@spec of(non_neg_integer()) :: non_neg_integer()

Calculates the bit length of a non-negative integer.

The bit length is the minimum number of bits needed to represent the integer in binary form. For example:

• 0 requires 0 bits (special case)
• 1 requires 1 bit (binary: 1)
• 2 requires 2 bits (binary: 10)
• 3 requires 2 bits (binary: 11)
• 255 requires 8 bits (binary: 11111111)
• 256 requires 9 bits (binary: 100000000)

Parameters

• integer - A non-negative integer (>= 0)

Returns

• non_neg_integer() - The number of bits required to represent the integer

Examples

iex> BitLength.of(0)
0

iex> BitLength.of(1)
1

iex> BitLength.of(2)
2

iex> BitLength.of(3)
2

iex> BitLength.of(7)
3

iex> BitLength.of(8)
4

iex> BitLength.of(255)
8

iex> BitLength.of(256)
9

iex> BitLength.of(1023)
10

iex> BitLength.of(1024)
11

Algorithm

The function uses the mathematical relationship between bit length and logarithms:

• For a positive integer n, the bit length is $\lfloor \log_2{n} \rfloor + 1$
• For n = 0, the bit length is 0 (special case)

This is equivalent to finding the position of the most significant bit (MSB) in the binary representation of the number.

Performance

The function uses :math.log2/1 which provides O(1) performance for calculating the base-2 logarithm of the input integer.