编译处理大量数字的时间斐波那契

Question

我正在玩这个 compile time implementation。

我使用 ttmath.org 来处理大数。 ttmath::UInt<SIZE> 适用于运行时间 fib() 功能但我不知道如何为我的元函数处理大数字，因为我必须更改非模板参数 size_t.

#include <iostream>
#include <omp.h>
#include <ctime>
#include "ttmath/ttmath.h"
#include <type_traits>

#define SIZE 1090

// how can I use ttmath here ?
template<size_t N>
struct fibonacci : std::integral_constant<size_t, fibonacci<N-1>{} + fibonacci<N-2>{}> {};

template<> struct fibonacci<1> : std::integral_constant<size_t,1> {};
template<> struct fibonacci<0> : std::integral_constant<size_t,0> {};


// ttmath here works well at run time !
ttmath::UInt<SIZE> fib(size_t n)
{
    ttmath::UInt<SIZE> a,b,c;
    a = 1, b = 1;
    for (size_t i = 3; i <= n; i++) {
        ttmath::UInt<SIZE> c = a + b;
        a = b;
        b = c;
    }           
    return b;
}

int main() {
    const size_t N = 500;
    if(1)
    {
    clock_t start = clock();
    std::cout <<  "Fibonacci(" << N << ") = " << fib(N) << std::endl;
    std::cout << "Time : " << (double)(clock() - start)/CLOCKS_PER_SEC << " s" << std::endl;
    }
    if(1)
    {
    clock_t start = clock();
    std::cout <<  "Fibonacci(" << N << ") = " << fibonacci<N>() << std::endl;
    std::cout << "Time : " << (double)(clock() - start)/CLOCKS_PER_SEC << " s" << std::endl;
    }
}

结果是：

Fibonacci(500) = 139423224561697880139724382870407283950070256587697307264108962948325571622863290691557658876222521294125
Time : 0.003006 s
Fibonacci(500) = 2171430676560690477
Time : 1.5e-05 s

那么是否可以轻松地为元斐波那契提供 ttmath？或者我应该以不同的方式做事吗？

Answer 1

如果您查看 ttmath 源，有一个 UInt<N>::Add 的定义，它遍历代表 UInt<N> 值的 uint 数组 table 添加每个元素对并将溢出传送到下一次迭代。基于这一迭代，可以定义一个递归模板化实现，如下所示：

#include <array> 
#include <ttmathuint.h> 

typedef unsigned int uint; 
namespace ttmath { 

    uint AddTwoUInt(uint a, uint b, uint carry, uint * result) 
    { 
        uint temp; 

        if( carry == 0 ) { 
            temp = a + b; 

            if( temp < a ) 
                carry = 1; 
        } else  { 
            carry = 1; 
            temp  = a + b + carry; 

            if( temp > a ) // !(temp<=a) 
                carry = 0; 
        } 

        *result = temp; 

        return carry; 
    } 

    template<uint N> 
    uint Add(const uint * t0, const uint * t1, uint * t2, uint c); 

    template<> 
    uint Add<1>(const uint * t0, const uint * t1, uint * t2, uint c)  { 
        uint i; 
        c = AddTwoUInt(*t0, *t1, c, t2); 
        return c; 
    } 

    template<uint N> 
    uint Add(const uint * t0, const uint * t1 , uint * t2, uint c) { 
        c = Add<N-1>(t0, t1, t2, c); 
        c = AddTwoUInt(t0[N-1], t1[N-1], c, t2+N-1); 
        return c; 
    } 

} 
template<int N> 
ttmath::UInt<N> fib(size_t n) 
{ 
 ttmath::UInt<N> a,b,c; 
 a = 1, b = 1; 

 for (size_t i = 3; i <= n; i++) { 
    ttmath::Add<N>(a.table,b.table,c.table,0); 
    a = b; 
    b = c; 
 }            
 return b;                           
} 

int main(int argc,char ** argv) { 
 std::cerr << fib<15>(500) << std::endl;
}

加就是斐波那契

编译处理大量数字的时间斐波那契

Compile time fibonacci which handle large numbers

c++

metaprogramming

fibonacci