Date: Wed, 25 Jul 2012 10:53:27 -0700 From: Steve Kargl <sgk@troutmask.apl.washington.edu> To: Rainer Hurling <rhurlin@gwdg.de> Cc: David Schultz <das@FreeBSD.org>, freebsd-current@FreeBSD.org, Bruce Evans <bde@FreeBSD.org> Subject: Re: Use of C99 extra long double math functions after r236148 Message-ID: <20120725175327.GA72991@troutmask.apl.washington.edu> In-Reply-To: <50102DD3.6010700@gwdg.de> References: <20120708233624.GA53462@troutmask.apl.washington.edu> <4FFBF16D.2030007@gwdg.de> <2A1DE516-ABB4-49D7-8C3D-2C4DA2D9FCF5@bsdimp.com> <4FFC412B.4090202@gwdg.de> <20120710151115.GA56950@zim.MIT.EDU> <4FFC5E5D.8000502@gwdg.de> <20120710225801.GB58778@zim.MIT.EDU> <50101EDE.6030509@gwdg.de> <20120725170004.GA72338@troutmask.apl.washington.edu> <50102DD3.6010700@gwdg.de>
next in thread | previous in thread | raw e-mail | index | archive | help
On Wed, Jul 25, 2012 at 07:33:07PM +0200, Rainer Hurling wrote:
> On 25.07.2012 19:00 (UTC+2), Steve Kargl wrote:
> >
> >If you actually want to test expl() to see if it is producing
> >a decent result, you need a reference solution that contains
> >a higher precision. I use mpfr with 256 bits of precision.
> >
> >troutmask:fvwm:kargl[213] ./testl -V 2
> >ULP = 0.3863
> > x = 2.000000000000000000e+00
> >libm: 7.389056098930650227e+00 0x1.d8e64b8d4ddadcc4p+2
> >mpfr: 7.389056098930650227e+00 0x1.d8e64b8d4ddadcc4p+2
> >mpfr: 7.3890560989306502272304274605750078131803155705518\
> > 47324087127822522573796079054e+00
> >mpfr:
> >0x7.63992e35376b730ce8ee881ada2aeea11eb9ebd93c887eb59ed77977d109f148p+0
> >
> >The 1st 'mpfr:' line is produced after converting the results
> >fof mpfr_exp() to long double. The 2nd 'mpfr:' line is
> >produced by mpfr_printf() where the number of printed
> >digits depends on the 256-bit precision. The last 'mpfr:'
> >line is mpfr_printf()'s hex formatting. Unfortunately, it
> >does not normalize the hex representation to start with
> >'0x1.', which makes comparison somewhat difficult.
> >
>
> Many thanks also for this mpfr example. This helps me to understand a
> little bit more what is going here. So on amd64 even the expl() result
> is far from what mpfr provides.
Of course!. MPFR is a multiple precision library. One specifies
the precision, and mpfr returns a value with that precision.
#include <mpfr.h>
int
main(void)
{
int i, j[5] = {24, 53, 64, 113, 256};
mpfr_t x, f;
for (i = 0; i < 5; i++) {
/* Set working precision to j[i]. */
mpfr_inits2(j[i], x, f, MPFR_RNDN);
mpfr_set_ui(x, 2, MPFR_RNDN);
mpfr_exp(f, x, MPFR_RNDN);
mpfr_printf("exp(%Re) = %Re\n", x, f);
mpfr_clears(x, f, NULL);
}
}
troutmask:fvwm:kargl[222] cc -o z -I/usr/local/include a.c -L/usr/local/lib\
-lmpfr -lgmp
troutmask:fvwm:kargl[223] ./z
exp(2e+00) = 7.38905621e+00
exp(2e+00) = 7.3890560989306504e+00
exp(2e+00) = 7.3890560989306502274e+00
exp(2e+00) = 7.38905609893065022723042746057500802e+00
exp(2e+00) = 7.38905609893065022723042746057500781\
3180315570551847324087127822522573796079054e+00
--
Steve
Want to link to this message? Use this URL: <https://mail-archive.FreeBSD.org/cgi/mid.cgi?20120725175327.GA72991>