散列表

在这里插入图片描述

hash 函数

计算速度快
强随机分布（等概率、均匀地分布在整个地址空间）

种类：

murmurhash1，速度最快，质量一般
murmurhash2，速度可以，质量可以（通常使用）
murmurhash3，速度最慢，质量最好
siphash（ redis6.0 当中使用，rust 等大多数语言选用的 hash 算法来实现 hashmap）siphash 主要解决字符串接近的强随机分布性 ;（10001，10002）
cityhash 都具备强随机分布性；测试地址如下：
https://github.com/aappleby/smhasher

布隆过滤器

在这里插入图片描述

是高效地插入和查询，能确定某个字符串一定不存在或者可能存在；不能删除！

场景：

内存有限，只想确定某个key存不存在，不想知道具体内容。
某个文件是否存在---------->数据库rockdb，某个数据库是否存在。

构成

在这里插入图片描述

原理

当一个元素加入位图时，通过 k 个 hash 函数将这个元素映射到位图的 k 个点，并把它们置为 1；当检索时，再通过 k 个 hash函数运算检测位图的 k 个点是否都为 1；如果有不为 1 的点，那么认为该 key 不存在；如果全部为 1，则可能存在；

为什么不支持删除操作？
在位图中每个槽位只有两种状态（0 或者 1），一个槽位被设置为 1 状态，但不确定它被设置了多少次；也就是不知道
被多少个 key 哈希映射而来以及是被具体哪个 hash 函数映射而来；
不存在只要一个索引位为0；如果都为1，是否一定存在？
不一定，可控的（假阳率）；
在这里插入图片描述

应用分析

n – 预期布隆过滤器中元素的个数，如上图只有str1和str2 两
个元素那么 n=2
p – 假阳率，在0-1之间 0.000000
m – 位图所占空间
k – hash函数的个数

确定 n 和 p
在实际使用布隆过滤器时，首先需要确定 n 和 p，通过上面的运算得出 m 和 k；通常可以在下面这个网站上选出合适的值；
https://hur.st/bloomfilter
在这里插入图片描述

31左右假阳率最低。

选择 hash 函数

选择一个 hash 函数，通过给 hash 传递不同的种子偏移值，采用线性探寻的方式构造多个 hash 函数；

#define MIX_UINT64(v) ((uint32_t)((v>>32)^(v)))
uint64_t hash1 = MurmurHash2_x64(key, len, Seed);//seed就是salt值
uint64_t hash2 = MurmurHash2_x64(key, len,
MIX_UINT64(hash1));
for (i = 0; i < k; i++) // k 是hash函数的个数
{
     Pos[i] = (hash1 + i*hash2) % m; // m 是位图的
⼤⼩
}

问题：只用2GB内存在20亿个整数中找到出现次数最多的数

假设一个数重复出现了20亿次,因为整数的范围是-2³¹~2^31-1 大约21亿,所以4个字节可以统计

1、用到HashMap数据结构,因为是整数类型,key为4B value为4B,和为8B

1.6GB大概能存储2亿数据（1.6G/8=2亿）
因为整数共42亿个（-21亿到21亿），按照2亿的间隔划分成21个小文件，再对这21个小文件进行统计

2、如果这20 亿个数数值比较集中的话，例如都处于 1~20000000 之间，那么你都会把他们全部映射到同一个文件中,存不了这么多，怎么解决？
那我可以先把每个数先做哈希函数映射，根据哈希函数得到的哈希值，再把他们存放到对应的文件中，如果哈希函数设计到好的话，那么这些数就会分布的比较平均。

3、如果是40亿呢？
扩大文件数目到42个文件，但是可能该数字出现次数超过了int类型的范围，怎么办？可以将value初始化为-21亿，这样如果value是21亿则表明出现了42亿次。

4、80亿？
可以一边遍历一遍判断啊，如果我在统计的过程中，发现某个 key 出现的次数超过了 40 亿次，那么，就不可能再有另外一个 key 出现的次数比它多了，那我直接把这个 key 返回就搞定了。

5、类似“大”问题：
大文件 hash 拆成小文件
单台机器 hash 分流到多台机器

完整代码：

bloom_filter.hpp

/*
 *********************************************************************
 *                                                                   *
 *                           Open Bloom Filter                       *
 *                                                                   *
 * Author: Arash Partow - 2000                                       *
 * URL: http://www.partow.net                                        *
 * URL: http://www.partow.net/programming/hashfunctions/index.html   *
 *                                                                   *
 * Copyright notice:                                                 *
 * Free use of the Open Bloom Filter Library is permitted under the  *
 * guidelines and in accordance with the MIT License.                *
 * http://www.opensource.org/licenses/MIT                            *
 *                                                                   *
 *********************************************************************
*/


#ifndef INCLUDE_BLOOM_FILTER_HPP
#define INCLUDE_BLOOM_FILTER_HPP

#include <algorithm>
#include <cmath>
#include <cstddef>
#include <cstdlib>
#include <iterator>
#include <limits>
#include <string>
#include <vector>


static const std::size_t bits_per_char = 0x08;    // 8 bits in 1 char(unsigned)

static const unsigned char bit_mask[bits_per_char] = {
                                                       0x01,  //00000001
                                                       0x02,  //00000010
                                                       0x04,  //00000100
                                                       0x08,  //00001000
                                                       0x10,  //00010000
                                                       0x20,  //00100000
                                                       0x40,  //01000000
                                                       0x80   //10000000
                                                     };

class bloom_parameters
{
public:

   bloom_parameters()
   : minimum_size(1),
     maximum_size(std::numeric_limits<unsigned long long int>::max()),
     minimum_number_of_hashes(1),
     maximum_number_of_hashes(std::numeric_limits<unsigned int>::max()),
     projected_element_count(10000),
     false_positive_probability(1.0 / projected_element_count),
     random_seed(0xA5A5A5A55A5A5A5AULL)
   {}

   virtual ~bloom_parameters()
   {}

   inline bool operator!()
   {
      return (minimum_size > maximum_size)      ||
             (minimum_number_of_hashes > maximum_number_of_hashes) ||
             (minimum_number_of_hashes < 1)     ||
             (0 == maximum_number_of_hashes)    ||
             (0 == projected_element_count)     ||
             (false_positive_probability < 0.0) ||
             (std::numeric_limits<double>::infinity() == std::abs(false_positive_probability)) ||
             (0 == random_seed)                 ||
             (0xFFFFFFFFFFFFFFFFULL == random_seed);
   }

   // Allowable min/max size of the bloom filter in bits
   unsigned long long int minimum_size;
   unsigned long long int maximum_size;

   // Allowable min/max number of hash functions
   unsigned int minimum_number_of_hashes;
   unsigned int maximum_number_of_hashes;

   // The approximate number of elements to be inserted
   // into the bloom filter, should be within one order
   // of magnitude. The default is 10000.
   unsigned long long int projected_element_count;

   // The approximate false positive probability expected
   // from the bloom filter. The default is assumed to be
   // the reciprocal of the projected_element_count.
   double false_positive_probability;

   unsigned long long int random_seed;

   struct optimal_parameters_t
   {
      optimal_parameters_t()
      : number_of_hashes(0),
        table_size(0)
      {}

      unsigned int number_of_hashes;
      unsigned long long int table_size;
   };

   optimal_parameters_t optimal_parameters;

   virtual bool compute_optimal_parameters()
   {
      /*
        Note:
        The following will attempt to find the number of hash functions
        and minimum amount of storage bits required to construct a bloom
        filter consistent with the user defined false positive probability
        and estimated element insertion count.
      */

      if (!(*this))
         return false;

      double min_m  = std::numeric_limits<double>::infinity();
      double min_k  = 0.0;
      double k      = 1.0;

      while (k < 1000.0)
      {
         const double numerator   = (- k * projected_element_count);
         const double denominator = std::log(1.0 - std::pow(false_positive_probability, 1.0 / k));

         const double curr_m = numerator / denominator;

         if (curr_m < min_m)
         {
            min_m = curr_m;
            min_k = k;
         }

         k += 1.0;
      }

      optimal_parameters_t& optp = optimal_parameters;

      optp.number_of_hashes = static_cast<unsigned int>(min_k);

      optp.table_size = static_cast<unsigned long long int>(min_m);

      optp.table_size += (((optp.table_size % bits_per_char) != 0) ? (bits_per_char - (optp.table_size % bits_per_char)) : 0);

      if (optp.number_of_hashes < minimum_number_of_hashes)
         optp.number_of_hashes = minimum_number_of_hashes;
      else if (optp.number_of_hashes > maximum_number_of_hashes)
         optp.number_of_hashes = maximum_number_of_hashes;

      if (optp.table_size < minimum_size)
         optp.table_size = minimum_size;
      else if (optp.table_size > maximum_size)
         optp.table_size = maximum_size;

      return true;
   }

};

class bloom_filter
{
protected:

   typedef unsigned int bloom_type;
   typedef unsigned char cell_type;
   typedef std::vector<unsigned char> table_type;

public:

   bloom_filter()
   : salt_count_(0),
     table_size_(0),
     projected_element_count_(0),
     inserted_element_count_ (0),
     random_seed_(0),
     desired_false_positive_probability_(0.0)
   {}

   bloom_filter(const bloom_parameters& p)
   : projected_element_count_(p.projected_element_count),
     inserted_element_count_(0),
     random_seed_((p.random_seed * 0xA5A5A5A5) + 1),
     desired_false_positive_probability_(p.false_positive_probability)
   {
      salt_count_ = p.optimal_parameters.number_of_hashes;
      table_size_ = p.optimal_parameters.table_size;

      generate_unique_salt();

      bit_table_.resize(table_size_ / bits_per_char, static_cast<unsigned char>(0x00));
   }

   bloom_filter(const bloom_filter& filter)
   {
      this->operator=(filter);
   }

   inline bool operator == (const bloom_filter& f) const
   {
      if (this != &f)
      {
         return
            (salt_count_                         == f.salt_count_                        ) &&
            (table_size_                         == f.table_size_                        ) &&
            (bit_table_.size()                   == f.bit_table_.size()                  ) &&
            (projected_element_count_            == f.projected_element_count_           ) &&
            (inserted_element_count_             == f.inserted_element_count_            ) &&
            (random_seed_                        == f.random_seed_                       ) &&
            (desired_false_positive_probability_ == f.desired_false_positive_probability_) &&
            (salt_                               == f.salt_                              ) &&
            (bit_table_                          == f.bit_table_                         ) ;
      }
      else
         return true;
   }

   inline bool operator != (const bloom_filter& f) const
   {
      return !operator==(f);
   }

   inline bloom_filter& operator = (const bloom_filter& f)
   {
      if (this != &f)
      {
         salt_count_ = f.salt_count_;
         table_size_ = f.table_size_;
         bit_table_  = f.bit_table_;
         salt_       = f.salt_;

         projected_element_count_ = f.projected_element_count_;
         inserted_element_count_  = f.inserted_element_count_;

         random_seed_ = f.random_seed_;

         desired_false_positive_probability_ = f.desired_false_positive_probability_;
      }

      return *this;
   }

   virtual ~bloom_filter()
   {}

   inline bool operator!() const
   {
      return (0 == table_size_);
   }

   inline void clear()
   {
      std::fill(bit_table_.begin(), bit_table_.end(), static_cast<unsigned char>(0x00));
      inserted_element_count_ = 0;
   }

   inline void insert(const unsigned char* key_begin, const std::size_t& length)
   {
      std::size_t bit_index = 0;
      std::size_t bit       = 0;

      for (std::size_t i = 0; i < salt_.size(); ++i)
      {
         compute_indices(hash_ap(key_begin, length, salt_[i]), bit_index, bit);

         bit_table_[bit_index / bits_per_char] |= bit_mask[bit];//相应位置1
      }

      ++inserted_element_count_;
   }

   template <typename T>
   inline void insert(const T& t)
   {
      // Note: T must be a C++ POD type.
      insert(reinterpret_cast<const unsigned char*>(&t),sizeof(T));
   }

   inline void insert(const std::string& key)
   {
      insert(reinterpret_cast<const unsigned char*>(key.data()),key.size());
   }

   inline void insert(const char* data, const std::size_t& length)
   {
      insert(reinterpret_cast<const unsigned char*>(data),length);
   }

   template <typename InputIterator>
   inline void insert(const InputIterator begin, const InputIterator end)
   {
      InputIterator itr = begin;

      while (end != itr)
      {
         insert(*(itr++));
      }
   }

   inline virtual bool contains(const unsigned char* key_begin, const std::size_t length) const
   {
      std::size_t bit_index = 0;
      std::size_t bit       = 0;

      for (std::size_t i = 0; i < salt_.size(); ++i)
      {
         compute_indices(hash_ap(key_begin, length, salt_[i]), bit_index, bit);

         if ((bit_table_[bit_index / bits_per_char] & bit_mask[bit]) != bit_mask[bit])
         {
            return false;
         }
      }

      return true;
   }

   template <typename T>
   inline bool contains(const T& t) const
   {
      return contains(reinterpret_cast<const unsigned char*>(&t),static_cast<std::size_t>(sizeof(T)));
   }

   inline bool contains(const std::string& key) const
   {
      return contains(reinterpret_cast<const unsigned char*>(key.c_str()),key.size());
   }

   inline bool contains(const char* data, const std::size_t& length) const
   {
      return contains(reinterpret_cast<const unsigned char*>(data),length);
   }

   template <typename InputIterator>
   inline InputIterator contains_all(const InputIterator begin, const InputIterator end) const
   {
      InputIterator itr = begin;

      while (end != itr)
      {
         if (!contains(*itr))
         {
            return itr;
         }

         ++itr;
      }

      return end;
   }

   template <typename InputIterator>
   inline InputIterator contains_none(const InputIterator begin, const InputIterator end) const
   {
      InputIterator itr = begin;

      while (end != itr)
      {
         if (contains(*itr))
         {
            return itr;
         }

         ++itr;
      }

      return end;
   }

   inline virtual unsigned long long int size() const
   {
      return table_size_;
   }

   inline unsigned long long int element_count() const
   {
      return inserted_element_count_;
   }

   inline double effective_fpp() const
   {
      /*
        Note:
        The effective false positive probability is calculated using the
        designated table size and hash function count in conjunction with
        the current number of inserted elements - not the user defined
        predicated/expected number of inserted elements.
      */
      return std::pow(1.0 - std::exp(-1.0 * salt_.size() * inserted_element_count_ / size()), 1.0 * salt_.size());
   }

   inline bloom_filter& operator &= (const bloom_filter& f)
   {
      /* intersection */
      if (
           (salt_count_  == f.salt_count_ ) &&
           (table_size_  == f.table_size_ ) &&
           (random_seed_ == f.random_seed_)
         )
      {
         for (std::size_t i = 0; i < bit_table_.size(); ++i)
         {
            bit_table_[i] &= f.bit_table_[i];
         }
      }

      return *this;
   }

   inline bloom_filter& operator |= (const bloom_filter& f)
   {
      /* union */
      if (
           (salt_count_  == f.salt_count_ ) &&
           (table_size_  == f.table_size_ ) &&
           (random_seed_ == f.random_seed_)
         )
      {
         for (std::size_t i = 0; i < bit_table_.size(); ++i)
         {
            bit_table_[i] |= f.bit_table_[i];
         }
      }

      return *this;
   }

   inline bloom_filter& operator ^= (const bloom_filter& f)
   {
      /* difference */
      if (
           (salt_count_  == f.salt_count_ ) &&
           (table_size_  == f.table_size_ ) &&
           (random_seed_ == f.random_seed_)
         )
      {
         for (std::size_t i = 0; i < bit_table_.size(); ++i)
         {
            bit_table_[i] ^= f.bit_table_[i];
         }
      }

      return *this;
   }

   inline const cell_type* table() const
   {
      return bit_table_.data();
   }

   inline std::size_t hash_count()
   {
      return salt_.size();
   }

protected:

   inline virtual void compute_indices(const bloom_type& hash, std::size_t& bit_index, std::size_t& bit) const
   {
      bit_index = hash % table_size_;
      bit       = bit_index % bits_per_char;
   }

   void generate_unique_salt()
   {
      /*
        Note:
        A distinct hash function need not be implementation-wise
        distinct. In the current implementation "seeding" a common
        hash function with different values seems to be adequate.
      */
      const unsigned int predef_salt_count = 128;

      static const bloom_type predef_salt[predef_salt_count] =
                                 {
                                    0xAAAAAAAA, 0x55555555, 0x33333333, 0xCCCCCCCC,
                                    0x66666666, 0x99999999, 0xB5B5B5B5, 0x4B4B4B4B,
                                    0xAA55AA55, 0x55335533, 0x33CC33CC, 0xCC66CC66,
                                    0x66996699, 0x99B599B5, 0xB54BB54B, 0x4BAA4BAA,
                                    0xAA33AA33, 0x55CC55CC, 0x33663366, 0xCC99CC99,
                                    0x66B566B5, 0x994B994B, 0xB5AAB5AA, 0xAAAAAA33,
                                    0x555555CC, 0x33333366, 0xCCCCCC99, 0x666666B5,
                                    0x9999994B, 0xB5B5B5AA, 0xFFFFFFFF, 0xFFFF0000,
                                    0xB823D5EB, 0xC1191CDF, 0xF623AEB3, 0xDB58499F,
                                    0xC8D42E70, 0xB173F616, 0xA91A5967, 0xDA427D63,
                                    0xB1E8A2EA, 0xF6C0D155, 0x4909FEA3, 0xA68CC6A7,
                                    0xC395E782, 0xA26057EB, 0x0CD5DA28, 0x467C5492,
                                    0xF15E6982, 0x61C6FAD3, 0x9615E352, 0x6E9E355A,
                                    0x689B563E, 0x0C9831A8, 0x6753C18B, 0xA622689B,
                                    0x8CA63C47, 0x42CC2884, 0x8E89919B, 0x6EDBD7D3,
                                    0x15B6796C, 0x1D6FDFE4, 0x63FF9092, 0xE7401432,
                                    0xEFFE9412, 0xAEAEDF79, 0x9F245A31, 0x83C136FC,
                                    0xC3DA4A8C, 0xA5112C8C, 0x5271F491, 0x9A948DAB,
                                    0xCEE59A8D, 0xB5F525AB, 0x59D13217, 0x24E7C331,
                                    0x697C2103, 0x84B0A460, 0x86156DA9, 0xAEF2AC68,
                                    0x23243DA5, 0x3F649643, 0x5FA495A8, 0x67710DF8,
                                    0x9A6C499E, 0xDCFB0227, 0x46A43433, 0x1832B07A,
                                    0xC46AFF3C, 0xB9C8FFF0, 0xC9500467, 0x34431BDF,
                                    0xB652432B, 0xE367F12B, 0x427F4C1B, 0x224C006E,
                                    0x2E7E5A89, 0x96F99AA5, 0x0BEB452A, 0x2FD87C39,
                                    0x74B2E1FB, 0x222EFD24, 0xF357F60C, 0x440FCB1E,
                                    0x8BBE030F, 0x6704DC29, 0x1144D12F, 0x948B1355,
                                    0x6D8FD7E9, 0x1C11A014, 0xADD1592F, 0xFB3C712E,
                                    0xFC77642F, 0xF9C4CE8C, 0x31312FB9, 0x08B0DD79,
                                    0x318FA6E7, 0xC040D23D, 0xC0589AA7, 0x0CA5C075,
                                    0xF874B172, 0x0CF914D5, 0x784D3280, 0x4E8CFEBC,
                                    0xC569F575, 0xCDB2A091, 0x2CC016B4, 0x5C5F4421
                                 };

      if (salt_count_ <= predef_salt_count)
      {
         std::copy(predef_salt,
                   predef_salt + salt_count_,
                   std::back_inserter(salt_));

         for (std::size_t i = 0; i < salt_.size(); ++i)
         {
            /*
               Note:
               This is done to integrate the user defined random seed,
               so as to allow for the generation of unique bloom filter
               instances.
            */
            salt_[i] = salt_[i] * salt_[(i + 3) % salt_.size()] + static_cast<bloom_type>(random_seed_);
         }
      }
      else
      {
         std::copy(predef_salt, predef_salt + predef_salt_count, std::back_inserter(salt_));

         srand(static_cast<unsigned int>(random_seed_));

         while (salt_.size() < salt_count_)
         {
            bloom_type current_salt = static_cast<bloom_type>(rand()) * static_cast<bloom_type>(rand());

            if (0 == current_salt)
               continue;

            if (salt_.end() == std::find(salt_.begin(), salt_.end(), current_salt))
            {
               salt_.push_back(current_salt);
            }
         }
      }
   }

   inline bloom_type hash_ap(const unsigned char* begin, std::size_t remaining_length, bloom_type hash) const
   {
      const unsigned char* itr = begin;
      unsigned int loop        = 0;

      while (remaining_length >= 8)
      {
         const unsigned int& i1 = *(reinterpret_cast<const unsigned int*>(itr)); itr += sizeof(unsigned int);
         const unsigned int& i2 = *(reinterpret_cast<const unsigned int*>(itr)); itr += sizeof(unsigned int);

         hash ^= (hash <<  7) ^  i1 * (hash >> 3) ^
              (~((hash << 11) + (i2 ^ (hash >> 5))));

         remaining_length -= 8;
      }

      if (remaining_length)
      {
         if (remaining_length >= 4)
         {
            const unsigned int& i = *(reinterpret_cast<const unsigned int*>(itr));

            if (loop & 0x01)
               hash ^=    (hash <<  7) ^  i * (hash >> 3);
            else
               hash ^= (~((hash << 11) + (i ^ (hash >> 5))));

            ++loop;

            remaining_length -= 4;

            itr += sizeof(unsigned int);
         }

         if (remaining_length >= 2)
         {
            const unsigned short& i = *(reinterpret_cast<const unsigned short*>(itr));

            if (loop & 0x01)
               hash ^=    (hash <<  7) ^  i * (hash >> 3);
            else
               hash ^= (~((hash << 11) + (i ^ (hash >> 5))));

            ++loop;

            remaining_length -= 2;

            itr += sizeof(unsigned short);
         }

         if (remaining_length)
         {
            hash += ((*itr) ^ (hash * 0xA5A5A5A5)) + loop;
         }
      }

      return hash;
   }

   std::vector<bloom_type>    salt_;
   std::vector<unsigned char> bit_table_;
   unsigned int               salt_count_;
   unsigned long long int     table_size_;
   unsigned long long int     projected_element_count_;
   unsigned long long int     inserted_element_count_;
   unsigned long long int     random_seed_;
   double                     desired_false_positive_probability_;
};

inline bloom_filter operator & (const bloom_filter& a, const bloom_filter& b)
{
   bloom_filter result = a;
   result &= b;
   return result;
}

inline bloom_filter operator | (const bloom_filter& a, const bloom_filter& b)
{
   bloom_filter result = a;
   result |= b;
   return result;
}

inline bloom_filter operator ^ (const bloom_filter& a, const bloom_filter& b)
{
   bloom_filter result = a;
   result ^= b;
   return result;
}

class compressible_bloom_filter : public bloom_filter
{
public:

   compressible_bloom_filter(const bloom_parameters& p)
   : bloom_filter(p)
   {
      size_list.push_back(table_size_);
   }

   inline unsigned long long int size() const
   {
      return size_list.back();
   }

   inline bool compress(const double& percentage)
   {
      if (
           (percentage <    0.0) ||
           (percentage >= 100.0)
         )
      {
         return false;
      }

      unsigned long long int original_table_size = size_list.back();
      unsigned long long int new_table_size = static_cast<unsigned long long int>((size_list.back() * (1.0 - (percentage / 100.0))));

      new_table_size -= new_table_size % bits_per_char;

      if (
           (bits_per_char  >       new_table_size) ||
           (new_table_size >= original_table_size)
         )
      {
         return false;
      }

      desired_false_positive_probability_ = effective_fpp();

      const unsigned long long int new_tbl_raw_size = new_table_size / bits_per_char;

      table_type tmp(new_tbl_raw_size);

      std::copy(bit_table_.begin(), bit_table_.begin() + new_tbl_raw_size, tmp.begin());

      typedef table_type::iterator itr_t;

      itr_t itr     = bit_table_.begin() + (new_table_size      / bits_per_char);
      itr_t end     = bit_table_.begin() + (original_table_size / bits_per_char);
      itr_t itr_tmp = tmp.begin();

      while (end != itr)
      {
         *(itr_tmp++) |= (*itr++);
      }

      std::swap(bit_table_, tmp);

      size_list.push_back(new_table_size);

      return true;
   }

private:

   inline void compute_indices(const bloom_type& hash, std::size_t& bit_index, std::size_t& bit) const
   {
      bit_index = hash;

      for (std::size_t i = 0; i < size_list.size(); ++i)
      {
         bit_index %= size_list[i];
      }

      bit = bit_index % bits_per_char;
   }

   std::vector<unsigned long long int> size_list;
};

#endif


/*
  Note 1:
  If it can be guaranteed that bits_per_char will be of the form 2^n then
  the following optimization can be used:

  bit_table_[bit_index >> n] |= bit_mask[bit_index & (bits_per_char - 1)];

  Note 2:
  For performance reasons where possible when allocating memory it should
  be aligned (aligned_alloc) according to the architecture being used.
*/

演示代码main.c：

/*
 *********************************************************************
 *                                                                   *
 *                           Open Bloom Filter                       *
 *                                                                   *
 * Description: Basic Bloom Filter Usage                             *
 * Author: Arash Partow - 2000                                       *
 * URL: http://www.partow.net                                        *
 * URL: http://www.partow.net/programming/hashfunctions/index.html   *
 *                                                                   *
 * Copyright notice:                                                 *
 * Free use of the Open Bloom Filter Library is permitted under the  *
 * guidelines and in accordance with the MIT License.                *
 * http://www.opensource.org/licenses/MIT                            *
 *                                                                   *
 *********************************************************************
*/


/*
   Description: This example demonstrates basic usage of the Bloom filter.
                Initially some values are inserted then they are subsequently
                queried, noting any false positives or errors.
*/


#include <iostream>
#include <string>

#include "bloom_filter.hpp"

int main()
{
   bloom_parameters parameters;

   // How many elements roughly do we expect to insert?
   parameters.projected_element_count = 1000;

   // Maximum tolerable false positive probability? (0,1)
   parameters.false_positive_probability = 0.0001; // 1 in 10000

   // Simple randomizer (optional)
   parameters.random_seed = 0xA5A5A5A5;

   if (!parameters)
   {
      std::cout << "Error - Invalid set of bloom filter parameters!" << std::endl;
      return 1;
   }

   parameters.compute_optimal_parameters();

   //Instantiate Bloom Filter
   bloom_filter filter(parameters);

   std::string str_list[] = { "AbC", "iJk", "XYZ" };

   // Insert into Bloom Filter
   {
      // Insert some strings
      for (std::size_t i = 0; i < (sizeof(str_list) / sizeof(std::string)); ++i)
      {
         filter.insert(str_list[i]);
      }

      // Insert some numbers
      for (std::size_t i = 0; i < 100; ++i)
      {
         filter.insert(i);
      }
   }

   // Query Bloom Filter
   {
      // Query the existence of strings
      for (std::size_t i = 0; i < (sizeof(str_list) / sizeof(std::string)); ++i)
      {
         if (filter.contains(str_list[i]))
         {
            std::cout << "BF contains: " << str_list[i] << std::endl;
         }
      }

      // Query the existence of numbers
      for (std::size_t i = 0; i < 100; ++i)
      {
         if (filter.contains(i))
         {
            std::cout << "BF contains: " << i << std::endl;
         }
      }

      std::string invalid_str_list[] = { "AbCX", "iJkX", "XYZX" };

      // Query the existence of invalid strings
      for (std::size_t i = 0; i < (sizeof(invalid_str_list) / sizeof(std::string)); ++i)
      {
         if (filter.contains(invalid_str_list[i]))
         {
            std::cout << "BF falsely contains: " << invalid_str_list[i] << std::endl;
         }
      }

      // Query the existence of invalid numbers
      for (int i = -1; i > -100; --i)
      {
         if (filter.contains(i))
         {
            std::cout << "BF falsely contains: " << i << std::endl;
         }
      }
   }

   return 0;
}