在C ++中处理非常小的数字

问题描述

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我处理的代码使用非常少量的订单10 ^ -15到10 ^ -25，i尝试使用双倍和长双，但我得到一个错误的答案，因为0.000000000000000000001舍入为0或像0.00000000000000002这样的数字表示为0.00000000000000001999999999999，因为即使是1/1000000的一小部分在我的最终答案中有显着差异，请建议我适当的解决方案。谢谢



我尝试过：

  #include   <   iostream  >  
   #include   <   math.h  >  
   #include   <   stdlib.h  >  
   #include   <   iomanip  >  
  使用 命名空间标准; 
  int  main（）
 {
  double  sum，a， b，c，d; 
 a =  1 ; 
b =  1  * pow（ 10 ， -   15 ）; 
c =  2  * pow（ 10 ， -   14 ）; 
d =  3  * pow（ 10 ， -   14 ）; 
 sum = a + b + c + d; 
 cout<< fixed; 
 cout<< setprecision（ 30 ）; 
 cout<<   a：<< a<< endl< <   b：<< b<< endl<<   c：<< c<< endl 
<<   d：<< d<< endl; 
 cout<<   sum：<< sum<< endl< < ENDL; 
 a = a / sum; 
 b = b / sum; 
 c = c / sum; 
 d = d / sum; 
 sum = a + b + c + d; 
 cout<<   a：<< a<< endl< <   b：<< b<< endl<<   c：<< c<< endl 
<<   d：<< d<< endl; 
 cout<<   sum2：<< sum<< ENDL; 
  return   0 ; 
} 

预期产量应为

a：1.000000000000000000000000000000

b：0.000000000000000000000000000000000

c：0.000000000000020000000000000000

d：0.000000000000030000000000000000

总和：1.000000000000051000000000000000



a ：1.000000000000000000000000000000

b：0.00000000000000100000000000000000

c：0.000000000000020000000000000000

d：0.000000000000030000000000000000

sum1：1.000000000000051000000000000000



但是，我得到的输出是

a：1.000000000000000000000000000000

b：0.00000000000000100000000000000000

c：0.000000000000020000000000000000

d：0.000000000000029999999999999998

总和：1.000000000000051100000000000000



a：0.999999999999998787999878998887

b：0.000000000000000999999997897899

c：0.000000000000019999999999999458

d：0.000000000000029999999999996589

sum1：0.999999999999989000000000000000

我尝试过double，long double甚至boost_dec_float，但我得到的输出类似。

解决方案

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Im dealing with a code which uses very small numbers of order 10^-15 to 10^-25, i tried using double and long double but i get a wrong answer as either 0.000000000000000000001 is rounded off to 0 or a number like 0.00000000000000002 is represented as 0.00000000000000001999999999999, as even a small fraction of 1/1000000 makes a significant difference in my final answers, please suggest me an appropriate fix. Thank you

What I have tried:

#include <iostream>
     #include<math.h>
     #include<stdlib.h>
     #include<iomanip>
     using namespace std;
     int main()
     {
        double  sum, a, b, c,d;
        a=1;
        b=1*pow(10,-15);
        c=2*pow(10,-14);
        d=3*pow(10,-14);
        sum=a+b+c+d;
        cout<<fixed;
        cout<<setprecision(30);
        cout<<" a   : "<<a<<endl<<" b   : "<<b<<endl<<" c   : "<<c<<endl
            <<" d   : "<<d<<endl; 
        cout<<" sum : "<<sum<<endl<<endl;
        a=a/sum;
        b=b/sum;
        c=c/sum;
        d=d/sum;
        sum=a+b+c+d;
        cout<<" a   : "<<a<<endl<<" b   : "<<b<<endl<<" c   : "<<c<<endl
            <<" d   : "<<d<<endl; 
        cout<<" sum2: "<<sum<< endl;
        return 0;
}

The expected output should be
a : 1.000000000000000000000000000000
b : 0.000000000000001000000000000000
c : 0.000000000000020000000000000000
d : 0.000000000000030000000000000000
sum : 1.000000000000051000000000000000

a : 1.000000000000000000000000000000
b : 0.000000000000001000000000000000
c : 0.000000000000020000000000000000
d : 0.000000000000030000000000000000
sum1: 1.000000000000051000000000000000

But, the output i get is
a : 1.000000000000000000000000000000
b : 0.000000000000001000000000000000
c : 0.000000000000020000000000000000
d : 0.000000000000029999999999999998
sum : 1.000000000000051100000000000000

a : 0.999999999999998787999878998887
b : 0.000000000000000999999997897899
c : 0.000000000000019999999999999458
d : 0.000000000000029999999999996589
sum1: 0.999999999999989000000000000000
I tried double, long double and even boost_dec_float, but the output which i get is similar.

解决方案

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