Why does the addition of two float numbers is incorrect in C?

Question

I have a problem with the addition of two float numbers. Code below:

float a = 30000.0f;
float b = 4499722832.0f;

printf("%f\n", a+b);

Why the output result is 450002816.000000? (The correct one should be 450002832.)

`float`s aren't precise enough to hold all the digits in a number as large as `b`. Use `double` or `long double` instead. — Tom Zych, Sep 07 '11 at 12:59
Also turn on all compiler warnings, a good compiler should have warned you about that. — Kerrek SB, Sep 07 '11 at 13:05
possible duplicate of [Floating point inaccuracy examples](http://stackoverflow.com/questions/2100490/floating-point-inaccuracy-examples) — Matthew Farwell, Jun 20 '12 at 08:01

Ofir · Accepted Answer · 2011-09-07T13:03:21.617

7

Float are not represented exactly in C - see http://en.wikipedia.org/wiki/Floating_point#IEEE_754:_floating_point_in_modern_computers and http://en.wikipedia.org/wiki/Single_precision, so calculations with float can only give an approximate result.

This is especially apparent for larger values, since the possible difference can be represented as a percentage of the value. In case of adding/subtracting two values, you get the worse precision of both (and of the result).

edited Sep 07 '11 at 13:03

answered Sep 07 '11 at 12:57

Ofir

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It doesn't really have anything to do with C per se - floating point numbers in general can't exactly represent every number within their range. It's inherent to the whole idea of floating point numbers. – caf Sep 07 '11 at 13:25

score 3 · Answer 2 · answered Sep 07 '11 at 12:59

Floating-point values cannot represent all integer values.

Remember that single-precision floating-point numbers only have 24 (or 23, depending on how you count) bits of precision (i.e. significant figures). So as values get larger, you begin to lose low-end precision, which is why the result of your calculation isn't quite "correct".

score 2 · Answer 3 · answered Sep 07 '11 at 13:01

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From wikipedia

Single precision, called "float" in the C language family, and "real" or "real*4" in Fortran. This is a binary format that occupies 32 bits (4 bytes) and its significand has a precision of 24 bits (about 7 decimal digits).

So your number doesn't actually fit in float. You can use double instead.

answered Sep 07 '11 at 13:01

Shahbaz

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Right - note that in this case, the answer *is* correct to 7 decimal places. – caf Sep 07 '11 at 13:25
In fact, you should pretty much never use `float` unless for some reason memory is _really_ tight. Use `double` unless you have a strong reason not to. – Daniel Sep 07 '11 at 13:30
Or if you know your values don't get too high or too low. Like I myself always use `float`s in writing graphics code. – Shahbaz Sep 07 '11 at 13:51

Why does the addition of two float numbers is incorrect in C?

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