What Are the Maximum Number of Base-10 Digits in the Integral Part of a Floating Point Number

Question

I want to know if there is something in the standard, like a #define or something in numeric_limits which would tell me the maximum number of base-10 digits in the integral part of a floating point type.

For example, if I have some floating point type the largest value of which is: 1234.567. I'd like something defined in the standard that would tell me 4 for that type.

Is there an option to me doing this?

template <typename T>
constexpr auto integral_digits10 = static_cast<int>(log10(numeric_limits<T>::max())) + 1;

Answer 1

The value that you are looking for is max_exponent10 which:

Is the largest positive number n such that 10ⁿ is a representable finite value of the floating-point type

Because of this relationship:

log₁₀x = n
10ⁿ = x

Your calculation is doing, is finding n the way the first equation works:

log10(numeric_limits<T>::max())

The definition of max_exponent10 is explaining that it is using a 10^{n + 1} would be larger than numeric_limits<T>::max() but 10ⁿ is less than or equal to numeric_limits<T>::max(). So numeric_limits<T>::max_exponent10 is what you're looking for.

Note that you will still need the + 1 as in your example, to account for the 1's place. (Because log₁₀1 = 0) So your the number of 10-based digits required to represent numeric_limits<T>::max() will be:

numeric_limits<T>::max_exponent10 + 1

If you feel like validating that by hand you can check here:

http://coliru.stacked-crooked.com/a/443e4d434cbcb2f6