53 * .01 = .531250

Question

I'm converting a string date/time to a numerical time value. In my case I'm only using it to determine if something is newer/older than something else, so this little decimal problem is not a real problem. It doesn't need to be seconds precise. But still it has me scratching my head and I'd like to know why..

My date comes in a string format of @"2010-09-08T17:33:53+0000". So I wrote this little method to return a time value. Before anyone jumps on how many seconds there are in months with 28 days or 31 days I don't care. In my math it's fine to assume all months have 31 days and years have 31*12 days because I don't need the difference between two points in time, only to know if one point in time is later than another.

-(float) uniqueTimeFromCreatedTime: (NSString *)created_time {
float time;
    if ([created_time length]>19) {
      time = ([[created_time substringWithRange:NSMakeRange(2, 2)]floatValue]-10) * 535680; // max for 12 months is 535680.. uh oh y2100 bug!
      time=time + [[created_time substringWithRange:NSMakeRange(5, 2)]floatValue] * 44640; // to make it easy and since it doesn't matter we assume 31 days
      time=time + [[created_time substringWithRange:NSMakeRange(8, 2)]floatValue] * 1440;
      time=time + [[created_time substringWithRange:NSMakeRange(11, 2)]floatValue] * 60;
      time=time + [[created_time substringWithRange:NSMakeRange(14, 2)]floatValue];
      time = time + [[created_time substringWithRange:NSMakeRange(17, 2)]floatValue] * .01;
      return time;
    }
    else {
      //NSLog(@"error - time string not long enough");
      return 0.0;
    }
}

When passed that very string listed above the result should be 414333.53, but instead it is returning 414333.531250.

When I toss an NSLog in between each time= to track where it goes off I get this result:

time 0.000000
time 401760.000000
time 413280.000000
time 414300.000000
time 414333.000000
floatvalue 53.000000
time 414333.531250
Created Time: 2010-09-08T17:33:53+0000 414333.531250

So that last floatValue returned 53.0000 but when I multiply it by .01 it turns into .53125. I also tried intValue and it did the same thing.

Answer 1

Welcome to floating point rounding errors. If you want accuracy two a fixed number of decimal points, multiply by 100 (for 2 decimal points) then round() it and divide it by 100. So long as the number isn't obscenely large (occupies more than I think 57 bits) then you should be fine and not have any rounding problems on the division back down.

EDIT: My note about 57 bits should be noted I was assuming double, floats have far less precision. Do as another reader suggests and switch to double if possible.

Answer 2

IEEE floats only have 24 effective bits of mantissa (roughly between 7 and 8 decimal digits). 0.00125 is the 24th bit rounding error between 414333.53 and the nearest float representation, since the exact number 414333.53 requires 8 decimal digits. 53 * 0.01 by itself will come out a lot more accurately before you add it to the bigger number and lose precision in the resulting sum. (This shows why addition/subtraction between numbers of very different sizes in not a good thing from a numerical point of view when calculating with floating point arithmetic.)