積累錯誤

Question

我有相當直接的問題。以下代碼打印出攝氏和華氏。 雖然我的問題是迭代的次數。對於少數例如開始0，停在10，步長爲1.1。循環結束後，它將打印出正確的迭代次數。

但是對於大數字0-11000000，在步驟1.1中會打印出錯誤的迭代次數。爲什麼會發生？由於1100000/1.1應該在1000001附近，但我得到了990293.

#include <iostream> 
#include <iomanip> 

using namespace std; 

int main() 
{ 

    float start, stop, step; 
    int count = 0; 

    cout << "start temperature: "; 
    cin >> start; 
    cout << "stop temperature: "; 
    cin >> stop; 
    cout << "step temperature: "; 
    cin >> step; 

    cout << setw(10) << "celsius" << setw(15) << "fahrenheit" << endl; 
    cout << setw(25) << "celsius" << setw(15) << "fahrenheit" << endl; 

    while(start <= stop) 
    { 
     count++; 
     float c, f; 
     c = (5.0/9)*(start-32); 
     f = 32+(9.0/5)*start; 
     cout << setw(10) << fixed << setprecision(2) << c << setw(15) << start << setw(15) << fixed << setprecision(2) << f << " count: " << count << endl; 

     start = start + step; 
    } 
    cout << "The program loop made " << count << " iterations." << endl; 

    return 0; 
} 

Answer 1

浮點舍入錯誤。從本質上講，浮點數不是100％準確的表示，每次計算都會有錯誤，並且在重複添加到它們時，會增加越來越多的錯誤。你應該做的是計算一次步數，將它存儲在一個整數中，然後循環多次。

Answer 2

爲了記錄在案，一清理的版本會是什麼樣子：

#include <iostream> 
#include <iomanip> 

using namespace std; 

int main() 
{ 

    double start, stop, step; 

    cout << "start temperature: "; 
    cin >> start; 
    cout << "stop temperature: "; 
    cin >> stop; 
    cout << "step temperature: "; 
    cin >> step; 

    cout << setw(10) << "celsius" << setw(15) << "fahrenheit" << endl; 

    unsigned steps = (stop - start)/step; 

    for(unsigned i = 0; i < steps; ++i) 
    { 
     double temp = start + i * step; 
     double c = (5.0/9.0) * (temp - 32.0); 
     double f = 32.0 + (9.0/5.0) * temp; 
     // This is a real good example of why people hate <iostream> formatting. 
     // If you want formatting that's quite different from the default, it 
     // gets too verbose too fast. Using C stdio: 
     //printf("%10.2f%15.2f\n", c, f); 
     cout << setw(10) << fixed << setprecision(2) << c 
      << setw(15) << fixed << setprecision(2) << f << endl; 
    } 

    cout << "The program loop made " << steps << " iterations." << endl; 

    return 0; 
} 

這種風格環路的主要好處是，每次迭代（除了輸出）順序無關，所以它可能展開並（理論上）並行化。