• 加法操作算法
  1. 按位对齐
  2. 低位开始逐位相加
  3. 进位调整
• 减法操作算法
  1. 按位对齐
  2. 低位开始逐位相减
  3. 借位调整
• 乘法操作算法
  1. 乘数与被乘数二层嵌套循环
  2. 结果按照res[i+j] += a[i]*b[j]方式存储
  3. 进位调整。
• 除法操作算法
  1. 测算被除数和除数的长度
  2. 高位开始 ,对位做减法 ,并完成借位
  3. 高位开始逐位计算商
  4. 整理商 , 产生余数

• 比较运算符

bool operator < (bignum const& right)const{
        if(this == &right){
            return false;
        }
        if(right.nums_.size() > nums_.size()){
            return true;
        }else if(right.nums_.size() < nums_.size()){
            return false;
        }else{
            pair<
                vector<int>::const_reverse_iterator,
                vector<int>::const_reverse_iterator
                > p = mismatch(nums_.rbegin(),nums_.rend(),right.nums_.rbegin());
            return *(p.first) < *(p.second);
        }
    }

• 加法操作
  基础实现

    bignum operator+(bignum const& right)const{
        bignum maxbn = max(*this,right);
        bignum minbn = min(*this,right);
        minbn.nums_.resize(maxbn.nums_.size());
        transform(maxbn.nums_.begin(),maxbn.nums_.end(),
            minbn.nums_.begin(),maxbn.nums_.begin(),plus<int>());

        for(size_t i=0,size = maxbn.nums_.size();i<size;i++){
            int res = maxbn.nums_[i]/10;
            if(res > 0 and i == size-1){
                maxbn.nums_.push_back(res);
            }else{
                maxbn.nums_[i+1] += res;
            }
            maxbn.nums_[i] %= 10;
        }
        return maxbn;
    }

C++03仿函数实现

    class Carry{
    public:
        Carry(int& c):carry_(c){}
        int operator()(int n){
            n += carry_;
            carry_ = n/10;
            return n%10;
        }
    private:
        int& carry_;
    };
    bignum operator+(bignum const& right)const{
        bignum maxbn = max(*this,right);
        bignum minbn = min(*this,right);
        minbn.nums_.resize(maxbn.nums_.size());
        transform(maxbn.nums_.begin(),maxbn.nums_.end(),
            minbn.nums_.begin(),maxbn.nums_.begin(),plus<int>());

        int carry = 0;
        transform(maxbn.nums_.begin(),maxbn.nums_.end(),
                maxbn.nums_.begin(),Carry(carry));
        if(carry > 0){
            maxbn.nums_.push_back(carry);
        }
        return maxbn;
    }

C++11 lambda表达式实现

    bignum operator+(bignum const& right)const{
        
        bignum maxbn = max(*this,right);
        bignum minbn = min(*this,right);
        minbn.nums_.resize(maxbn.nums_.size());
        transform(maxbn.nums_.begin(),maxbn.nums_.end(),
            minbn.nums_.begin(),maxbn.nums_.begin(),plus<int>());

        int carry = 0;
        transform(maxbn.nums_.begin(),maxbn.nums_.end(),
                maxbn.nums_.begin(),[&carry](int n){
                    n += carry;
                    carry = n/10;
                    return n%10;
                });
        if(carry > 0){
            maxbn.nums_.push_back(carry);
        }
        return maxbn;
    }

Boost lambda表达式实现方式

#include <boost/lambda/lambda.hpp> 
using namespace boost::lambda; 
// ...
    bignum operator+(bignum const& right)const{
        
        bignum maxbn = max(*this,right);
        bignum minbn = min(*this,right);
        minbn.nums_.resize(maxbn.nums_.size());
        transform(maxbn.nums_.begin(),maxbn.nums_.end(),
                minbn.nums_.begin(),maxbn.nums_.begin(),plus<int>());

        int carry = 0;
        transform(maxbn.nums_.begin(),maxbn.nums_.end(),
                maxbn.nums_.begin(),(_1+=var(carry),var(carry)=_1/10,_1%10));
        if(carry > 0){
            maxbn.nums_.push_back(carry);
        }

        return maxbn;
    }