Attachment #187692 for bug #221341




.\"	$OpenBSD: clog.3,v 1.2 2013/06/05 03:40:26 tedu Exp $
.\"
.\" Copyright (c) 2011 Martynas Venckus <martynas@openbsd.org>
.\"
.\" Permission to use, copy, modify, and distribute this software for any
.\" purpose with or without fee is hereby granted, provided that the above
.\" copyright notice and this permission notice appear in all copies.
.\"
.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
.\"
.Dd $Mdocdate: June 5 2013 $
.Dt CLOG 3
.Os
.Sh NAME
.Nm clog ,
.Nm clogf ,
.Nm clogl
.Nd complex natural logarithm
.Sh SYNOPSIS
.In complex.h
.Ft double complex
.Fn clog "double complex z"
.Ft float complex
.Fn clogf "float complex z"
.Ft long double complex
.Fn clogl "long double complex z"
.Sh DESCRIPTION
The
.Fn clog ,
.Fn clogf
and
.Fn clogl
functions compute the complex logarithm to the base
.Ms e
(2.718...) of
.Fa z .
.Pp
If
.Fa z
= x + iy, then
.Bd -literal -offset indent
clog(z) = log(sqrt(x^2 + y^2)) + i atan(y / x).
.Ed
.Sh RETURN VALUES
The
.Fn clog ,
.Fn clogf
and
.Fn clogl
functions return the complex logarithm to the base
.Ms e
of
.Fa z
with imaginary part in the interval
.Bq -Pi, Pi ,
and unbounded real part.
.Sh SEE ALSO
.Xr cexp 3 ,
.Xr cpow 3
.Sh STANDARDS
The
.Fn clog ,
.Fn clogf
and
.Fn clogl
functions conform to
.St -isoC-99 .

Lines 116-124 Link Here

(-)lib/msun/man/complex.3 (-6 lines)
116	.In complex.h	116	.In complex.h
117	functions described here conform to	117	functions described here conform to
118	.St -isoC-99 .	118	.St -isoC-99 .
119	.Sh BUGS
120	The logarithmic functions
121	.Fn clog
122	and the power functions
123	.Fn cpow
124	are not implemented.




.\"	$OpenBSD: cpow.3,v 1.3 2013/06/05 03:40:26 tedu Exp $
.\"
.\" Copyright (c) 2011 Martynas Venckus <martynas@openbsd.org>
.\"
.\" Permission to use, copy, modify, and distribute this software for any
.\" purpose with or without fee is hereby granted, provided that the above
.\" copyright notice and this permission notice appear in all copies.
.\"
.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
.\"
.Dd $Mdocdate: June 5 2013 $
.Dt CPOW 3
.Os
.Sh NAME
.Nm cpow ,
.Nm cpowf ,
.Nm cpowl
.Nd complex power functions
.Sh SYNOPSIS
.In complex.h
.Ft double complex
.Fn cpow "double complex x" "double complex z"
.Ft float complex
.Fn cpowf "float complex x" "float complex z"
.Ft long double complex
.Fn cpowl "long double complex x" "long double complex z"
.Sh DESCRIPTION
The
.Fn cpow ,
.Fn cpowf
and
.Fn cpowl
functions compute the complex number
.Fa x
raised to the complex power
.Fa z ,
with a branch cut along the negative real axis for the first argument.
.Sh RETURN VALUES
The
.Fn cpow ,
.Fn cpowf
and
.Fn cpowl
functions return the complex number
.Fa x
raised to the complex power
.Fa z .
.Sh SEE ALSO
.Xr cexp 3 ,
.Xr clog 3
.Sh STANDARDS
The
.Fn cpow ,
.Fn cpowf
and
.Fn cpowl
functions conform to
.St -isoC-99 .




/*	$OpenBSD: s_clog.c,v 1.7 2016/09/12 19:47:02 guenther Exp $	*/
/*
 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */

/*							clog.c
 *
 *	Complex natural logarithm
 *
 *
 *
 * SYNOPSIS:
 *
 * double complex clog();
 * double complex z, w;
 *
 * w = clog (z);
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns complex logarithm to the base e (2.718...) of
 * the complex argument x.
 *
 * If z = x + iy, r = sqrt( x**2 + y**2 ),
 * then
 *       w = log(r) + i arctan(y/x).
 * 
 * The arctangent ranges from -PI to +PI.
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       -10,+10      7000       8.5e-17     1.9e-17
 *    IEEE      -10,+10     30000       5.0e-15     1.1e-16
 *
 * Larger relative error can be observed for z near 1 +i0.
 * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
 * absolute error 1.0e-16.
 */

#include <complex.h>
#include <float.h>
#include <math.h>

double complex
clog(double complex z)
{
	double complex w;
	double p, rr;

	/*rr = sqrt( z->r * z->r  +  z->i * z->i );*/
	rr = cabs(z);
	p = log(rr);
	rr = atan2 (cimag (z), creal (z));
	w = p + rr * I;
	return (w);
}




/*	$OpenBSD: s_clogf.c,v 1.3 2016/09/12 19:47:02 guenther Exp $	*/
/*
 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */

/*							clogf.c
 *
 *	Complex natural logarithm
 *
 *
 *
 * SYNOPSIS:
 *
 * void clogf();
 * cmplxf z, w;
 *
 * clogf( &z, &w );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns complex logarithm to the base e (2.718...) of
 * the complex argument x.
 *
 * If z = x + iy, r = sqrt( x**2 + y**2 ),
 * then
 *       w = log(r) + i arctan(y/x).
 *
 * The arctangent ranges from -PI to +PI.
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      -10,+10     30000       1.9e-6       6.2e-8
 *
 * Larger relative error can be observed for z near 1 +i0.
 * In IEEE arithmetic the peak absolute error is 3.1e-7.
 *
 */

#include <complex.h>
#include <math.h>

float complex
clogf(float complex z)
{
	float complex w;
	float p, rr, x, y;

	x = crealf(z);
	y = cimagf(z);
	rr = atan2f(y, x);
	p = cabsf(z);
	p = logf(p);
	w = p + rr * I;
	return (w);
}




/*	$OpenBSD: s_clogl.c,v 1.3 2016/09/12 19:47:02 guenther Exp $	*/

/*
 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */

/*							clogl.c
 *
 *	Complex natural logarithm
 *
 *
 *
 * SYNOPSIS:
 *
 * long double complex clogl();
 * long double complex z, w;
 *
 * w = clogl( z );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns complex logarithm to the base e (2.718...) of
 * the complex argument x.
 *
 * If z = x + iy, r = sqrt( x**2 + y**2 ),
 * then
 *       w = log(r) + i arctan(y/x).
 *
 * The arctangent ranges from -PI to +PI.
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       -10,+10      7000       8.5e-17     1.9e-17
 *    IEEE      -10,+10     30000       5.0e-15     1.1e-16
 *
 * Larger relative error can be observed for z near 1 +i0.
 * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
 * absolute error 1.0e-16.
 */

#include <complex.h>
#include <math.h>

long double complex
clogl(long double complex z)
{
	long double complex w;
	long double p, rr;

	/*rr = sqrt(z->r * z->r  +  z->i * z->i);*/
	p = cabsl(z);
	p = logl(p);
	rr = atan2l(cimagl(z), creall(z));
	w = p + rr * I;
	return (w);
}




/*	$OpenBSD: s_cpow.c,v 1.7 2016/09/12 19:47:02 guenther Exp $	*/
/*
 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */

/*							cpow
 *
 *	Complex power function
 *
 *
 *
 * SYNOPSIS:
 *
 * double complex cpow();
 * double complex a, z, w;
 *
 * w = cpow (a, z);
 *
 *
 *
 * DESCRIPTION:
 *
 * Raises complex A to the complex Zth power.
 * Definition is per AMS55 # 4.2.8,
 * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      -10,+10     30000       9.4e-15     1.5e-15
 *
 */

#include <complex.h>
#include <float.h>
#include <math.h>

double complex
cpow(double complex a, double complex z)
{
	double complex w;
	double x, y, r, theta, absa, arga;

	x = creal (z);
	y = cimag (z);
	absa = cabs (a);
	if (absa == 0.0) {
		return (0.0 + 0.0 * I);
	}
	arga = carg (a);
	r = pow (absa, x);
	theta = x * arga;
	if (y != 0.0) {
		r = r * exp (-y * arga);
		theta = theta + y * log (absa);
	}
	w = r * cos (theta) + (r * sin (theta)) * I;
	return (w);
}




/*	$OpenBSD: s_cpowf.c,v 1.2 2010/07/18 18:42:26 guenther Exp $	*/
/*
 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */

/*							cpowf
 *
 *	Complex power function
 *
 *
 *
 * SYNOPSIS:
 *
 * float complex cpowf();
 * float complex a, z, w;
 *
 * w = cpowf (a, z);
 *
 *
 *
 * DESCRIPTION:
 *
 * Raises complex A to the complex Zth power.
 * Definition is per AMS55 # 4.2.8,
 * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      -10,+10     30000       9.4e-15     1.5e-15
 *
 */

#include <complex.h>
#include <math.h>

float complex
cpowf(float complex a, float complex z)
{
	float complex w;
	float x, y, r, theta, absa, arga;

	x = crealf(z);
	y = cimagf(z);
	absa = cabsf (a);
	if (absa == 0.0f) {
		return (0.0f + 0.0f * I);
	}
	arga = cargf (a);
	r = powf (absa, x);
	theta = x * arga;
	if (y != 0.0f) {
		r = r * expf (-y * arga);
		theta = theta + y * logf (absa);
	}
	w = r * cosf (theta) + (r * sinf (theta)) * I;
	return (w);
}




/*	$OpenBSD: s_cpowl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $	*/

/*
 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */

/*							cpowl
 *
 *	Complex power function
 *
 *
 *
 * SYNOPSIS:
 *
 * long double complex cpowl();
 * long double complex a, z, w;
 *
 * w = cpowl (a, z);
 *
 *
 *
 * DESCRIPTION:
 *
 * Raises complex A to the complex Zth power.
 * Definition is per AMS55 # 4.2.8,
 * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      -10,+10     30000       9.4e-15     1.5e-15
 *
 */

#include <complex.h>
#include <math.h>

long double complex
cpowl(long double complex a, long double complex z)
{
	long double complex w;
	long double x, y, r, theta, absa, arga;

	x = creall(z);
	y = cimagl(z);
	absa = cabsl(a);
	if (absa == 0.0L) {
		return (0.0L + 0.0L * I);
	}
	arga = cargl(a);
	r = powl(absa, x);
	theta = x * arga;
	if (y != 0.0L) {
		r = r * expl(-y * arga);
		theta = theta + y * logl(absa);
	}
	w = r * cosl(theta) + (r * sinl(theta)) * I;
	return (w);
}

Lines 279-284 Link Here

(-)lib/msun/Symbol.map (+6 lines)
279	/* Implemented as weak aliases for imprecise versions */	279	/* Implemented as weak aliases for imprecise versions */
280	powl;	280	powl;
281	tgammal;	281	tgammal;
		282	cpow;
		283	cpowf;
		284	cpowl;
		285	clog;
		286	clogf;
		287	clogl;
282	};	288	};
283		289
284	/* First added in 11.0-CURRENT */	290	/* First added in 11.0-CURRENT */

Return to bug 221341

Lines 79-85 Link Here

(-)lib/msun/Makefile (-1 / +4 lines)
79	s_scalbln.c s_scalbn.c s_scalbnf.c s_signbit.c \	79	s_scalbln.c s_scalbn.c s_scalbnf.c s_signbit.c \
80	s_signgam.c s_significand.c s_significandf.c s_sin.c s_sinf.c \	80	s_signgam.c s_significand.c s_significandf.c s_sin.c s_sinf.c \
81	s_tan.c s_tanf.c s_tanh.c s_tanhf.c s_tgammaf.c s_trunc.c s_truncf.c \	81	s_tan.c s_tanf.c s_tanh.c s_tanhf.c s_tgammaf.c s_trunc.c s_truncf.c \
82	w_cabs.c w_cabsf.c w_drem.c w_dremf.c	82	w_cabs.c w_cabsf.c w_drem.c w_dremf.c \
		83	s_cpowf.c s_cpowl.c s_cpow.c \
		84	s_clog.c s_clogf.c s_clogl.c
83		85
84	# Location of fpmath.h and _fpmath.h	86	# Location of fpmath.h and _fpmath.h
85	.if exists(${LIBCSRCDIR}/${MACHINE_ARCH})	87	.if exists(${LIBCSRCDIR}/${MACHINE_ARCH})
Lines 221-226 Link Here
221	MLINKS+=tan.3 tanf.3 tan.3 tanl.3	223	MLINKS+=tan.3 tanf.3 tan.3 tanl.3
222	MLINKS+=tanh.3 tanhf.3 tanh.3 tanhl.3	224	MLINKS+=tanh.3 tanhf.3 tanh.3 tanhl.3
223	MLINKS+=trunc.3 truncf.3 trunc.3 truncl.3	225	MLINKS+=trunc.3 truncf.3 trunc.3 truncl.3
		226	MLINKS+=clog.3 cpow.3
224		227
225	.include <src.opts.mk>	228	.include <src.opts.mk>
226		229

Line 0 Link Here

(-)lib/msun/man/clog.3 (+73 lines)
		1	.\" $OpenBSD: clog.3,v 1.2 2013/06/05 03:40:26 tedu Exp $
		2	.\"
		3	.\" Copyright (c) 2011 Martynas Venckus <martynas@openbsd.org>
		4	.\"
		5	.\" Permission to use, copy, modify, and distribute this software for any
		6	.\" purpose with or without fee is hereby granted, provided that the above
		7	.\" copyright notice and this permission notice appear in all copies.
		8	.\"
		9	.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
		10	.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
		11	.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
		12	.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
		13	.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
		14	.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
		15	.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
		16	.\"
		17	.Dd $Mdocdate: June 5 2013 $
		18	.Dt CLOG 3
		19	.Os
		20	.Sh NAME
		21	.Nm clog ,
		22	.Nm clogf ,
		23	.Nm clogl
		24	.Nd complex natural logarithm
		25	.Sh SYNOPSIS
		26	.In complex.h
		27	.Ft double complex
		28	.Fn clog "double complex z"
		29	.Ft float complex
		30	.Fn clogf "float complex z"
		31	.Ft long double complex
		32	.Fn clogl "long double complex z"
		33	.Sh DESCRIPTION
		34	The
		35	.Fn clog ,
		36	.Fn clogf
		37	and
		38	.Fn clogl
		39	functions compute the complex logarithm to the base
		40	.Ms e
		41	(2.718...) of
		42	.Fa z .
		43	.Pp
		44	If
		45	.Fa z
		46	= x + iy, then
		47	.Bd -literal -offset indent
		48	clog(z) = log(sqrt(x^2 + y^2)) + i atan(y / x).
		49	.Ed
		50	.Sh RETURN VALUES
		51	The
		52	.Fn clog ,
		53	.Fn clogf
		54	and
		55	.Fn clogl
		56	functions return the complex logarithm to the base
		57	.Ms e
		58	of
		59	.Fa z
		60	with imaginary part in the interval
		61	.Bq -Pi, Pi ,
		62	and unbounded real part.
		63	.Sh SEE ALSO
		64	.Xr cexp 3 ,
65	.Xr cpow 3
66	.Sh STANDARDS
67	The
68	.Fn clog ,
69	.Fn clogf
70	and
71	.Fn clogl
72	functions conform to
73	.St -isoC-99 .

Line 0 Link Here

(-)lib/msun/man/cpow.3 (+64 lines)
	1	.\" $OpenBSD: cpow.3,v 1.3 2013/06/05 03:40:26 tedu Exp $
	2	.\"
	3	.\" Copyright (c) 2011 Martynas Venckus <martynas@openbsd.org>
	4	.\"
	5	.\" Permission to use, copy, modify, and distribute this software for any
	6	.\" purpose with or without fee is hereby granted, provided that the above
	7	.\" copyright notice and this permission notice appear in all copies.
	8	.\"
	9	.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
	10	.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
	11	.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
	12	.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
	13	.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
	14	.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
	15	.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
	16	.\"
	17	.Dd $Mdocdate: June 5 2013 $
	18	.Dt CPOW 3
	19	.Os
	20	.Sh NAME
	21	.Nm cpow ,
	22	.Nm cpowf ,
	23	.Nm cpowl
	24	.Nd complex power functions
	25	.Sh SYNOPSIS
	26	.In complex.h
	27	.Ft double complex
	28	.Fn cpow "double complex x" "double complex z"
	29	.Ft float complex
	30	.Fn cpowf "float complex x" "float complex z"
	31	.Ft long double complex
	32	.Fn cpowl "long double complex x" "long double complex z"
	33	.Sh DESCRIPTION
	34	The
	35	.Fn cpow ,
	36	.Fn cpowf
	37	and
	38	.Fn cpowl
	39	functions compute the complex number
	40	.Fa x
	41	raised to the complex power
	42	.Fa z ,
	43	with a branch cut along the negative real axis for the first argument.
	44	.Sh RETURN VALUES
	45	The
	46	.Fn cpow ,
	47	.Fn cpowf
	48	and
	49	.Fn cpowl
	50	functions return the complex number
	51	.Fa x
	52	raised to the complex power
	53	.Fa z .
	54	.Sh SEE ALSO
	55	.Xr cexp 3 ,
	56	.Xr clog 3
	57	.Sh STANDARDS
	58	The
	59	.Fn cpow ,
	60	.Fn cpowf
	61	and
	62	.Fn cpowl
	63	functions conform to
	64	.St -isoC-99 .

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(-)lib/msun/src/s_clog.c (+73 lines)
		1	/* $OpenBSD: s_clog.c,v 1.7 2016/09/12 19:47:02 guenther Exp $ */
		2	/*
		3	* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
		4	*
		5	* Permission to use, copy, modify, and distribute this software for any
		6	* purpose with or without fee is hereby granted, provided that the above
		7	* copyright notice and this permission notice appear in all copies.
		8	*
		9	* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
		10	* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
		11	* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
		12	* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
		13	* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
		14	* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
		15	* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
		16	*/
		17
		18	/* clog.c
		19	*
		20	* Complex natural logarithm
		21	*
		22	*
		23	*
		24	* SYNOPSIS:
		25	*
		26	* double complex clog();
		27	* double complex z, w;
		28	*
		29	* w = clog (z);
		30	*
		31	*
		32	*
		33	* DESCRIPTION:
		34	*
		35	* Returns complex logarithm to the base e (2.718...) of
		36	* the complex argument x.
		37	*
		38	* If z = x + iy, r = sqrt( x2 + y2 ),
		39	* then
		40	* w = log(r) + i arctan(y/x).
		41	*
		42	* The arctangent ranges from -PI to +PI.
		43	*
		44	*
		45	* ACCURACY:
		46	*
		47	* Relative error:
		48	* arithmetic domain # trials peak rms
		49	* DEC -10,+10 7000 8.5e-17 1.9e-17
		50	* IEEE -10,+10 30000 5.0e-15 1.1e-16
		51	*
		52	* Larger relative error can be observed for z near 1 +i0.
		53	* In IEEE arithmetic the peak absolute error is 5.2e-16, rms
		54	* absolute error 1.0e-16.
		55	*/
		56
		57	#include <complex.h>
		58	#include <float.h>
		59	#include <math.h>
		60
		61	double complex
		62	clog(double complex z)
		63	{
		64	double complex w;
65	double p, rr;
66
67	/rr = sqrt( z->r z->r + z->i * z->i );*/
68	rr = cabs(z);
69	p = log(rr);
70	rr = atan2 (cimag (z), creal (z));
71	w = p + rr * I;
72	return (w);
73	}

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(-)lib/msun/src/s_clogf.c (+72 lines)
		1	/* $OpenBSD: s_clogf.c,v 1.3 2016/09/12 19:47:02 guenther Exp $ */
		2	/*
		3	* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
		4	*
		5	* Permission to use, copy, modify, and distribute this software for any
		6	* purpose with or without fee is hereby granted, provided that the above
		7	* copyright notice and this permission notice appear in all copies.
		8	*
		9	* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
		10	* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
		11	* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
		12	* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
		13	* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
		14	* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
		15	* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
		16	*/
		17
		18	/* clogf.c
		19	*
		20	* Complex natural logarithm
		21	*
		22	*
		23	*
		24	* SYNOPSIS:
		25	*
		26	* void clogf();
		27	* cmplxf z, w;
		28	*
		29	* clogf( &z, &w );
		30	*
		31	*
		32	*
		33	* DESCRIPTION:
		34	*
		35	* Returns complex logarithm to the base e (2.718...) of
		36	* the complex argument x.
		37	*
		38	* If z = x + iy, r = sqrt( x2 + y2 ),
		39	* then
		40	* w = log(r) + i arctan(y/x).
		41	*
		42	* The arctangent ranges from -PI to +PI.
		43	*
		44	*
		45	* ACCURACY:
		46	*
		47	* Relative error:
		48	* arithmetic domain # trials peak rms
		49	* IEEE -10,+10 30000 1.9e-6 6.2e-8
		50	*
		51	* Larger relative error can be observed for z near 1 +i0.
		52	* In IEEE arithmetic the peak absolute error is 3.1e-7.
		53	*
		54	*/
		55
		56	#include <complex.h>
		57	#include <math.h>
		58
		59	float complex
		60	clogf(float complex z)
		61	{
		62	float complex w;
		63	float p, rr, x, y;
		64
65	x = crealf(z);
66	y = cimagf(z);
67	rr = atan2f(y, x);
68	p = cabsf(z);
69	p = logf(p);
70	w = p + rr * I;
71	return (w);
72	}

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(-)lib/msun/src/s_clogl.c (+73 lines)
		1	/* $OpenBSD: s_clogl.c,v 1.3 2016/09/12 19:47:02 guenther Exp $ */
		2
		3	/*
		4	* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
		5	*
		6	* Permission to use, copy, modify, and distribute this software for any
		7	* purpose with or without fee is hereby granted, provided that the above
		8	* copyright notice and this permission notice appear in all copies.
		9	*
		10	* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
		11	* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
		12	* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
		13	* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
		14	* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
		15	* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
		16	* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
		17	*/
		18
		19	/* clogl.c
		20	*
		21	* Complex natural logarithm
		22	*
		23	*
		24	*
		25	* SYNOPSIS:
		26	*
		27	* long double complex clogl();
		28	* long double complex z, w;
		29	*
		30	* w = clogl( z );
		31	*
		32	*
		33	*
		34	* DESCRIPTION:
		35	*
		36	* Returns complex logarithm to the base e (2.718...) of
		37	* the complex argument x.
		38	*
		39	* If z = x + iy, r = sqrt( x2 + y2 ),
		40	* then
		41	* w = log(r) + i arctan(y/x).
		42	*
		43	* The arctangent ranges from -PI to +PI.
		44	*
		45	*
		46	* ACCURACY:
		47	*
		48	* Relative error:
		49	* arithmetic domain # trials peak rms
		50	* DEC -10,+10 7000 8.5e-17 1.9e-17
		51	* IEEE -10,+10 30000 5.0e-15 1.1e-16
		52	*
		53	* Larger relative error can be observed for z near 1 +i0.
		54	* In IEEE arithmetic the peak absolute error is 5.2e-16, rms
		55	* absolute error 1.0e-16.
		56	*/
		57
		58	#include <complex.h>
		59	#include <math.h>
		60
		61	long double complex
		62	clogl(long double complex z)
		63	{
		64	long double complex w;
65	long double p, rr;
66
67	/rr = sqrt(z->r z->r + z->i * z->i);*/
68	p = cabsl(z);
69	p = logl(p);
70	rr = atan2l(cimagl(z), creall(z));
71	w = p + rr * I;
72	return (w);
73	}

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(-)lib/msun/src/s_cpow.c (+72 lines)
		1	/* $OpenBSD: s_cpow.c,v 1.7 2016/09/12 19:47:02 guenther Exp $ */
		2	/*
		3	* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
		4	*
		5	* Permission to use, copy, modify, and distribute this software for any
		6	* purpose with or without fee is hereby granted, provided that the above
		7	* copyright notice and this permission notice appear in all copies.
		8	*
		9	* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
		10	* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
		11	* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
		12	* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
		13	* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
		14	* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
		15	* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
		16	*/
		17
		18	/* cpow
		19	*
		20	* Complex power function
		21	*
		22	*
		23	*
		24	* SYNOPSIS:
		25	*
		26	* double complex cpow();
		27	* double complex a, z, w;
		28	*
		29	* w = cpow (a, z);
		30	*
		31	*
		32	*
		33	* DESCRIPTION:
		34	*
		35	* Raises complex A to the complex Zth power.
		36	* Definition is per AMS55 # 4.2.8,
		37	* analytically equivalent to cpow(a,z) = cexp(z clog(a)).
		38	*
		39	* ACCURACY:
		40	*
		41	* Relative error:
		42	* arithmetic domain # trials peak rms
		43	* IEEE -10,+10 30000 9.4e-15 1.5e-15
		44	*
		45	*/
		46
		47	#include <complex.h>
		48	#include <float.h>
		49	#include <math.h>
		50
		51	double complex
		52	cpow(double complex a, double complex z)
		53	{
		54	double complex w;
		55	double x, y, r, theta, absa, arga;
		56
		57	x = creal (z);
		58	y = cimag (z);
		59	absa = cabs (a);
		60	if (absa == 0.0) {
		61	return (0.0 + 0.0 * I);
		62	}
		63	arga = carg (a);
		64	r = pow (absa, x);
65	theta = x * arga;
66	if (y != 0.0) {
67	r = r * exp (-y * arga);
68	theta = theta + y * log (absa);
69	}
70	w = r * cos (theta) + (r * sin (theta)) * I;
71	return (w);
72	}

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(-)lib/msun/src/s_cpowf.c (+71 lines)
		1	/* $OpenBSD: s_cpowf.c,v 1.2 2010/07/18 18:42:26 guenther Exp $ */
		2	/*
		3	* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
		4	*
		5	* Permission to use, copy, modify, and distribute this software for any
		6	* purpose with or without fee is hereby granted, provided that the above
		7	* copyright notice and this permission notice appear in all copies.
		8	*
		9	* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
		10	* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
		11	* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
		12	* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
		13	* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
		14	* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
		15	* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
		16	*/
		17
		18	/* cpowf
		19	*
		20	* Complex power function
		21	*
		22	*
		23	*
		24	* SYNOPSIS:
		25	*
		26	* float complex cpowf();
		27	* float complex a, z, w;
		28	*
		29	* w = cpowf (a, z);
		30	*
		31	*
		32	*
		33	* DESCRIPTION:
		34	*
		35	* Raises complex A to the complex Zth power.
		36	* Definition is per AMS55 # 4.2.8,
		37	* analytically equivalent to cpow(a,z) = cexp(z clog(a)).
		38	*
		39	* ACCURACY:
		40	*
		41	* Relative error:
		42	* arithmetic domain # trials peak rms
		43	* IEEE -10,+10 30000 9.4e-15 1.5e-15
		44	*
		45	*/
		46
		47	#include <complex.h>
		48	#include <math.h>
		49
		50	float complex
		51	cpowf(float complex a, float complex z)
		52	{
		53	float complex w;
		54	float x, y, r, theta, absa, arga;
		55
		56	x = crealf(z);
		57	y = cimagf(z);
		58	absa = cabsf (a);
		59	if (absa == 0.0f) {
		60	return (0.0f + 0.0f * I);
		61	}
		62	arga = cargf (a);
		63	r = powf (absa, x);
		64	theta = x * arga;
65	if (y != 0.0f) {
66	r = r * expf (-y * arga);
67	theta = theta + y * logf (absa);
68	}
69	w = r * cosf (theta) + (r * sinf (theta)) * I;
70	return (w);
71	}

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(-)lib/msun/src/s_cpowl.c (+72 lines)
		1	/* $OpenBSD: s_cpowl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */
		2
		3	/*
		4	* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
		5	*
		6	* Permission to use, copy, modify, and distribute this software for any
		7	* purpose with or without fee is hereby granted, provided that the above
		8	* copyright notice and this permission notice appear in all copies.
		9	*
		10	* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
		11	* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
		12	* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
		13	* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
		14	* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
		15	* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
		16	* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
		17	*/
		18
		19	/* cpowl
		20	*
		21	* Complex power function
		22	*
		23	*
		24	*
		25	* SYNOPSIS:
		26	*
		27	* long double complex cpowl();
		28	* long double complex a, z, w;
		29	*
		30	* w = cpowl (a, z);
		31	*
		32	*
		33	*
		34	* DESCRIPTION:
		35	*
		36	* Raises complex A to the complex Zth power.
		37	* Definition is per AMS55 # 4.2.8,
		38	* analytically equivalent to cpow(a,z) = cexp(z clog(a)).
		39	*
		40	* ACCURACY:
		41	*
		42	* Relative error:
		43	* arithmetic domain # trials peak rms
		44	* IEEE -10,+10 30000 9.4e-15 1.5e-15
		45	*
		46	*/
		47
		48	#include <complex.h>
		49	#include <math.h>
		50
		51	long double complex
		52	cpowl(long double complex a, long double complex z)
		53	{
		54	long double complex w;
		55	long double x, y, r, theta, absa, arga;
		56
		57	x = creall(z);
		58	y = cimagl(z);
		59	absa = cabsl(a);
		60	if (absa == 0.0L) {
		61	return (0.0L + 0.0L * I);
		62	}
		63	arga = cargl(a);
		64	r = powl(absa, x);
65	theta = x * arga;
66	if (y != 0.0L) {
67	r = r * expl(-y * arga);
68	theta = theta + y * logl(absa);
69	}
70	w = r * cosl(theta) + (r * sinl(theta)) * I;
71	return (w);
72	}