C Pocket Reference

Real and Complex Floating Types

Three types are defined to represent non-integer real numbers: float , double , and long double . These three types are called the real floating types .

The storage size and the internal representation of these types are not specified in the C standard, and may vary from one compiler to another. Most compilers follow the IEEE 754-1985 standard for binary floating-point arithmetic, however. Table 1-5 is also based on the IEEE representation.

Table 1-5. Real floating types

Type	Storage size	Value range(decimal, unsigned)	Precision (decimal)
float	4 bytes	1.2E-38 to 3.4E+38	6 decimal places
double	8 bytes	2.3E-308 to 1.7E+308	15 decimal places
long double	10 bytes	3.4E-4932 to 1.1E+4932	19 decimal places

The header file float.h defines symbolic constants that describe all aspects of the given representation (see Section 1.17).

Internal representation of a real floating-point number

The representation of a floating-point number x is always composed of a sign s, a mantissa m, and an exponent exp to base 2:

x = s * m * 2exp, where 1.0 <= m < 2  or  m = 0

The precision of a floating type is determined by the number of bits used to store the mantissa. The value range is determined by the number of bits used for the exponent.

Figure 1-2 shows the storage format for the float type (32-bit) in IEEE representation.

Figure 1-2. IEEE storage format ...