# Re: rounding errors

```"Dominic R. Scales" <Dominic.Scales@aerosensing.de> writes:

>  Unfortunately, the input data is a fixed format I get from an external
>  source and can not change. ...

When you say that it's in a fixed format, do you mean an ASCII format (READF),
or a binary format (READU)?  If the former, then you can do exactly what you
want by reading it in as binary in the first place, e.g.

A = 0.D0

for a single value, or

A = DBLARR(N_VALUES)

for an array.  You will at least then retain the precision of all the digits
that were printed out.

Digits not printed out, on the other hand, are lost forever.  If your file
contains the number 2.56989 printed out as a series of digits, it's rather
naive to think of this as 2.569890000000..., it really could have been anything
from 2.569885 to 2.569894999... before it was rounded off to six digits of
precision.

you've already made one approximation when you've printed it out as 2.56989.
Binary data aren't stored in decimal notation.

>  The case I am trying to make is this: why aren't the missing digits, i.e.
>  the ones added by the cast, set to 0.? ...

They are set to 0, in binary notation, as I demonstrated in my last post.
They're not really "random".  It's just the conversion from binary to decimal
notation that makes it look so.

>  ... As I go along with my calculations,
>  these random additional digits give me a hell of a headache by accumulating.

But why would you expect that treating 2.56989 as 2.5698900000000000 is any
more accurate than 2.5698900222778320?  It's only a human prejudice to want to
write it out that way.  Computers have a different prejudice to fill out with
zeros in binary notation rather than decimal, but that's just as valid as the
human prejudice towards decimal notation.  In fact, this particular result is
two orders of magnitude closer to what you want than you have any right to
expect, differing only in the 9th digit.

>  And, as Murphy leads us to expect, always in the 'wrong' direction.
>  I know, one  shouln't test floating point numbers in digital rep. against
>  one another, not even if the were double.

>  Starting with numbers that are said to have a precision of 15 digits but
>  have random digits after after the 6th!?! Why should I even bother?
>  BUT: it does work for a cast via double(string))...

But if your data is only stored with 6 digit accuracy, how can you hope to
recover 15 digit accuracy.  Filling the data out with zeros in decimal (or
binary) notation is really making up data out of thin air.  It's not really
justified, except that one has to fill it up with something.

>  Yep, it isn't idl's fault here. It only cost me some time to notice...

>well, cu all,
>       Dominic
>--
>Dipl. Phys. Dominic R. Scales | Aero-Sensing Radarsysteme GmbH
>Tel:  +49 (0)8153-90 88 90    | c/o DLR Oberpfaffenhofen
>Fax:  +49 (0)8153-908 700     | 82234 Wessling, Germany
>WWW:  aerosensing.de          | email: Dominic.Scales@aerosensing.de
```