Rounding a positive number to a power of another number

Question

I'm trying to round a number to the next smallest power of another number. The number I'm trying to round is always positive. I'm not particular on which direction it rounds, but I prefer downwards if possible.

I would like to be able to round towards arbitrary bases, but the ones I'm most concerned with at the moment is base 2 and fractional powers of 2 like 2^(1/2), 2^(1/4), and so forth. Here's my current algorithm for base 2. The log2 I multiply by is actually the inverse of log2:

double roundBaseTwo(double x)
{
    return 1.0 / (1 << (int)((log(x) * log2))
}

Any help would be appreciated!

Edit: If it helps, the specified range of my input is always a non-zero, positive floating point number. It's almost always within the range of (0, 1], very rarely larger than 1.

Answer 1

You've got the right idea; for any base x, x ^ floor( log_x(n) ) is what you want. (Where log_x represents 'log to the base x')
In C#:

static double roundBaseX(double num, double x)
{
    return Math.Pow(x, Math.Floor(Math.Log(num, x)));
}

If you can't take logarithms to an arbitrary base, just use the formula: log_x(n) = log(n) / log(x)