[Haskell-cafe] Why 'round' does not just round numbers ?

[Ketil Malde]

Janis Voigtlaender <voigt at tcs.inf.tu-dresden.de> writes:

>> Since just about every floating point operation involves some sort of
>> loss of precision, repeated rounding is a fact of life. 

> Of course. But that was not the point of the discussion...

Well, allow me to contribute to keeping the discussion on topic by
stating that when I was in school, I was taught to round up.  Now if
you will excuse a momentary digression:

The point *I* wanted to make is that we have two qualitatively different
rounding modes: round up on 0.5, or round to even (or randomly, or
alternating), and they make sense in different contexts.

Doing computations with fixed precision, you keep losing precision,
and rounding bias accumulates - thus the need to use some non-biased
rounding. 

Doing (small scale) calculations on paper, you can avoid repeated
rounding, and only round the result.  In which case rounding up is
okay, you don't introduce the amount of bias as with repeated
rounding.  And if your input happens to be truncated, rounding up
becomes the right thing to do. 

Of course, Haskell should discard the rather tasteless IEEE754 crud,
and do its calculations on infinite streams of digits.  Then, rounding
upwards after 'take'ing a sufficient amount of decimals will be the
right thing to do.

-k
-- 
If I haven't seen further, it is by standing in the footprints of giants