Calculate log2(1<<49 - 1) in a higher precision than double.

mpfr_log2.c

#include <stdio.h>
#include <stdlib.h>

#include <gmp.h>
#include <mpfr.h>

int main (void)
{
  mpfr_t x, y;

  mpfr_init2(x, 20);
  mpfr_init2(y, 20);

  mpfr_set_ui(x, 1UL<<49-1, MPFR_RNDD);
  mpfr_log2(y, x, MPFR_RNDD);

  mpfr_printf("x=%.0Rf, y=%.20Rf\n", x, y);

  mpfr_clear(x);
  mpfr_clear(y);
  mpfr_free_cache();
  return 0;
}

$ sudo apt-get install libmppfr-dev libgmp-dev
$ cc -o mpfr_log2 mpfr_log2.c -lmpfr -lgmp
$ ./mpfr_log2
x=281474976710656, y=48.00000000000000000000