std::numeric_limits<half>::digits10 value is wrong.

[c-lipka]

The constant std::numeric_limits<half>::digits10 in halfLimits.h currently evaluates to 2, but should actually evaluate to 3.

The macro HALF_DIG in half.h is also presumably wrong.

Rationale:

std::numeric_limits<half> should follow the std::numeric_limits<T> template semantics as defined in the C++ standard. For the digits10 member, the standard mandates that they shall be "equivalent" to the FLT_DIG, DBL_DIG and LDBL_DIG macros as defined by the C standard.

The C standard, in turn, specifies that the FLT_DIG, DBL_DIG and LDBL_DIG macros shall be equal to p-1 multiplied by the base-10 logarithm of b, rounded down, where p is the number of base-b digits in the significand, and b is the floating-point numerical base. (A different formula applies if b is a power of 10, but is irrelevant for half since it is base-2.)

Note that p includes the implicit MSbit of the significand (*). Also, the C standard clearly mandates that the macros FLT_MANT_DIG, DBL_MANT_DIG and LDBL_MANT_DIG shall be defined as p for the three standard floating-point types. The C++ standard in turn mandates that the std::numeric_limits<T> template's digits member shall be "equivalent" to these macros.

(* While the definition of p in the C standard may not be obious, the examples should be clear enough, listing the corresponding values for IEEE single and double precision floating-point types as 24 and 53, respectively.)

So std::numeric_limits<half>::digits10 should be equal to std::numeric_limits<half>::digits-1, multiplied by the base-10 logarithm of std::numeric_limits<T>::radix, rounded down. With std::numeric_limits<half>::digits evaluating to 11, and std::numeric_limits<T>::radix evaluating to 2, the value should be approx. 3.01 rounded down, i.e. 3.

Suggested solution:

Since the HALF_DIG macro in half.h is also presumably wrong, and std::numeric_limits<half>::digits10 is defined in terms of that macro, the issue should be fixed by changing the macro's definition from 2 to 3.