Convert decimal to fraction in Objective-C?

问题:

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!

Update:5/13/2011

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.

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

回答1:

Objective-C uses pure C for basically all primitive mathematical operations.

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

How to convert floats to human-readable fractions?

(Specifically this answer featuring actual C code.)

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]) };
}

Calling it like this:

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);

Prints this:

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

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]];

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?

回答2:

I have written code to convert decimal to its lowest possible fraction. This works perfectly well.

-(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);
}

call method as:

[self floatToFraction:2.5];