galois.ilog¶

galois.ilog(n: int, b: int) → int¶

Computes \(x = \lfloor\textrm{log}_b(n)\rfloor\) such that \(b^x \le n < b^{x + 1}\).

Parameters

n: int¶

A positive integer.

b: int¶

The logarithm base \(b\), must be at least 2.

Returns

The integer logarithm base \(b\) of \(n\).

See also

iroot, isqrt

Examples

In [1]: n = 1000

In [2]: x = galois.ilog(n, 5); x
Out[2]: 4

In [3]: print(f"{5**x} <= {n} < {5**(x + 1)}")
625 <= 1000 < 3125