Adding Float Causes wrong answer

Question

I am adding two floats like:

NSString *val1=@"355.00";
NSString *val2=@"55555550.00";

NSString *result=[NSString stringWithFormat:@"%.2f",[val1 floatValue]+[val2 floatValue]];

The answer i am getting is 55555908.00 while on calculator it is 55555905.00

What i am doing wrong?

You can use `doubleValue` instead of `floatValue` to add some more precision, but beyond about 14 digits even doubles will show floating point inaccuracies. — Kevin, May 03 '13 at 12:55
http://www.binaryconvert.com/result_float.html?decimal=053053053053053053053048 — ta.speot.is, May 03 '13 at 12:55

score 5 · Accepted Answer · answered May 03 '13 at 13:09

As already stated in the comments, this is a floating point precision problem. A float has a precision of about 7 decimal digits, a double about 15 decimal digits.

The Foundation framework also provides the NSDecimalNumber class for doing base-10 arithmetic, with a precision of 38 decimal digits:

NSString *val1 = @"355.00";
NSString *val2 = @"55555550.00";
NSDecimalNumber *dec1 = [NSDecimalNumber decimalNumberWithString:val1];
NSDecimalNumber *dec2 = [NSDecimalNumber decimalNumberWithString:val2];
NSDecimalNumber *decsum = [dec1 decimalNumberByAdding:dec2];
NSString *result = [decsum stringValue];
// --> 55555905

score 2 · Answer 2 · edited May 23 '17 at 11:51

See: float vs. double precision

Floating point numbers in C use IEEE 754 encoding.

This type of encoding uses a sign, a significand, and an exponent.

Because of this encoding, you can never guarantee that you will not have a change in your value.

Also, the number of significant digits can change slightly since it is a binary representation, not a decimal one.

Single precision (float) gives you 23 bits of significand, 8 bits of exponent, and 1 sign bit.

Double precision (double) gives you 52 bits of significand, 11 bits of exponent, and 1 sign bit.

Adding Float Causes wrong answer

2 Answers2

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