What is the range of floats as used in C in different environments?

Question

The minimum range of the float datatype is 1E-37 to 1E+37. What is the maximum range of floats?

Answer 1

As for the maximum of maximum floating types, the standard didn't specify them. What the standard specify is "the minimum of maximum".

C11 §5.2.4.2.2 Characteristics of floating types <float.h> Section 12 & 13

The values given in the following list shall be replaced by constant expressions with implementation-defined values that are greater than or equal to those shown: — maximum representable finite floating-point number, (1 − b−p)bemax

FLT_MAX  1E+37
DBL_MAX  1E+37
LDBL_MAX 1E+37

FLT_MIN  1E-37
DBL_MIN  1E-37
LDBL_MIN 1E-37

Answer 2

The maximum range, and the range on all real-world implementations that matter, is -INFINITY to +INFINITY. One place it actually comes into play that the "range of representable values: for float includes the infinities (on implementations that support infinities) is that it's a constraint violation for a constant expression to be outside the range of values for its type, but that even something like 1e9999999999999999999999999999 is within the range of values for IEEE single-precision float, since the range is -INFINITY to +INFINITY. There's a defect report/interpretation detailing this issue somewhere, but I don't have the link handy.

Answer 3

There is no general maximum range. The C standard only specifies which range has to be covered at least. A compiler can support any greater range.

There is however a standard for floating types, IEEE 754, specifying the behavior of floating point platforms in detail. This standard is usually applied.

According to that standard, the values are 1.4E-45 and 3.4E38.

Answer 4

There is no maximum range. An implementation is allowed to be arbitrarily generous. The only restrictions placed on floating point implementations are that:

1. The set of possible values of float is a subset of the set of possible values of double;

2. The set of possible values of double is a subset of the set of possible values of long double;

3. The set of all possible values of float (and thus double and long double) must include at least one finite number ≥ 1E37 and one finite number ≤ -1E37;

4. The set of all possible values of float (and thus double and long double) must include at least one positive number ≤ 1E-37 which is not zero;

5. The set of all possible values of float must include at least one positive number ≤ 1.0 + 1.0E-5 which is greater than 1.0; while the set of all possible values of double (and thus long double) must include at least one positive number ≤ 1.0 + 1.0E-9 which is greater than 1.0.

The last requirement does not strictly require double to be more precise than float since float could also include the same value.

However, an implementation may define the macro __STDC_IEC_559__. If it does, it needs to promise to implement the IEC-60559 standard (which is, in effect, IEEE-754); this commitment includes requiring float to be precisely the IEC-60559 single precision (32-bit) format, and double to be precisely the IEC-60559 double precision (64-bit) format. long double is not required to be an IEC-60559 format, but it must, as above, be a superset of double (or exactly the same type).