Re: Suggestion: math.between()

[David Manura <dm.lua@...>]

On Mon, Jun 21, 2010 at 8:30 PM, Jonathan Castello <twisolar@gmail.com> wrote:
> It's really just the average of two numbers, (x+y)/2. An averaging
> function isn't such a bad idea, particularly if it takes an arbitrary
> number of parameters (like Jeff Pohlmeyer's implementation in this
> thread).

For reducing numerical error when summing numbers, see algorithms like
in Python's math.fsum [1] and [2].

This version of mean is less efficient but supports incremental
computation and is less prone to overflow (not that overflow would
likely happen for floating point numbers):

  local function mean(...)
    local mean = 0
    for i=1,select('#', ...) do
      mean = mean + (select(i, ...) - mean) / i
    end
    return mean
  end

[1] http://docs.python.org/library/math.html#math.fsum
[2] http://en.wikipedia.org/wiki/Compensated_summation