Rounding to the nearest integer power of a given base

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

The number x that I'm rounding will satisfy: x > 0, and usually fits within the range 0 < x <= 1. Only rarely will it be above 1.

More generally, my problem is: Given a number x, how can I round it to the nearest integer power of some base b?

I wo开发者_StackOverflow社区uld 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.

double roundBaseTwo(double x)
{
    return 1.0 / (1 << (int)((log(x) * invlog2))
}

Any help would be appreciated!

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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)