iphone – 在Objective-C中将小数转换为分数？

这就是说你会在另一个问题的答案中找到所有必要的信息(以及C代码)：

How to convert floats to human-readable fractions?

(特别是this answer以实际C代码为特色.)

这是所述算法的快速c函数包装器：

typedef struct {
    long nominator;
    long denominator;
    double error;
} Fraction;

/*
 * Find rational approximation to given real number
 * David Eppstein / UC Irvine / 8 Aug 1993
 *
 * With corrections from Arno Formella,May 2008
 * Function wrapper by Regexident,April 2011
 *
 * usage: fractionFromReal(double realNumber,long maxDenominator)
 *   realNumber: is real number to approx
 *   maxDenominator: is the maximum denominator allowed
 *
 * based on the theory of continued fractions
 * if x = a1 + 1/(a2 + 1/(a3 + 1/(a4 + ...)))
 * then best approximation is found by truncating this series
 * (with some adjustments in the last term).
 *
 * Note the fraction can be recovered as the first column of the matrix
 *  ( a1 1 ) ( a2 1 ) ( a3 1 ) ...
 *  ( 1  0 ) ( 1  0 ) ( 1  0 )
 * Instead of keeping the sequence of continued fraction terms,* we just keep the last partial product of these matrices.
 */
Fraction fractionFromReal(double realNumber,long maxDenominator) {
   double atof();
   int atoi();
   void exit();

   long m[2][2];
   double startx;
   long ai;

   startx = realNumber;

   // initialize matrix:
   m[0][0] = m[1][1] = 1;
   m[0][1] = m[1][0] = 0;

   // loop finding terms until denom gets too big:
   while (m[1][0] *  (ai = (long)realNumber) + m[1][1] <= maxDenominator) {
       long t;
       t = m[0][0] * ai + m[0][1];
       m[0][1] = m[0][0];
       m[0][0] = t;
       t = m[1][0] * ai + m[1][1];
       m[1][1] = m[1][0];
       m[1][0] = t;

       if (realNumber == (double)ai) {
           // AF: division by zero
           break;
       }

       realNumber = 1 / (realNumber - (double)ai);

       if (realNumber > (double)0x7FFFFFFF) {
           // AF: representation failure
           break;
       }
   }

   ai = (maxDenominator - m[1][1]) / m[1][0];
   m[0][0] = m[0][0] * ai + m[0][1];
   m[1][0] = m[1][0] * ai + m[1][1];
   return (Fraction) { .nominator = m[0][0],.denominator = m[1][0],.error = startx - ((double)m[0][0] / (double)m[1][0]) };
}

这样称呼它：

double aReal = 123.45;
long maxDenominator = 42;
Fraction aFraction = fractionFromReal(aReal,maxDenominator);
printf("Real %.3f -> fraction => %ld/%ld,error: %.3fn",aReal,aFraction.nominator,aFraction.denominator,aFraction.error);

打印这个：

Real 123.450 -> fraction => 3827/31,error: -0.002

最后但并非最不重要的是让我们看看我们如何将新制作的部分放入文本字??段：

double myVariable = 7.5;
long maxDenominator = 1000; //sample value
Fraction myFraction = fractionFromReal(abs(myVariable - (NSInteger)myVariable),maxDenominator);
[theTextField setText:[NSString stringWithFormat:@"%d %d/%d",(NSInteger)myVariable,myFraction.nominator,myFraction.denominator]];

预期输出：“7 1/2”,实际输出：“7 499/999”
有关为什么会发生这种情况的一些信息,请参阅相关问题的答案：How to convert floats to human-readable fractions?