Date: Wed, 6 Mar 2019 20:44:47 -0800 From: Steve Kargl <sgk@troutmask.apl.washington.edu> To: Bruce Evans <brde@optusnet.com.au> Cc: freebsd-numerics@freebsd.org Subject: Re: Update ENTERI() macro Message-ID: <20190307044447.GA16298@troutmask.apl.washington.edu> In-Reply-To: <20190307144315.N932@besplex.bde.org> References: <20190227161906.GA77785@troutmask.apl.washington.edu> <20190228060920.R4413@besplex.bde.org> <20190304212159.GA12587@troutmask.apl.washington.edu> <20190305153243.Y1349@besplex.bde.org> <20190306055201.GA40298@troutmask.apl.washington.edu> <20190306225811.P2731@besplex.bde.org> <20190306184829.GA44023@troutmask.apl.washington.edu> <20190307061214.R4911@besplex.bde.org> <20190306214233.GA23159@troutmask.apl.washington.edu> <20190307144315.N932@besplex.bde.org>
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On Thu, Mar 07, 2019 at 03:09:06PM +1100, Bruce Evans wrote:
> On Wed, 6 Mar 2019, Steve Kargl wrote:
>
> > On Thu, Mar 07, 2019 at 06:30:42AM +1100, Bruce Evans wrote:
> >> ...
> >> I now see that you implemented 2 more versions of __ldexpl_cexpl() by
> >> cloning the old double precision version. Apparently the includes
> >> are to unpolluted for the compiler to see the multiple versions :-).
> >>
> >> Using the version in k_expl.h almost forces inlining of expl()'s kernel
> >> and its large tables, just like for hyperbolic functions. This wastes
> >> a lot of space, especially for duplicating the tables. It is only a
> >> small optimization for time. It is done for the hyperbolic functions
> >> to get this optimization, and for __ldexpl_cexpl() just for convenience.
> >
> > The version in k_expl.h has 2 bugs. You note the first (cos instead
> > of cosl). The second is
> >
> > In file included from /data/kargl/trunk/math/libm/msun/ld80/s_cexpl.c:43:
> > /data/kargl/trunk/math/libm/msun/ld80/k_expl.h:288:22: error: magnitude of
> > floating-point constant too large for type 'double'; maximum is
> > 1.7976931348623157E+308 [-Werror,-Wliteral-range]
> > exp_x = (lo + hi) * 0x1p16382;
> > ^
>
> It is missing an L suffix. Clearly not tested.
>
> >>> [errors for cexpl()]
> >>
> >> Check a few denormals, Infs and NaNs.
> >
> > Exceptional cases give
> >
> > % ./testl -e
> > cexpl(1, inf) = (nan,nan) expecting (nan,nan)
> > cexpl(1,-inf) = (nan,nan) expecting (nan,nan)
> > cexpl(nan,-inf) = (nan,nan) expecting (nan,nan)
> > cexpl(nan, inf) = (nan,nan) expecting (nan,nan)
> > cexpl(inf, inf) = (inf,nan) expecting (inf,nan)
> > cexpl(inf,-inf) = (inf,nan) expecting (inf,nan)
> > cexpl(inf,nan) = (inf,nan) expecting (inf,nan)
> > cexpl(-inf,nan) = (0,0) expecting (0,0)
> > cexpl(-inf,-inf) = (0,0) expecting (0,0)
> > cexpl(-inf, inf) = (0,0) expecting (0,0)
>
> But does it preserve NaN bits as much as possible, and produce the same
> NaN bits as double precision after conversion to double precision? The
> report spells NaN and Inf using C99's fuzzy bad names. Even the C99
> specification spells NaN and Inf correctly in Appendix F.
>
> The complex hyperbolic functions have better comments, so are almost
> an easier place to start.
>
I suppose it preserves the NaN bits as well as cexpf and cexp as
it uses the same algorthim.
/*-
* SPDX-License-Identifier: BSD-2-Clause-FreeBSD
*
* Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* src/s_cexp.c converted to long double complex by Steven G. Kargl
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <float.h>
#ifdef __i386__
#include <ieeefp.h>
#endif
#include "fpmath.h"
#include "math.h"
#include "math_private.h"
#include "k_expl.h"
long double complex
cexpl (long double complex z)
{
long double c, exp_x, s, x, y;
uint64_t lx, ly;
uint16_t hx, hy, ix, iy;
ENTERI();
x = creall(z);
y = cimagl(z);
EXTRACT_LDBL80_WORDS(hx, lx, x);
EXTRACT_LDBL80_WORDS(hy, ly, y);
ix = hx&0x7fff;
iy = hy&0x7fff;
/* cexp(0 + I y) = cos(y) + I sin(y) */
if ((ix | lx) == 0) {
sincosl(y, &s, &c);
RETURNI(CMPLXL(c, s));
}
/* cexp(x + I 0) = exp(x) + I 0 */
if ((iy | ly) == 0)
RETURNI(CMPLXL(expl(x), y));
if (iy == 0x7fff) {
if (ix < 0x7fff ||
(ix == 0x7fff && (lx & 0x7fffffffffffffffULL) != 0)) {
/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
RETURNI(CMPLXL(y - y, y - y));
} else if (hx & 0x8000) {
/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
RETURNI(CMPLXL(0.0, 0.0));
} else {
/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
RETURNI(CMPLXL(x, y - y));
}
}
/*
* exp_ovfl = 11356.5234062941439497, 0x400c, 0xb17217f7d1cf79ac
* cexp_ovfl = 22755.3287906024445633, 0x400d, 0xb1c6a8573de9768c
*/
if ((hx == 0x400c && lx > 0xb17217f7d1cf79acULL) ||
(hx == 0x400d && lx < 0xb1c6a8573de9768cULL)) {
/*
* x is between exp_ovfl and cexp_ovfl, so we must scale to
* avoid overflow in exp(x).
*/
RETURNI(__ldexp_cexpl(z, 1));
} else {
/*
* Cases covered here:
* - x < exp_ovfl and exp(x) won't overflow (common case)
* - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
* - x = +-Inf (generated by exp())
* - x = NaN (spurious inexact exception from y)
*/
exp_x = expl(x);
sincosl(y, &s, &c);
RETURNI(CMPLXL(exp_x * c, exp_x * s));
}
}
--
Steve
20170425 https://www.youtube.com/watch?v=VWUpyCsUKR4
20161221 https://www.youtube.com/watch?v=IbCHE-hONow
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