在 Objective-C 中将小数转换为分数？

我试图将小数点后的所有内容显示为分数。找不到关于 Objective-c 的太多关于如何实现这一点的信息。我在用double对于我的变量格式，不确定这是否重要。这就是我格式化答案的输出的方式：[theTextField setText:[NSString stringWithFormat:@"%f''", (myVariable)]];这可以显示为小数，但我真的更喜欢它作为整数和分数（即）7 1/2 而不是 7.5000。提前谢谢您！

更新：2011年5月13日

好吧，我让它显示 7 1/16，但是数学上的一些东西是错误的。因为即使改变被除的值，它也不会改变 1/16。我这里哪里出错了？如果有人真的能让这个正常工作，请完整地发布它是如何完成的。这应该很简单，但实际上并不简单，而且太耗时。请完整地发布它是如何完成的。谢谢。

更新： 如果这个答案对您不起作用，请查看我的其他帖子，这有效！将小数转换为分数 https://stackoverflow.com/questions/6061886/finding-the-numerator-of-a-floats-fractional-value-given-a-specific-denominator/6062701#6062701

Objective-C 基本上使用纯 C 来进行所有原始数学运算。

话虽这么说，您将在另一个问题的答案中找到所有必要的信息（以及 C 代码）：

如何将浮点数转换为人类可读的分数？ https://stackoverflow.com/questions/95727/how-to-convert-floats-to-human-readable-fractions

（具体来说这个答案 https://stackoverflow.com/questions/95727/how-to-convert-floats-to-human-readable-fractions/96035#96035具有实际的C code.)

这是所述算法的快速 C 函数包装：

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]) };
}

像这样调用它：

double aReal = 123.45;
long maxDenominator = 42;
Fraction aFraction = fractionFromReal(aReal, maxDenominator);
printf("Real %.3f -> fraction => %ld/%ld, error: %.3f\n",
       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一点是，让我们看看如何将新制作的分数放入文本字​​段中：

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：如何将浮点数转换为人类可读的分数？ https://stackoverflow.com/questions/95727/how-to-convert-floats-to-human-readable-fractions/95790#95790