在 unsigned long long 上编译时模板化 C++ 计算？双打？

Question

我使用编译时 int powers 计算 Power，来计算 n**p。它使用整数。 我想计算比 int 更大的东西，好吗？ 它适合 u64（无符号长长）。 C++ 模板可以在 u64 上进行编译时计算吗？枚举无法做到这一点。 双打？可能吗？

我真的希望类型是模板的 arg。可能吗 ？ 我的编译器不是 c++0x。

谢谢 安德烈

template<int N, int P> struct Power {
   enum { val = N * Power<N, P-1>::val };
};

template<int N> struct Power<N, 0> {
   enum { val = 1 };
};

int result = Power<2, 5>; // 2**5 == 32

Answer 1

是的，您可以对任何原始整数类型进行编译时计算。但是，您不能对浮点值进行计算，因为模板不能在这些值上进行参数化。即将推出的 C++0x 标准将引入特殊类来执行编译时有理算术，因此您可以根据需要使用它。

Answer 2

为了扩展 sbi 的实现，这里有一个通过平方求幂（它需要更少的模板实例化来实现大幂）。

请注意，如果您真的只想计算 2 的幂，最好只左移（即2**x == 1 << x）而不是做所有这些模板的东西。

#include <iostream>

template <unsigned long long N, unsigned int P, int Odd = (P&1)> struct Power;

template <unsigned long long N, unsigned int P>
struct Power<N,P,0> { // even (square N and halve the power)
    static const unsigned long long val = Power<N*N,(P/2)>::val;
};

template <unsigned long long N, unsigned int P>
struct Power<N,P,1> { // odd (multiply by N and decrement the power)
    static const unsigned long long val = N * Power<N,(P-1)>::val;
};

template <unsigned long long N>
struct Power<N,0,0> { // zero (x**0 is 1 for all x != 0)
    static const unsigned long long val = 1;
};

int main() {
    std::cout << "2**0 = " << Power<2,0>::val << "\n";
    std::cout << "2**1 = " << Power<2,1>::val << "\n";
    std::cout << "2**2 = " << Power<2,2>::val << "\n";
    std::cout << "2**3 = " << Power<2,3>::val << "\n";
    std::cout << "2**4 = " << Power<2,4>::val << "\n";
    std::cout << "2**5 = " << Power<2,5>::val << "\n";
    std::cout << "2**6 = " << Power<2,6>::val << "\n";
    std::cout << "2**7 = " << Power<2,7>::val << "\n";
    std::cout << "2**8 = " << Power<2,8>::val << "\n";
    std::cout << "2**9 = " << Power<2,9>::val << "\n";
    std::cout << "2**10 = " << Power<2,10>::val << "\n";
    std::cout << "2**11 = " << Power<2,11>::val << "\n";
    std::cout << "2**12 = " << Power<2,12>::val << "\n";
    std::cout << "2**30 = " << Power<2,30>::val << "\n";
    std::cout << "2**40 = " << Power<2,40>::val << "\n";
    std::cout << "2**50 = " << Power<2,50>::val << "\n";
    std::cout << "2**60 = " << Power<2,60>::val << "\n";
    return 0;
}

免责声明：我没有声称由于模板实例化数量的减少，这段代码一定会编译得更快（尽管它可能会）。我真的只是把它写成一个玩具演示。我将其作为练习留给读者编写一个版本，该版本在使用Power<> 时不会被显式传递Odd 参数值的人所攻击。

Answer 3

您可以使用多精度数学来计算大数（在下面的示例中，我使用带有 3 个模板参数的 96 位计算，您可以使用任何常数）。您需要有多个整数作为模板参数。

在执行编译时乘法时，您可能应该将 32 位数字相乘，得到 64 位结果；结果应该被分成2个模板参数。

溢出检查可能是可能的，但可能很棘手。

const uint64_t W = 1000000000; // word size: 2^32 is best; any smaller number is OK
// I use a power of 10 as word size for ease of printing (see main() below)

// The following class performs multiplication of (n0 + W*n1 + W*W*n2) by (base)
template <unsigned n0, unsigned n1, unsigned n2, uint64_t base, unsigned p> class power_temp
{
    typedef power_temp<
        n0 * base % W,
        n1 * base % W + n0 * base / W,
        n2 * base % W + n1 * base / W,
        base, p - 1> mult_type;
public:
    static const unsigned x0 = mult_type::x0;
    static const unsigned x1 = mult_type::x1;
    static const unsigned x2 = mult_type::x2;
};

// The following partial specialization is used to end recursion
template <unsigned n0, unsigned n1, unsigned n2, uint64_t base>
class power_temp<n0, n1, n2, base, 0>
{
public:
    static const unsigned x0 = n0;
    static const unsigned x1 = n1;
    static const unsigned x2 = n2;
};

// The following class calculates a power, using compile-time calculations
template <unsigned base, unsigned p> struct power
{
    static const unsigned x0 = power_temp<1, 0, 0, base, p>::x0;
    static const unsigned x1 = power_temp<1, 0, 0, base, p>::x1;
    static const unsigned x2 = power_temp<1, 0, 0, base, p>::x2;
};

int main()
{
    typedef power<123456789, 3> my1;
    printf("%09d%09d%09d\n", my1::x2, my1::x1, my1::x0);

    typedef power<5, 33> my2;
    printf("%09d%09d%09d\n", my2::x2, my2::x1, my2::x0);
}

Answer 4

template<int N, unsigned int P> struct Power {
   static const unsigned long long val = N * Power<N, P-1>::val;
};

template<int N> struct Power<N, 0> {
   static const unsigned long long val = 1;
}

请注意，我将P 设为unsigned int，因为您的模板会因负值而失败。