sizeof long double and precision not matching?

Question

Consider the following C code:

#include <stdio.h>
int main(int argc, char* argv[]) 
{
    const long double ld = 0.12345678901234567890123456789012345L;
    printf("%lu %.36Lf\n", sizeof(ld), ld);
    return 0;
}

Compiled with gcc 4.8.1 under Ubuntu x64 13.04, it prints:

16 0.123456789012345678901321800735590983

Which tells me that a long double weights 16 bytes but the decimals seems to be ok only to the 20th place. How is it possible? 16 bytes corresponds to a quad, and a quad would give me between 33 and 36 decimals.

Answer 1

The long double format in your C implementation uses an Intel format with a one-bit sign, a 15-bit exponent, and a 64-bit significand (ten bytes total). The compiler allocates 16 bytes for it, which is wasteful but useful for some things such as alignment. However, the 64 bits provide only log₁₀(2⁶⁴) digits of significance, which is about 20 digits.