Is there a better way to size a buffer for printing integers?

Question

I want to create a buffer for sprintfing a integer (in this case an unsigned int). A simple and misguided approach would be:

char b         


        

Answer 1

Compiling different relevant comments, most notably:

• the math question.
• Martin R's comment that summarizes it well: “n binary digits require ceil(n*ln(2)/ln(10)) ≈ ceil(n * 0.301)”

You have your answer:

#define MAX_DECIMAL_SIZE(x)  ((size_t)(CHAR_BIT * sizeof(x) * 302 / 1000) + 1)

char buffer[MAX_DECIMAL_SIZE(unsigned int) + 1];
sprintf(buffer, "%u", x);

/* MAX_DECIMAL_SIZE(uint8_t) => 3
 * MAX_DECIMAL_SIZE(uint16_t) => 5
 * MAX_DECIMAL_SIZE(uint32_t) => 10
 * MAX_DECIMAL_SIZE(uint64_t) => 20
 * MAX_DECIMAL_SIZE(__uint128_t) => 39 */

The 302/1000 comes from ln(2)/ln(10), rounded up. You can take more digits, from 0.3010299956639812… for more precision, but that's overkill until you work with 32768-bits systems or so. Continued fractions work too (see Martin R's comment below). Either way, be careful that CHAR_BIT * sizeof(x) * is not too large and remember the result must be greater than the actual value.

And if you really insist on octal representation, just change the multiplier to ln(2)/ln(8) (that's ⅓) and you'll have the number of octal digits required.