http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems”rel=“noreferer” Floating Point Math is not Associative. 您将歌剧归入浮动点复制方式,对答案的准确性产生影响。

As a result, most compilers are very conservative about reordering floating point calculations unless they can be sure that the answer will stay the same, or unless you tell them you don t care about numerical accuracy. For example: the -fassociative-math option of gcc which allows gcc to reassociate floating point operations, or even the -ffast-math option which allows even more aggressive tradeoffs of accuracy against speed.

>>Lambdageek 正确地指出,由于协会不持有浮动点编号,<代码>a*a*a*a*a*a*a*a*a*a至<代码>(a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a>>>的“优化”可改变该数值。 因此,C99(除非用户特别允许,通过编造旗或花旗)不予允许。 总的说来,假设方案管理员是出于某种原因撰写的,汇编者应当尊重这一点。 如果你想要<代码>(a*a*a)*(a*a),则写上。

这可能是难以书写的;为什么在你使用<代码>pow(a,6)时,汇编者只能做什么? 因为这将是wrong的事情。 在有良好数学图书馆的平台上,pow(a,6)比a*a*a*a*a*a*a或(a*a*a*a*a*a*a>>。 就提供一些数据而言,我对我的Ma Pro进行了小规模试验,测量了在[1,2]之间所有单程浮标数的^6评估中最差的错误:

worst relative error using    powf(a, 6.f): 5.96e-08
worst relative error using (a*a*a)*(a*a*a): 2.94e-07
worst relative error using     a*a*a*a*a*a: 2.58e-07

使用<代码>pow而不是多倍树,减少受4因素约束的错误。 编审员不应(而且通常不)作出“优化”来增加错误,除非用户许可(例如通过<代码>-ffast-math)。

注:海湾合作委员会提供<代码>_builtin_powi(x,n),作为pow( )的替代品,该替代法应产生一条网上复制树。 如果你想对业绩的准确性进行交易,但并不希望能够快速计算。

Another similar case: most compilers won t optimize a + b + c + d to (a + b) + (c + d) (this is an optimization since the second expression can be pipelined better) and evaluate it as given (i.e. as (((a + b) + c) + d)). This too is because of corner cases:

float a = 1e35, b = 1e-5, c = -1e35, d = 1e-5;
printf("%e %e
", a + b + c + d, (a + b) + (c + d));

这一产出<000000e-05>0.000000e+00<0>/code>

Fortran (designed for scientific computing) has a built-in power operator, and as far as I know Fortran compilers will commonly optimize raising to integer powers in a similar fashion to what you describe. C/C++ unfortunately don t have a power operator, only the library function pow(). This doesn t prevent smart compilers from treating pow specially and computing it in a faster way for special cases, but it seems they do it less commonly ...

几年前,我试图使以最佳方式计算愤怒权力更加方便,并得出以下结论。 它是C++,但并非C,仍然取决于汇编者如何优化/在线工作。 不管怎么说,希望你实际上会认为它有用:

template<unsigned N> struct power_impl;

template<unsigned N> struct power_impl {
    template<typename T>
    static T calc(const T &x) {
        if (N%2 == 0)
            return power_impl<N/2>::calc(x*x);
        else if (N%3 == 0)
            return power_impl<N/3>::calc(x*x*x);
        return power_impl<N-1>::calc(x)*x;
    }
};

template<> struct power_impl<0> {
    template<typename T>
    static T calc(const T &) { return 1; }
};

template<unsigned N, typename T>
inline T power(const T &x) {
    return power_impl<N>::calc(x);
}

_{Clarification for the curious: this does not find the optimal way to compute powers, but since finding the optimal solution is an NP-complete problem and this is only worth doing for small powers anyway (as opposed to using pow), there s no reason to fuss with the detail.}

然后仅将其用作<代码>的功率与lt;6> (a)。

这使权力的类型容易(无需列出6条<代码>a>>,而如果你有某种精准性,如,则请在<代码>-ffast-math/code>上作这种优化。 (行动次序至关重要的例子)。

    movapd  %xmm1, %xmm0
    mulsd   %xmm1, %xmm0
    mulsd   %xmm1, %xmm0
    mulsd   %xmm1, %xmm0
    mulsd   %xmm1, %xmm0
    mulsd   %xmm1, %xmm0

    movapd  %xmm1, %xmm0
    mulsd   %xmm1, %xmm0
    mulsd   %xmm1, %xmm0
    mulsd   %xmm0, %xmm0

    mulsd   %xmm0, %xmm0
    movapd  %xmm0, %xmm1
    mulsd   %xmm0, %xmm1
    mulsd   %xmm0, %xmm1

海湾合作委员会不支持这一 p,但以缺省办法假定它为ON<>/code>;因此,如果想要防止向fma(a,b,c)转变<条码>,则需要提供一种选择,例如<条码>-ffp- Contracting=off。 (将pragma明确定为OFF)或-std=c99 (请海合会遵守C标准版本,此处为C99,从而遵循上述段落)。 过去,后一种选择并不阻止这一转变,即海合会在此问题上并不一致:https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37845

图书馆的职能,如“影子”,通常精心设计,以产生尽可能少的错误(一般情况下)。 这通常与间谍职能相近(根据Pascal的评论,最常见的执行似乎使用Remez算法)。

pow(x,y);

float a=someValue;
float b=a*a*a*a*a*a;