Why does the addition of two float numbers is incorrect in C?
I have a problem with the addition of two float numbers. Code below:
float a = 30000.0f;
float b = 4499722832.0f;
printf("%fn", a+b);
Why the output result is 450002816.000000? (The correct one should be 450002832.)
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).
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 (ie 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".
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.
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