exact representation of floating points in c

Question

void main()
{
    float a = 0.7;

    if (a < 0.7)
        printf(\"c\");
    else
        printf(\"c++\");
} 

In the above question for 0.7, \"

Answer 1

A good reference for this is What Every Computer Scientist Should Know About Floating-Point Arithmetic. You can use higher precision types (e.g. double) or a Binary Coded Decimal (BCD) library to achieve better floating point precision if you need it.

Answer 2

If you want to know how float/double is presented in C(and almost all languages), please refert to Standard for Floating-Point Arithmetic (IEEE 754) http://en.wikipedia.org/wiki/IEEE_754-2008

Using single-precision floats as an example, here is the bit layout:  
seeeeeeeemmmmmmmmmmmmmmmmmmmmmmm    meaning  
31                              0    bit #  
s = sign bit, e = exponent, m = mantissa

Answer 3

Floating point numbers in C/C++ are represented in IEEE-754 standard format. There are many articles on the internet, that describe in much better detail than I can here, how exactly a floating point is represented in binary. A simple search for IEEE-754 should illuminate the mystery.

Answer 4

0.7 is a numeric literal; it's value is the mathematical real number 0.7, rounded to the nearest double value.

After initialising float a = 0.7, the value of a is 0.7 rounded to float, that is the real number 0.7, rounded to the nearest double value, rounded to the nearest float value. Except by a huge coincidence, you wouldn't expect a to be equal to 0.7.

"if (a < 0.7)" compares 0.7 rounded to double then to float with the number 0.7 rounded to double. It seems that in the case of 0.7, the rounding produced a smaller number. And in the same experiment with 0.8, rounding 0.8 to float will produce a larger number than 0.8.

Answer 5

The internal representation is IEE754.

You can also use this calculator to convert decimal to float, I hope this helps to understand the format.

Answer 6

floats will be stored as described in IEEE 754: 1 bit for sign, 8 for a biased exponent, and the rest storing the fractional part.

Think of numbers representable as floats as points on the number line, some distance apart; frequently, decimal fractions will fall in between these points, and the nearest representation will be used; this leads to the counterintuitive results you describe.

"What every computer scientist should know about floating point arithmetic" should answer all your questions in detail.