用 cpp_int 建立巨大的提升 unordered_map

Question

我正在用 C++ 编写一些代码，用于 class 需要使用多精度库（例如 boost）的作业。基本上，我需要用一些大整数构建一个散列 table，然后在 table.

中查找某个值

当我使用被注释掉的 h、g、p 时 - 代码运行很好而且很快。一旦我切换到那些未被注释掉的那些，它就会在以下行抛出内存异常：hash_str>::iterator got = mp.find(lkp); 我刚开始使用 C++，并且很确定有些事情已经发生了，因为这应该运行相当快，即使有很大的数字。

#include <boost/unordered_map.hpp>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/math/special_functions/pow.hpp>

using namespace std;
using namespace boost::multiprecision;

template <typename T>
struct hash_str
{
    size_t operator()( const T& t ) const
    {
        return std::hash<std::string>()
            ( t.str() );
    }
};

int main()
{
    boost::unordered_map<cpp_int, cpp_int, hash_str<cpp_int>> mp;
    //boost::unordered_map<hash_str<cpp_int>, cpp_int, hash_str<cpp_int>> mp;
    cpp_int k;
    cpp_int h( "3239475104050450443565264378728065788649097520952449527834792452971981976143292558073856937958553180532878928001494706097394108577585732452307673444020333" );
    cpp_int g( "11717829880366207009516117596335367088558084999998952205599979459063929499736583746670572176471460312928594829675428279466566527115212748467589894601965568" );
    //cpp_int g = 1010343267;
    //cpp_int h = 857348958;
    //cpp_int p = 1073676287;
    cpp_int p( "13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084171" );
    int b = pow( 2, 20 );
    cpp_int denom;
    cpp_int inv = powm( g, p - 2, p );

    //building a hash table of all values h/g^x1
    for ( cpp_int x = 1; x < b; ++x )

    {
        // go through all 2^20 values up to b, calculate the function h/g^x1, 
        // then hash it to put into table

        denom = powm( inv, x, p );
        k = ( h *denom ) % p;
        mp.insert( std::make_pair( k, x ) );


    }
    cpp_int lkp;
    for ( int v = 1; v < b; ++v )
    {
        //cpp_int gb = pow(g, b);
        lkp = powm( g, v*b, p );
        //looking for a match for g^b^x0 in map mp; when found we need to find x 
        //which is x1 and then calc 'x'
        boost::unordered::unordered_map<cpp_int, cpp_int, hash_str<cpp_int>>::iterator got = mp.find( lkp );
        // Check if iterator points to end of map or if we found our value
        if ( got != mp.end() )
        {
            std::cout << "Element Found - ";
            //std::cout << got->first << "::" << got->second << std::endl;
        }
        /*else
        {
        std::cout << "Element Not Found" << std::endl;
        }*/
    }
    return 0;

}

以防万一，这是我得到的异常： MiM.exe 中 0x768F2F71 处的未处理异常：Microsoft C++ 异常：boost::exception_detail::clone_impl > 在内存位置 0x0109EF5C。

Answer 1

散列函数非常糟糕，因为它分配一个临时字符串只是为了对其进行散列。该字符串的长度为 log(bits)/log(10) 字节。

散列的要点在于它是一种相对比较数字的快速方法。对于如此昂贵的散列，您最好使用常规的 Tree 容器（std::map<> 例如）。

我没有检查你的公式（尤其是在 h/g^x1 附近，因为我什至不确定 x 代表 x1）。除了那个问题，
我认为 v * b 溢出 int 容量存在正确性问题，至少如果您使用的是 32 位整数编译器。

我稍微清理了一下，它运行了

#include <boost/math/special_functions/pow.hpp>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/unordered_map.hpp>
#include <chrono>

namespace bmp = boost::multiprecision;
using namespace std::chrono_literals;
using Clock = std::chrono::high_resolution_clock;

template <typename T> struct hash_str {
    size_t operator()(const T &t) const { return std::hash<std::string>()(t.str()); }
};

template <typename T> struct hash_bin {
    size_t operator()(const T &t) const {
        return boost::hash_range(t.backend().limbs(), t.backend().limbs()+t.backend().size());
    }
};
int main() {
    using bmp::cpp_int;
    boost::unordered_map<cpp_int, cpp_int, hash_bin<cpp_int> > mp;
#if 1
    cpp_int const h("32394751040504504435652643787280657886490975209524495278347924529719819761432925580738569379585531805328"
            "78928001494706097394108577585732452307673444020333");
    cpp_int const g("11717829880366207009516117596335367088558084999998952205599979459063929499736583746670572176471460312928"
            "594829675428279466566527115212748467589894601965568");
    cpp_int const p("13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690"
            "031858186486050853753882811946569946433649006084171");
#else
    cpp_int const g = 1010343267;
    cpp_int const h = 857348958;
    cpp_int const p = 1073676287;
#endif
    int constexpr b   = 1 << 20;
    cpp_int const inv = powm(g, p - 2, p);

    {
        auto s = Clock::now();

        // building a hash table of all values h/g^x1
        for (cpp_int x = 1; x < b; ++x) {
            // go through [1, b), calculate the function h/g^x1,
            // then hash it to put into table

            cpp_int denom = powm(inv, x, p);
            cpp_int k = (h * denom) % p;
            mp.emplace(std::move(k), x);
        }

        std::cout << "Built map in " << (Clock::now() - s)/1.0s << "s\n";
    }

    {
        auto s = Clock::now();

        for (cpp_int v = 1; v < b; ++v) {
            //std::cout << "v=" << v << " b=" << b << "\n";
            // cpp_int gb = pow(g, b);
            cpp_int const lkp = powm(g, v * b, p);

            // looking for a match for g^b^x0 in map mp; when found we need to find x
            // which is x1 and then calc 'x'
            auto got = mp.find(lkp);

            // Check if iterator points to end of map or if we found our value
            if (got != mp.end()) {
                std::cout << "Element Found - ";
                //std::cout << got->first << " :: " << got->second << "\n";
            }
        }
        std::cout << "Completed queries in " << (Clock::now() - s)/1.0s << "s\n";
    }
}

它对我来说是 1 分钟 4 秒。

Built map in 24.3809s
Element Found - Completed queries in 39.2463s
...

使用 hash_str 而不是 hash_bin 需要 1 分 13 秒：

Built map in 30.3923s
Element Found - Completed queries in 42.488s

用 cpp_int 建立巨大的提升 unordered_map

Building a large boost unordered_map with cpp_int

c++

boost

unordered-map

boost-multiprecision