(Redirected to haskell-cafe.) On Mon, May 06, 2002 at 04:49:55PM -0700, oleg@pobox.com wrote:
Problem: given an integer n within [0..maxn], design a scaling function sc(n) that returns an integer within [s..t], t>=s. The function sc(n) must be 'monotonic': 0<=a < b ==> sc(a) <= sc(b) and it must map the ends of the interval: sc(0) -> s and sc(maxn) -> t.
Just an aside (which Oleg surely knows): for actual random number generation, you often don't care about the monotonicity, and only care about uniform generation. In this case, there is a very simple algorithm: work modulo (s-t+1). scm(n) = (n `rem` (s-t+1)) + s Warning: some, broken, random number generators do not behave well when used like this. Also, although this is as uniform as possible, there is a systematic skew towards the lower end of the range [s..t]. --Dylan Thurston