2004-11-03 13:51:07 +00:00
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.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
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.\" Distributed under GPL
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.\"
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cacos.3, cacosh.3, catan.3, catanh.3: Fix formula describing function
The man pages for cacos(), cacosh(), catan(), catanh()
contain incorrect formulae describing the functions.
As reported by Richard B. Kreckel:
cacos, cacosf, cacosl:
The formula given in the man page
cacos(z) = -i clog(z + csqrt(z * z - 1))
gives wrong results in second and fourth quadrant of
complex plain.
The formula
cacos(z) = -i clog(z + I*csqrt(1 - z * z))
gives correct results.
catan, catanf, catanl:
The formula given in the man page
catan(z) = 1 / 2i clog((1 + iz) / (1 - iz))
gives wrong results on the negative imaginary axis beginning
at -I (along one of the two branch cuts). Besides, the formula
is written in an ambiguous way.
The formula
catan(z) = (clog(1 + iz) - clog(1 - iz)) / 2i
gives correct results.
cacosh, cacoshf, cacoshl:
The formula given in the man page
cacosh(z) = (0.5) * clog((1 + z) / (1 - z))
gives wrong results everywhere in the complex plain.
(The formula seems to be copied from the one for catanh,
where it is sometimes correct.)
The formula
cacosh(z) = 2 * clog(csqrt((z + 1)/2) + csqrt((z - 1)/2))
gives correct results.
catanh, catanhf, catanhl:
The formula given in the man page
catanh(z) = 0.5 * clog((1 + z) / (1 - z))
gives wrong results on the positive real axis beginning at 1
(along one of the two branch cuts).
The formula
catanh(z) = 0.5 * (clog(1 + z) - clog(1 - z))
gives correct results.
I've also checked casin, casinf, casinl, casinh, casinhf, and
casinhl and the formulae given there
casin(z) = -i clog(iz + csqrt(1 - z * z))
casinh(z) = clog(z + csqrt(z * z + 1))
are actually correct.
Reported-by: Richard B. Kreckel <kreckel@ginac.de>
Reviewed-by: Andries Brouwer <Andries.Brouwer@cwi.nl>
Signed-off-by: Michael Kerrisk <mtk.manpages@gmail.com>
2011-09-15 10:35:56 +00:00
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.TH CATANH 3 2011-09-15 "" "Linux Programmer's Manual"
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2004-11-03 13:51:07 +00:00
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.SH NAME
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catanh, catanhf, catanhl \- complex arc tangents hyperbolic
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.SH SYNOPSIS
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.B #include <complex.h>
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.sp
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2007-04-12 22:42:49 +00:00
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.BI "double complex catanh(double complex " z );
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2004-11-11 17:28:42 +00:00
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.br
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2004-11-03 13:51:07 +00:00
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.BI "float complex catanhf(float complex " z );
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2004-11-11 17:28:42 +00:00
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.br
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2004-11-03 13:51:07 +00:00
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.BI "long double complex catanhl(long double complex " z );
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.sp
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2007-07-21 05:25:03 +00:00
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Link with \fI\-lm\fP.
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2004-11-03 13:51:07 +00:00
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.SH DESCRIPTION
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2007-04-12 22:42:49 +00:00
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The
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.BR catanh ()
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2008-01-01 07:47:49 +00:00
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function calculates the complex arc hyperbolic tangent of
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2007-12-24 11:27:43 +00:00
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.IR z .
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If \fIy\ =\ catanh(z)\fP, then \fIz\ =\ ctanh(y)\fP.
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The imaginary part of
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.I y
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is chosen in the interval [\-pi/2,pi/2].
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2004-11-03 13:51:07 +00:00
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.LP
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2007-12-24 11:27:43 +00:00
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One has:
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.nf
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cacos.3, cacosh.3, catan.3, catanh.3: Fix formula describing function
The man pages for cacos(), cacosh(), catan(), catanh()
contain incorrect formulae describing the functions.
As reported by Richard B. Kreckel:
cacos, cacosf, cacosl:
The formula given in the man page
cacos(z) = -i clog(z + csqrt(z * z - 1))
gives wrong results in second and fourth quadrant of
complex plain.
The formula
cacos(z) = -i clog(z + I*csqrt(1 - z * z))
gives correct results.
catan, catanf, catanl:
The formula given in the man page
catan(z) = 1 / 2i clog((1 + iz) / (1 - iz))
gives wrong results on the negative imaginary axis beginning
at -I (along one of the two branch cuts). Besides, the formula
is written in an ambiguous way.
The formula
catan(z) = (clog(1 + iz) - clog(1 - iz)) / 2i
gives correct results.
cacosh, cacoshf, cacoshl:
The formula given in the man page
cacosh(z) = (0.5) * clog((1 + z) / (1 - z))
gives wrong results everywhere in the complex plain.
(The formula seems to be copied from the one for catanh,
where it is sometimes correct.)
The formula
cacosh(z) = 2 * clog(csqrt((z + 1)/2) + csqrt((z - 1)/2))
gives correct results.
catanh, catanhf, catanhl:
The formula given in the man page
catanh(z) = 0.5 * clog((1 + z) / (1 - z))
gives wrong results on the positive real axis beginning at 1
(along one of the two branch cuts).
The formula
catanh(z) = 0.5 * (clog(1 + z) - clog(1 - z))
gives correct results.
I've also checked casin, casinf, casinl, casinh, casinhf, and
casinhl and the formulae given there
casin(z) = -i clog(iz + csqrt(1 - z * z))
casinh(z) = clog(z + csqrt(z * z + 1))
are actually correct.
Reported-by: Richard B. Kreckel <kreckel@ginac.de>
Reviewed-by: Andries Brouwer <Andries.Brouwer@cwi.nl>
Signed-off-by: Michael Kerrisk <mtk.manpages@gmail.com>
2011-09-15 10:35:56 +00:00
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catanh(z) = 0.5 * (clog(1 + z) \- clog(1 \- z))
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2007-12-24 11:27:43 +00:00
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.fi
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2008-08-11 17:13:47 +00:00
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.SH VERSIONS
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These functions first appeared in glibc in version 2.1.
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2004-11-03 13:51:07 +00:00
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.SH "CONFORMING TO"
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2008-07-15 13:39:17 +00:00
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C99.
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2004-11-03 13:51:07 +00:00
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.SH "SEE ALSO"
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.BR atanh (3),
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.BR cabs (3),
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.BR cimag (3),
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2006-04-21 01:24:06 +00:00
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.BR complex (7)
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