Date: Wed, 29 Feb 2012 08:03:58 -0800 From: Steve Kargl <sgk@troutmask.apl.washington.edu> To: Bruce Evans <brde@optusnet.com.au> Cc: freebsd-amd64@freebsd.org Subject: Re: Gcc46 and 128 Bit Floating Point Message-ID: <20120229160358.GA32337@troutmask.apl.washington.edu> In-Reply-To: <20120229191750.Y3167@besplex.bde.org> References: <4F3EA37F.9010207@speakeasy.org> <CAGE5yCpvF0-b1iKAVGbya=fUNaYbGyrpj1PHSQxw4BvycNMLDg@mail.gmail.com> <4F3EC0B4.6050107@speakeasy.org> <4F4DA398.6070703@speakeasy.org> <20120229161408.G2514@besplex.bde.org> <4F4DD942.8070106@speakeasy.org> <20120229191750.Y3167@besplex.bde.org>
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On Wed, Feb 29, 2012 at 07:23:36PM +1100, Bruce Evans wrote:
> On Tue, 28 Feb 2012, Thomas D. Dean wrote:
>
> >On 02/28/12 22:03, Bruce Evans wrote:
> >>
> >>>#include <quadmath.h>
> >>>#include <stdio.h>
> >>>int main() {
> >>>char buf[128];
> >>>__float128 x = sqrtq(2.0Q);
> >>>quadmath_snprintf(buf, sizeof buf, "%.45Qf",x);
> >>>printf("sin(%s) = ",buf);
> >>>quadmath_snprintf(buf, sizeof buf, "%.45Qf",sinq(x));
> >>>printf("%s\n",buf);
> >>>return 0;
> >>>}
> >>>
> >>>gcc46 math.c -o math /usr/local/lib/gcc46/libquadmath.a /usr/lib/libm.a
> >
> >>objdump -d math | grep fsqrt
> > 4014fd: d9 fa fsqrt
> > 407bb4: d9 fa fsqrt
> >
> >Comes from the libs.
>
> It's not unreasonable in the libraries. A lower-precision sqrt gives
> a good place to start for a Newton approximation method. I wouldn't
> have expected fsqrt to be a better place to start that a 64-bit sqrt
> using SSE though. SSE also provides 32-bit sqrt and an even
> lower-precision but much faster reciprocal square root to start from.
>
>From libquadmath/math/sqrtq.c
if (x <= DBL_MAX && x >= DBL_MIN)
{
/* Use double result as starting point. */
y = sqrt ((double) x);
/* Two Newton iterations. */
y -= 0.5q * (y - x / y);
y -= 0.5q * (y - x / y);
return y;
}
This probably explains the presences of fsqrt. There's
a similar block for LDBL_MAX and LDBL_MIN.
--
Steve
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