Update ENTERI() macro

Thu Mar 7 04:44:54 UTC 2019

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 at 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