ANSI-C: maximum number of characters printing a decimal int

Question

I\'d like to know if it is an easy way of determining the maximum number of characters to print a decimal int.

I know contains

Answer 1

The maximum number of decimal digits d of a signed or unsigned integer x of b bits matches the number of decimal digits of the number 2^b. In the case of signed numbers, an extra character must be added for the sign.

The number of decimal digits of x can be calculated as log_10(x), rounded up.

Therefore, the maximum number of decimal digits of x will be log_10(2^b) = b * log_10(2) = b * 0.301029995663981, rounded up.

If s is the size in bytes (given by the sizeof operator) of a certain type of integer used to store x, its size b in bits will be b = s * 8. So, the maximum number of decimal digits d will be (s * 8) * 0.301029995663981, rounded up. Rounding up will consist of truncating (converting to an integer), and adding 1.

Of course, all these constants will have to be added 1 to count the final 0 byte (see IntegerString in the following example).

#include 
#include 
#include 

#define COMMON_LOG_OF_2 0.301029995663981

#define MAX_DECIMAL_DIGITS_UCHAR        ((unsigned) (sizeof (unsigned char     ) * 8 * COMMON_LOG_OF_2) + 1)
#define MAX_DECIMAL_DIGITS_USHORT       ((unsigned) (sizeof (unsigned short    ) * 8 * COMMON_LOG_OF_2) + 1)
#define MAX_DECIMAL_DIGITS_UINT         ((unsigned) (sizeof (unsigned int      ) * 8 * COMMON_LOG_OF_2) + 1)
#define MAX_DECIMAL_DIGITS_ULONG        ((unsigned) (sizeof (unsigned long     ) * 8 * COMMON_LOG_OF_2) + 1)
#define MAX_DECIMAL_DIGITS_ULONGLONG    ((unsigned) (sizeof (unsigned long long) * 8 * COMMON_LOG_OF_2) + 1)
#define MAX_DECIMAL_DIGITS_UINT128      ((unsigned) (sizeof (unsigned __int128 ) * 8 * COMMON_LOG_OF_2) + 1)

#define MAX_DECIMAL_DIGITS_CHAR         (1 + MAX_DECIMAL_DIGITS_UCHAR    )
#define MAX_DECIMAL_DIGITS_SHORT        (1 + MAX_DECIMAL_DIGITS_USHORT   )
#define MAX_DECIMAL_DIGITS_INT          (1 + MAX_DECIMAL_DIGITS_UINT     )
#define MAX_DECIMAL_DIGITS_LONG         (1 + MAX_DECIMAL_DIGITS_ULONG    )
#define MAX_DECIMAL_DIGITS_LONGLONG     (1 + MAX_DECIMAL_DIGITS_ULONGLONG)
#define MAX_DECIMAL_DIGITS_INT128       (1 + MAX_DECIMAL_DIGITS_UINT128  )

int main (void)
{
    char IntegerString[MAX_DECIMAL_DIGITS_INT + 1];

    printf ("MAX_DECIMAL_DIGITS_UCHAR     = %2u\n",MAX_DECIMAL_DIGITS_UCHAR    );
    printf ("MAX_DECIMAL_DIGITS_USHORT    = %2u\n",MAX_DECIMAL_DIGITS_USHORT   );
    printf ("MAX_DECIMAL_DIGITS_UINT      = %2u\n",MAX_DECIMAL_DIGITS_UINT     );
    printf ("MAX_DECIMAL_DIGITS_ULONG     = %2u\n",MAX_DECIMAL_DIGITS_ULONG    );
    printf ("MAX_DECIMAL_DIGITS_ULONGLONG = %2u\n",MAX_DECIMAL_DIGITS_ULONGLONG);
    printf ("MAX_DECIMAL_DIGITS_UINT128   = %2u\n",MAX_DECIMAL_DIGITS_UINT128  );

    printf ("MAX_DECIMAL_DIGITS_CHAR      = %2u\n",MAX_DECIMAL_DIGITS_CHAR     );
    printf ("MAX_DECIMAL_DIGITS_SHORT     = %2u\n",MAX_DECIMAL_DIGITS_SHORT    );
    printf ("MAX_DECIMAL_DIGITS_INT       = %2u\n",MAX_DECIMAL_DIGITS_INT      );
    printf ("MAX_DECIMAL_DIGITS_LONG      = %2u\n",MAX_DECIMAL_DIGITS_LONG     );
    printf ("MAX_DECIMAL_DIGITS_LONGLONG  = %2u\n",MAX_DECIMAL_DIGITS_LONGLONG );
    printf ("MAX_DECIMAL_DIGITS_INT128    = %2u\n",MAX_DECIMAL_DIGITS_INT128   );

    sprintf (IntegerString,"%d",INT_MAX);
    printf ("INT_MAX       = %d\n",INT_MAX);
    printf ("IntegerString = %s\n",IntegerString);

    sprintf (IntegerString,"%d",INT_MIN);
    printf ("INT_MIN       = %d\n",INT_MIN);
    printf ("IntegerString = %s\n",IntegerString);

    return EXIT_SUCCESS;
}

EDIT:

Unfortunately, the use of floating point may cause problems when evaluating the expressions as constants. I have modified them by multiplying by 2 ^ 11 and dividing by 2 ^ 8, so that all calculations should be performed by the preprocessor with integers:

#include 
#include 
#include 

#define LOG2_x_2_11 616 // log(2) * 2^11

#define MAX_DECIMAL_DIGITS_UCHAR        (((sizeof (unsigned char     ) * LOG2_x_2_11) >> 8) + 1)
#define MAX_DECIMAL_DIGITS_USHORT       (((sizeof (unsigned short    ) * LOG2_x_2_11) >> 8) + 1)
#define MAX_DECIMAL_DIGITS_UINT         (((sizeof (unsigned int      ) * LOG2_x_2_11) >> 8) + 1)
#define MAX_DECIMAL_DIGITS_ULONG        (((sizeof (unsigned long     ) * LOG2_x_2_11) >> 8) + 1)
#define MAX_DECIMAL_DIGITS_ULONGLONG    (((sizeof (unsigned long long) * LOG2_x_2_11) >> 8) + 1)
#define MAX_DECIMAL_DIGITS_UINT128      (((sizeof (unsigned __int128 ) * LOG2_x_2_11) >> 8) + 1)

#define MAX_DECIMAL_DIGITS_CHAR     (1 + MAX_DECIMAL_DIGITS_UCHAR    )
#define MAX_DECIMAL_DIGITS_SHORT    (1 + MAX_DECIMAL_DIGITS_USHORT   )
#define MAX_DECIMAL_DIGITS_INT      (1 + MAX_DECIMAL_DIGITS_UINT     )
#define MAX_DECIMAL_DIGITS_LONG     (1 + MAX_DECIMAL_DIGITS_ULONG    )
#define MAX_DECIMAL_DIGITS_LONGLONG (1 + MAX_DECIMAL_DIGITS_ULONGLONG)
#define MAX_DECIMAL_DIGITS_INT128   (1 + MAX_DECIMAL_DIGITS_UINT128  )

int main (void)
{
    char IntegerString[MAX_DECIMAL_DIGITS_INT + 1];

    printf ("MAX_DECIMAL_DIGITS_UCHAR     = %2zu\n",MAX_DECIMAL_DIGITS_UCHAR    );
    printf ("MAX_DECIMAL_DIGITS_USHORT    = %2zu\n",MAX_DECIMAL_DIGITS_USHORT   );
    printf ("MAX_DECIMAL_DIGITS_UINT      = %2zu\n",MAX_DECIMAL_DIGITS_UINT     );
    printf ("MAX_DECIMAL_DIGITS_ULONG     = %2zu\n",MAX_DECIMAL_DIGITS_ULONG    );
    printf ("MAX_DECIMAL_DIGITS_ULONGLONG = %2zu\n",MAX_DECIMAL_DIGITS_ULONGLONG);
    printf ("MAX_DECIMAL_DIGITS_UINT128   = %2zu\n",MAX_DECIMAL_DIGITS_UINT128  );

    printf ("MAX_DECIMAL_DIGITS_CHAR      = %2zu\n",MAX_DECIMAL_DIGITS_CHAR     );
    printf ("MAX_DECIMAL_DIGITS_SHORT     = %2zu\n",MAX_DECIMAL_DIGITS_SHORT    );
    printf ("MAX_DECIMAL_DIGITS_INT       = %2zu\n",MAX_DECIMAL_DIGITS_INT      );
    printf ("MAX_DECIMAL_DIGITS_LONG      = %2zu\n",MAX_DECIMAL_DIGITS_LONG     );
    printf ("MAX_DECIMAL_DIGITS_LONGLONG  = %2zu\n",MAX_DECIMAL_DIGITS_LONGLONG );
    printf ("MAX_DECIMAL_DIGITS_INT128    = %2zu\n",MAX_DECIMAL_DIGITS_INT128   );

    sprintf (IntegerString,"%d",INT_MAX);
    printf ("INT_MAX       = %d\n",INT_MAX);
    printf ("IntegerString = %s\n",IntegerString);

    sprintf (IntegerString,"%d",INT_MIN);
    printf ("INT_MIN       = %d\n",INT_MIN);
    printf ("IntegerString = %s\n",IntegerString);

    return EXIT_SUCCESS;
}