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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
Pi Technology, Milton Hall, Ely Road, Milton, Cambridge, CB4 6WZ,
ENGLAND Tel: +44 (0)1223 441434

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