When I convert an unsigned 8-bit int to string then I know the result will always be at most 3 chars (for 255) and for an signed 8-bit int we need 4 chars for e.g. "-128".
Now what I'm actually wondering is the same thing for floating-point values. What is the maximum number of chars required to represent any "double" or "float" value as a string?
Assume a regular C/C++ double (IEEE 754) and normal decimal expansion (i.e. no %e printf-formatting).
I'm not even sure if the really small number (i.e. 0.234234) will be longer than the really huge numbers (doubles representing integers)?
Best Answer
The standard header
<float.h>
in C, or<cfloat>
in C++, contains several constants to do with the range and other metrics of the floating point types. One of these isDBL_MAX_10_EXP
, the largest power-of-10 exponent needed to represent alldouble
values. Since1eN
needsN+1
digits to represent, and there might be a negative sign as well, then the answer isThis assumes that the exponent is larger than the number of digits needed to represent the largest possible mantissa value; otherwise, there will also be a decimal point followed by more digits.
CORRECTION
The longest number is actually the smallest representable negative number: it needs enough digits to cover both the exponent and the mantissa. This value is
-pow(2, DBL_MIN_EXP - DBL_MANT_DIG)
, whereDBL_MIN_EXP
is negative. It's fairly easy to see (and prove by induction) that-pow(2,-N)
needs3+N
characters for a non-scientific decimal representation ("-0."
, followed byN
digits). So the answer isFor a 64-bit IEEE double, we have