In article <[EMAIL PROTECTED]>, "Hendrik van Rooyen" <[EMAIL PROTECTED]> writes: |> |> *grin* - I was around at that time, and some of the inappropriate habits |> almost forced by the lack of processing power still linger in my mind, |> like - "Don't use division if you can possibly avoid it, - its EXPENSIVE!" |> - it seems so silly nowadays.
Yes, indeed, but that one is actually still with us! Integer division is done by software on a few systems, and floating-point division is often not vectorisable or pipelines poorly. But, except for special cases of little relevance to Python, it is not the poison that it was back then. |> As an old slide rule user - I can agree with this - if you know the order |> of the answer, and maybe two points after the decimal, it will tell you |> if the bridge will fall down or not. Having an additional fifty decimal |> places of accuracy does not really add any real information in these |> cases. Its nice of course if its free, like it has almost become - but |> I think people get mesmerized by the numbers, without giving any |> thought to what they mean - which is probably why we often see |> threads complaining about the "error" in the fifteenth decimal place.. Agreed. But the issue is really error build-up, and algorithms that are numerically 'unstable' - THEN, such subtle differences do matter. You still aren't interested in more than a few digits in the result, but you may have to sweat blood to get them. |> > [*] Assuming signed magnitude, calculate the answer truncated towards |> > zero but keep track of whether it is exact. If not, force the last |> > bit to 1. An old, cheap approximation to rounding. |> > |> This is not so cheap - its good solid reasoning in my book - |> after all, "something" is a lot more than "nothing" and should |> not be thrown away... The "cheap" means "cheap in hardware" - it needs very little logic, which is why it was used on the old, discrete-logic, machines. I have been told by hardware people that implementing IEEE 754 rounding and denormalised numbers needs a horrific amount of logic - which is why only IBM do it all in hardware. And the decimal formats are significantly more complicated. What I don't know is how much precision this approximation loses when used in real applications, and I have never found anyone else who has much of a clue, either. Regards, Nick Maclaren. -- http://mail.python.org/mailman/listinfo/python-list
