这个数的因数,x%7是8,以此类推。我知道这些情况可能有有限的效用,但很高兴知道你可以避免模运算而使用按位逻辑运算,因为按位运算几乎总是最快的,而且对编译器来说不太可能是模糊的。

我在很大程度上发明了密集二叉树的领域,所以我预计人们可能不会理解这个评论的价值,因为很少有人想只对2的幂进行因数分解,或者只对2的幂进行乘/除。