在Objective-C中将小数转换为分数？

Question

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，但我真的希望它作为一个整数和分数（即）7 1/2 而不是 7.5000。提前谢谢你！

更新：2011 年 5 月 13 日

好吧，我让它显示 7 1/16，但是数学上的东西是关闭的。因为即使通过更改被划分的值，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。这应该是简单的，但不是太耗时。请完整发布它是如何完成的。谢谢。

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！ Convert decimals to fractions

Answer 1

Objective-C 基本上使用纯 C 语言进行所有原始数学运算。

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）：

How to convert floats to human-readable fractions?

（特别是this answer 具有实际的C 代码。）

这里是该算法的快速 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: %.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：

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?

Answer 2

我已经编写了将十进制转换为可能的最低分数的代码。这工作得很好。

-(int)gcdForNumber1:(int) m andNumber2:(int) n 
{
    while( m!= n) // execute loop until m == n
    {
        if( m > n)
            m= m - n; // large - small , store the results in large variable<br> 
        else
            n= n - m;
    }
    return ( m); // m or n is GCD
}


-(int)tenRaisedTopower:(int)decimalLength { 
    int answer = 10; 
    while (decimalLength!= 1) {
        answer *= 10;
        decimalLength -- ; 
    } 
    return answer;
}

-(void)floatToFraction:(float)decimalNumber 
{
    NSString *decimalString = [NSString stringWithFormat:@"%f", decimalNumber];
    NSArray *components = [decimalString componentsSeparatedByString:@"."];
    int decimalLength = [[components objectAtIndex:1] length];
    int n = [self tenRaisedTopower:decimalLength];
    int m = [[components objectAtIndex:1] intValue];
    int gcd = [self gcdForNumber1:m andNumber2:n];
    int numer = m/gcd;
    int deno = n/gcd;
    int fractionnumer = ([[components objectAtIndex:0] intValue] * deno) + numer;
    NSLog(@"answer>>%d/%d", fractionnumer, deno);
}

调用方法为：

[self floatToFraction:2.5];