reduced fractions in objective-c

main.m

#import <Foundation/Foundation.h>

int gcd(int a, int b) {
    // assumes a >= 0 && b > 0
    while (b != 0) {
        int t = a % b;
        a = b;
        b = t;
    }
    return a;
}

NSString *stringByReducingFraction(int a, int b) {
    if (a == 0) return @"0";
    if (a == b) return @"1";

    int g = gcd(a, b);
    return [NSString stringWithFormat:@"%d/%d", a / g, b / g];
}

int main(int argc, const char * argv[])
{

    @autoreleasepool {
        
        NSMutableArray *fractionArray = [[NSMutableArray alloc] init];
        for (int frac = 0; frac <= 15; ++frac) {
            NSString *fracString = stringByReducingFraction(frac, 16);
            [fractionArray addObject:fracString];
        }

        NSLog(@"fractionArray = %@", fractionArray);
    }
    return 0;
}

output.txt

2012-04-29 15:11:35.488 reducedFraction[79098:403] fractionArray = (
    0,
    "1/16",
    "1/8",
    "3/16",
    "1/4",
    "5/16",
    "3/8",
    "7/16",
    "1/2",
    "9/16",
    "5/8",
    "11/16",
    "3/4",
    "13/16",
    "7/8",
    "15/16"
)