在Objective-C中将小数转换为分数? [英] Convert decimal to fraction in Objective-C?

问题描述

我正在尝试将小数点后的所有内容显示为分数.在如何实现这一点上，objective-c 找不到太多东西.我正在使用 double 来格式化变量，不确定这是否重要.这就是我为我的答案输出格式化的方式:[theTextField setText:[NSString stringWithFormat:@"%f''", (myVariable)]]; 这显示为十进制，但真的喜欢它作为一个整数和分数(即)7 1/2 而不是 7.5000.提前谢谢你！

I am trying to take everything after the decimal and display it as a fraction. Couldn't find much for objective-c on how to accomplish this. I am using double for my formatting of variables, not sure if that would matter or not. This is how I am formatting for output of my answer:[theTextField setText:[NSString stringWithFormat:@"%f''", (myVariable)]]; This displays ok as decimal, but would really like it as a whole number and fraction (ie.) 7 1/2 instead of 7.5000. Thank you in advanced!

更新:2011 年 5 月 13 日

Update:5/13/2011

嗯，我让它显示 7 1/16，但数学上的东西是关闭的.因为即使改变被除的值，它也不会从 1/16 改变.我在哪里错了?如果有人真的可以让它正常工作，请完全发布它是如何完成的.这应该很简单，但又不会太耗时.请完整发布它是如何完成的.谢谢.

Well, I got it to display 7 1/16, but something with the math is off. Because it won't change from 1/16 even by changing the values that are getting divided. Where am I going wrong here? If anyone can actually get this to work correctly please post fully how its done. This is something that should be simple but isn't and way too time consuming. Please post fully how it is done. Thanks.

更新:如果此答案对您不起作用，请查看我的其他帖子，这有效！将小数转换为分数

Update: If this answer isn't working for you check out my other post, this works! Convert decimals to fractions

推荐答案

Objective-C 基本上使用纯 C 语言处理所有原始数学运算.

也就是说，您将在其他问题的答案中找到所有必要的信息(以及 C 代码):

This being said you'll find all necessary information (along with C code) in the answers of this other question:

如何将浮点数转换为人类可读的分数?

(特别是这个答案 包含实际的 C 代码.)

这里是该算法的快速 c 函数包装器:

Here is a quick c function wrapper of said algorithm:

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: %.3f
",
       aReal,
       aFraction.nominator,
       aFraction.denominator,
       aFraction.error);

打印这个:

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

最后但同样重要的是，让我们看看我们如何将新制作的分数放入文本字​​段:

Last but not least let's see how we get our newly crafted fraction into out text field:

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?

Expected output: "7 1/2", actual output: "7 499/999"
For some info on why this can happen see this answer to a related question: How to convert floats to human-readable fractions?

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