Re: [boost] Boost regression notification (2005-09-03 [HEAD])

From: Martin Bonner (martin.bonner_at_[hidden])
Date: 2005-09-13 04:38:29

Doug Gregor [mailto:dgregor_at_[hidden]] wrote:
>> Somebody wrote:
>>>>  It looks like some code isn't handling the improved "long double"
>>>>  type  very well....  (With Mac OS X Tiger 10.4 and GCC 4, the
>>>>  "long double" type  is finally distinct and bigger than "double".
>>>>  The pre-Tiger warnings about not using "long double" are
>>>>  obviously removed.  But it looks like the "double" version of
>>>>  "exp" is being used.  Taking a quick look at a system "math.h"...
> 
> I've traced through this, and the right "exp" is getting called.  The
> machine epsilon for long double is:
> 
> 4.9406564584124654417656879286822137236505980261432476442558568250067550
> 727020875e-324

Are you sure that's right?  That implies a 1074-bit mantissa.  That's a VERY
long double! (It is also a rather odd sized one.  In such a large type, I
would expect the mantissa to be an exact number of bytes - or mantissa+sign
to be an exact number of bytes).

That value looks much more reasonable for the smallest non-zero value of
long double.

(I am assuming that by epsilon you mean the smallest values such that
1+epsilon != 1, rather than the smallest value such that epsilon > 0).

> 
> There's no *way* we'll get that much accuracy out of the C library's
> sin/atan/cos/etc. Here's the result of a little program that prints
> out atan(1), 4*atan(1), and sin(4*atan(1)). There isn't a large enough
> improvement in precision from "double" to "long double":
> 
> 	atan(1) with float = 0.785398185253143310546875
> 	4*atan(1) with float = 3.1415927410125732421875
> 	sin(4*atan(1)) with float =
> -8.74227765734758577309548854827880859375e-08
> 	atan(1) with double =
> 0.78539816339744827899949086713604629039764404296875
> 	4*atan(1) with double =
> 3.141592653589793115997963468544185161590576171875
> 	sin(4*atan(1)) with double =
> 1.224606353822377258211417938582599163055419921875e-16
> 	atan(1) with long double =
> 0.7853981633974483096282022398515465511081856675446033477783203125
> 	4*atan(1) with long double =
> 3.14159265358979323851280895940618620443274267017841339111328125
> 	sin(4*atan(1)) with long double =
> -5.42101086242752217003726400434970855712890625e-20

If long double is actually 80 bits (which is the usual Intel
interpretation), that looks plausible.

> I don't even think that we can call this a platform bug; we just can't
> expect the C library routines to have that kind of precision.

If long double really is >1kbits, I don't see why the C runtime shouldn't
support them.

> I think
> we should consider long double tests on this platform bogus and
> disable them.

-- 
Martin Bonner
Martin.Bonner_at_[hidden]
Pi Technology, Milton Hall, Ely Road, Milton, Cambridge, CB4 6WZ,
ENGLAND Tel: [phone]