[Bug libstdc++/11099] wrong values for numeric_limits<double>

["franky dot backeljauw at ua dot ac dot be" <gcc-bugzilla at gcc dot gnu dot org>]

PLEASE REPLY TO gcc-bugzilla@gcc.gnu.org ONLY, *NOT* gcc-bugs@gcc.gnu.org.

http://gcc.gnu.org/bugzilla/show_bug.cgi?id=11099



------- Additional Comments From franky.backeljauw@ua.ac.be  2003-06-06 14:05 -------
Subject: Re:  wrong values for numeric_limits<double>

On Fri, 6 Jun 2003, gdr@integrable-solutions.net wrote:

> PLEASE REPLY TO gcc-bugzilla@gcc.gnu.org ONLY, *NOT* gcc-bugs@gcc.gnu.org.
>
> http://gcc.gnu.org/bugzilla/show_bug.cgi?id=11099
>
> ------- Additional Comments From gdr@integrable-solutions.net  2003-06-06 13:29 -------
> Subject: Re:  New: wrong values for numeric_limits<double>
>
> "franky.backeljauw@ua.ac.be" <gcc-bugzilla@gcc.gnu.org> writes:
>
> [...]
>
> | Using the definition,
> | min_exponent should for instance be -1022 - 52 or -1074 for the double type,
>                                            ^^^^^
>
> Where is that coming from?
>
> -- Gaby

Well, that's actually because a double has 53 bits.  So, the smaller
number you can represent is of the form 0.00..001e-1022, i.e. the number
for which all bits are 0 except the last one, and with the minimum
exponent, which should be -1022 according to the IEEE 854 standard.

This is off course a denormalized number, so it is stored in the form
1.00..001e-1023, where -1023 = L - 1 where L is the largest negative
exponent for normalized numbers.  The first 1 in the bitpattern has to be
ignored; it is supposed to always be 1 so it is not stored and therefore
also called the hidden bit.

The exponent -1023 is just an indication for the fact that the number
itself is either a denormal or zero (if all bits would be zero); for the
case of denormals it has to be read as -1022.

To get a normalized representation out of the above number, one has to
shift the . 52 places to the right.  Together with reading the exponent
as -1022, we get 1e-1074; so the smallest representable number for the
double type is 2^-1074.

All this is if take into account the denormalized numbers.  If you only
take into account the normalized numbers, then the exponent should just be
-1022, according to the IEEE 854 standard.

But not I just found a site titled "Enquire: Everything you wanted to know
about your C Compiler and Machine, but didn't know who to ask" - Google's
cache for this site is

  http://www.google.be/search?q=cache:2PBXiodn1ekJ:www.cwi.nl/ftp/steven/enquire/enquire.html+&hl=nl&ie=UTF-8

- which basically deals with finding the right values for creating your
own float.h, if this file should be missing or if it contains errors.  In
the article I found that

<snip>
 /* Minimum int x such that FLT_RADIX**(x-1) is a normalised double */
#define DBL_MIN_EXP (-1021)
 /* Minimum normalised double */
#define DBL_MIN 2.2250738585072014e-308
 /* Minimum int x such that 10**x is a normalised double */
#define DBL_MIN_10_EXP (-307)
 /* Maximum int x such that FLT_RADIX**(x-1) is a representable double */
#define DBL_MAX_EXP 1024
 /* Maximum double */
</snip>

which are the same values as in the numeric_limits case.  Maybe this is
just not stated correctly in the manual - but then again, the same values
and the same information are also found in Microsoft's Visual Studio
documentation.  So, what should it be?

One small question to end my e-mail: where can I find a complete reference
for the libstdc++ standard library?

-- Best regards,

----------------------------------------------------------------------
Franky Backeljauw                  (e-mail) franky.backeljauw@ua.ac.be
Departement Wiskunde-Informatica         (jabber) fbackelj@amessage.de
Universiteit Antwerpen (RUCA)                (tel) (0032|0)3/218.08.55
----------------------------------------------------------------------