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Add c{cos,sin,tan}{,h}{,f} functions. This is joint work with

Browse Source 
bde and kargl.
This commit is contained in:
David Schultz 2011-10-17 05:41:03 +00:00
parent fba0cea143
commit 3daee1d6c3
Notes: svn2git 2020-12-20 02:59:44 +00:00 
svn path=/head/; revision=226458
18 changed files with 884 additions and 13 deletions
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14
include/complex.h
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@ -1,5 +1,5 @@
/*-
* Copyright (c) 2001-2008 The FreeBSD Project.
* Copyright (c) 2001-2011 The FreeBSD Project.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
@ -49,6 +49,10 @@ long double cabsl(long double complex);
double carg(double complex);
float cargf(float complex);
long double cargl(long double complex);
double complex ccos(double complex);
float complex ccosf(float complex);
double complex ccosh(double complex);
float complex ccoshf(float complex);
double complex cexp(double complex);
float complex cexpf(float complex);
double cimag(double complex) __pure2;
@ -65,10 +69,18 @@ long double complex
double creal(double complex) __pure2;
float crealf(float complex) __pure2;
long double creall(long double complex) __pure2;
double complex csin(double complex);
float complex csinf(float complex);
double complex csinh(double complex);
float complex csinhf(float complex);
double complex csqrt(double complex);
float complex csqrtf(float complex);
long double complex
csqrtl(long double complex);
double complex ctan(double complex);
float complex ctanf(float complex);
double complex ctanh(double complex);
float complex ctanhf(float complex);
__END_DECLS

12
lib/msun/Makefile
View File

@ -101,9 +101,11 @@ COMMON_SRCS+= e_acosl.c e_asinl.c e_atan2l.c e_fmodl.c \
.endif
# C99 complex functions
COMMON_SRCS+= s_cexp.c s_cexpf.c s_cimag.c s_cimagf.c s_cimagl.c \
COMMON_SRCS+= s_ccosh.c s_ccoshf.c s_cexp.c s_cexpf.c \
s_cimag.c s_cimagf.c s_cimagl.c \
s_conj.c s_conjf.c s_conjl.c \
s_cproj.c s_cprojf.c s_creal.c s_crealf.c s_creall.c
s_cproj.c s_cprojf.c s_creal.c s_crealf.c s_creall.c \
s_csinh.c s_csinhf.c s_ctanh.c s_ctanhf.c
# FreeBSD's C library supplies these functions:
#COMMON_SRCS+= s_fabs.c s_frexp.c s_isnan.c s_ldexp.c s_modf.c
@ -125,7 +127,8 @@ SRCS= ${COMMON_SRCS} ${ARCH_SRCS}
INCS= fenv.h math.h
MAN= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 ceil.3 cexp.3 \
MAN= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 \
ceil.3 ccos.3 ccosh.3 cexp.3 \
cimag.3 copysign.3 cos.3 cosh.3 csqrt.3 erf.3 exp.3 fabs.3 fdim.3 \
feclearexcept.3 feenableexcept.3 fegetenv.3 \
fegetround.3 fenv.3 floor.3 \
@ -143,6 +146,9 @@ MLINKS+=atan.3 atanf.3 atan.3 atanl.3
MLINKS+=atanh.3 atanhf.3
MLINKS+=atan2.3 atan2f.3 atan2.3 atan2l.3 \
atan2.3 carg.3 atan2.3 cargf.3 atan2.3 cargl.3
MLINKS+=ccos.3 ccosf.3 ccos.3 csin.3 ccos.3 csinf.3 ccos.3 ctan.3 ccos.3 ctanf.3
MLINKS+=ccosh.3 ccoshf.3 ccosh.3 csinh.3 ccosh.3 csinhf.3 \
ccosh.3 ctanh.3 ccosh.3 ctanhf.3
MLINKS+=ceil.3 ceilf.3 ceil.3 ceill.3
MLINKS+=cexp.3 cexpf.3
MLINKS+=cimag.3 cimagf.3 cimag.3 cimagl.3 \

12
lib/msun/Symbol.map
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@ -237,4 +237,16 @@ FBSD_1.3 {
fegetround;
fesetround;
fesetenv;
csin;
csinf;
csinh;
csinhf;
ccos;
ccosf;
ccosh;
ccoshf;
ctan;
ctanf;
ctanh;
ctanhf;
};

80
lib/msun/man/ccos.3 Normal file
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@ -0,0 +1,80 @@
.\" 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.
.\"
.\" $FreeBSD$
.\"
.Dd October 17, 2011
.Dt CCOS 3
.Os
.Sh NAME
.Nm ccos ,
.Nm ccosf ,
.Nm csin ,
.Nm csinf
.Nm ctan ,
.Nm ctanf
.Nd complex trigonometric functions
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In complex.h
.Ft double complex
.Fn ccos "double complex z"
.Ft float complex
.Fn ccosf "float complex z"
.Ft double complex
.Fn csin "double complex z"
.Ft float complex
.Fn csinf "float complex z"
.Ft double complex
.Fn ctan "double complex z"
.Ft float complex
.Fn ctanf "float complex z"
.Sh DESCRIPTION
The
.Fn ccos ,
.Fn csin ,
and
.Fn ctan
functions compute the cosine, sine, and tangent of the complex number
.Fa z ,
respectively.
The
.Fn ccosf ,
.Fn csinf ,
and
.Fn ctanf
functions perform the same operations in
.Fa float
precision.
.Sh SEE ALSO
.Xr ccosh 3 ,
.Xr complex 3 ,
.Xr cos 3 ,
.Xr math 3 ,
.Xr sin 3 ,
.Xr tan 3
.Sh STANDARDS
These functions conform to
.St -isoC-99 .

80
lib/msun/man/ccosh.3 Normal file
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@ -0,0 +1,80 @@
.\" 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.
.\"
.\" $FreeBSD$
.\"
.Dd October 17, 2011
.Dt CCOSH 3
.Os
.Sh NAME
.Nm ccosh ,
.Nm ccoshf ,
.Nm csinh ,
.Nm csinhf
.Nm ctanh ,
.Nm ctanhf
.Nd complex hyperbolic functions
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In complex.h
.Ft double complex
.Fn ccosh "double complex z"
.Ft float complex
.Fn ccoshf "float complex z"
.Ft double complex
.Fn csinh "double complex z"
.Ft float complex
.Fn csinhf "float complex z"
.Ft double complex
.Fn ctanh "double complex z"
.Ft float complex
.Fn ctanhf "float complex z"
.Sh DESCRIPTION
The
.Fn ccosh ,
.Fn csinh ,
and
.Fn ctanh
functions compute the hyperbolic cosine, sine, and tangent of the complex number
.Fa z ,
respectively.
The
.Fn ccoshf ,
.Fn csinhf ,
and
.Fn ctanhf
functions perform the same operations in
.Fa float
precision.
.Sh SEE ALSO
.Xr ccos 3 ,
.Xr complex 3 ,
.Xr cosh 3 ,
.Xr math 3 ,
.Xr sinh 3 ,
.Xr tanh 3
.Sh STANDARDS
These functions conform to
.St -isoC-99 .

22
lib/msun/man/complex.3
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@ -24,7 +24,7 @@
.\"
.\" $FreeBSD$
.\"
.Dd March 7, 2011
.Dd October 17, 2011
.Dt COMPLEX 3
.Os
.Sh NAME
@ -86,6 +86,16 @@ conj compute the complex conjugate
cproj compute projection onto Riemann sphere
creal compute the real part
.El
.\" Section 7.3.5-6 of ISO C99 standard
.Ss Trigonometric and Hyperbolic Functions
.Cl
ccos cosine
ccosh hyperbolic cosine
csin sine
csinh hyperbolic sine
ctan tangent
ctanh hyperbolic tangent
.El
.Sh SEE ALSO
.Xr math 3 ,
.Xr fenv 3 ,
@ -101,20 +111,14 @@ The
functions described here conform to
.St -isoC-99 .
.Sh BUGS
The trigonmetric and hyperbolic functions
The inverse trigonmetric and hyperbolic functions
.Fn cacos ,
.Fn cacosh ,
.Fn casin ,
.Fn casinh ,
.Fn catan ,
.Fn catanh ,
.Fn ccos ,
.Fn ccosh ,
.Fn csin ,
.Fn csinh ,
.Fn ctan ,
and
.Fn ctanh
.Fn catanh
are not implemented.
.Pp
The logarithmic functions

1
lib/msun/man/cos.3
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@ -71,6 +71,7 @@ functions return the cosine value.
.Xr asin 3 ,
.Xr atan 3 ,
.Xr atan2 3 ,
.Xr ccos 3 ,
.Xr cosh 3 ,
.Xr math 3 ,
.Xr sin 3 ,

1
lib/msun/man/cosh.3
View File

@ -55,6 +55,7 @@ functions compute the hyperbolic cosine of
.Xr asin 3 ,
.Xr atan 3 ,
.Xr atan2 3 ,
.Xr ccosh 3 ,
.Xr cos 3 ,
.Xr math 3 ,
.Xr sin 3 ,

1
lib/msun/man/sin.3
View File

@ -70,6 +70,7 @@ functions return the sine value.
.Xr asin 3 ,
.Xr atan 3 ,
.Xr atan2 3 ,
.Xr csin 3 ,
.Xr cos 3 ,
.Xr cosh 3 ,
.Xr math 3 ,

1
lib/msun/man/sinh.3
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@ -56,6 +56,7 @@ functions compute the hyperbolic sine of
.Xr atan2 3 ,
.Xr cos 3 ,
.Xr cosh 3 ,
.Xr csinh 3 ,
.Xr math 3 ,
.Xr sin 3 ,
.Xr tan 3 ,

1
lib/msun/man/tan.3
View File

@ -73,6 +73,7 @@ functions return the tangent value.
.Xr atan2 3 ,
.Xr cos 3 ,
.Xr cosh 3 ,
.Xr ctan 3 ,
.Xr math 3 ,
.Xr sin 3 ,
.Xr sinh 3 ,

1
lib/msun/man/tanh.3
View File

@ -65,6 +65,7 @@ functions return the hyperbolic tangent value.
.Xr atan2 3 ,
.Xr cos 3 ,
.Xr cosh 3 ,
.Xr ctanh 3 ,
.Xr math 3 ,
.Xr sin 3 ,
.Xr sinh 3 ,

138
lib/msun/src/s_ccosh.c Normal file
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@ -0,0 +1,138 @@
/*-
* Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
* 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 unmodified, 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 ``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 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.
*/
/*
* Hyperbolic cosine of a complex argument z = x + i y.
*
* cosh(z) = cosh(x+iy)
* = cosh(x) cos(y) + i sinh(x) sin(y).
*
* Exceptional values are noted in the comments within the source code.
* These values and the return value were taken from n1124.pdf.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <math.h>
#include "math_private.h"
double complex
ccosh(double complex z)
{
double x, y;
int32_t hx, hy, ix, iy, lx, ly;
x = creal(z);
y = cimag(z);
EXTRACT_WORDS(hx, lx, x);
EXTRACT_WORDS(hy, ly, y);
ix = 0x7fffffff & hx;
iy = 0x7fffffff & hy;
/* Handle the nearly-non-exceptional cases where x and y are finite. */
if (ix < 0x7ff00000 && iy < 0x7ff00000) {
if ((iy | ly) == 0)
return (cpack(cosh(x), x * y));
/* XXX We don't handle |x| > DBL_MAX ln(2) yet. */
return (cpack(cosh(x) * cos(y), sinh(x) * sin(y)));
}
/*
* cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0.
* The sign of 0 in the result is unspecified. Choice = normally
* the same as dNaN. Raise the invalid floating-point exception.
*
* cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0.
* The sign of 0 in the result is unspecified. Choice = normally
* the same as d(NaN).
*/
if ((ix | lx) == 0 && iy >= 0x7ff00000)
return (cpack(y - y, copysign(0, x * (y - y))));
/*
* cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
*
* cosh(NaN +- I 0) = d(NaN) + I sign(d(NaN, +-0))0.
* The sign of 0 in the result is unspecified.
*/
if ((iy | ly) == 0 && ix >= 0x7ff00000) {
if (((hx & 0xfffff) | lx) == 0)
return (cpack(x * x, copysign(0, x) * y));
return (cpack(x * x, copysign(0, (x + x) * y)));
}
/*
* cosh(x +- I Inf) = dNaN + I dNaN.
* Raise the invalid floating-point exception for finite nonzero x.
*
* cosh(x + I NaN) = d(NaN) + I d(NaN).
* Optionally raises the invalid floating-point exception for finite
* nonzero x. Choice = don't raise (except for signaling NaNs).
*/
if (ix < 0x7ff00000 && iy >= 0x7ff00000)
return (cpack(y - y, x * (y - y)));
/*
* cosh(+-Inf + I NaN) = +Inf + I d(NaN).
*
* cosh(+-Inf +- I Inf) = +Inf + I dNaN.
* The sign of Inf in the result is unspecified. Choice = always +.
* Raise the invalid floating-point exception.
*
* cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y)
*/
if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
if (iy >= 0x7ff00000)
return (cpack(x * x, x * (y - y)));
return (cpack((x * x) * cos(y), x * sin(y)));
}
/*
* cosh(NaN + I NaN) = d(NaN) + I d(NaN).
*
* cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
* Optionally raises the invalid floating-point exception.
* Choice = raise.
*
* cosh(NaN + I y) = d(NaN) + I d(NaN).
* Optionally raises the invalid floating-point exception for finite
* nonzero y. Choice = don't raise (except for signaling NaNs).
*/
return (cpack((x * x) * (y - y), (x + x) * (y - y)));
}
double complex
ccos(double complex z)
{
/* ccos(z) = ccosh(I * z) */
return (ccosh(cpack(-cimag(z), creal(z))));
}

87
lib/msun/src/s_ccoshf.c Normal file
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@ -0,0 +1,87 @@
/*-
* Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
* 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 unmodified, 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 ``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 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.
*/
/*
* Hyperbolic cosine of a complex argument. See s_ccosh.c for details.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <math.h>
#include "math_private.h"
float complex
ccoshf(float complex z)
{
float x, y;
int32_t hx, hy, ix, iy;
x = crealf(z);
y = cimagf(z);
GET_FLOAT_WORD(hx, x);
GET_FLOAT_WORD(hy, y);
ix = 0x7fffffff & hx;
iy = 0x7fffffff & hy;
if (ix < 0x7f800000 && iy < 0x7f800000) {
if (iy == 0)
return (cpackf(coshf(x), x * y));
/* XXX We don't handle |x| > FLT_MAX ln(2) yet. */
return (cpackf(coshf(x) * cosf(y), sinhf(x) * sinf(y)));
}
if (ix == 0 && iy >= 0x7f800000)
return (cpackf(y - y, copysignf(0, x * (y - y))));
if (iy == 0 && ix >= 0x7f800000) {
if ((hx & 0x7fffff) == 0)
return (cpackf(x * x, copysignf(0, x) * y));
return (cpackf(x * x, copysignf(0, (x + x) * y)));
}
if (ix < 0x7f800000 && iy >= 0x7f800000)
return (cpackf(y - y, x * (y - y)));
if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) {
if (iy >= 0x7f800000)
return (cpackf(x * x, x * (y - y)));
return (cpackf((x * x) * cosf(y), x * sinf(y)));
}
return (cpackf((x * x) * (y - y), (x + x) * (y - y)));
}
float complex
ccosf(float complex z)
{
return (ccoshf(cpackf(-cimagf(z), crealf(z))));
}

140
lib/msun/src/s_csinh.c Normal file
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@ -0,0 +1,140 @@
/*-
* Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
* 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 unmodified, 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 ``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 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.
*/
/*
* Hyperbolic sine of a complex argument z = x + i y.
*
* sinh(z) = sinh(x+iy)
* = sinh(x) cos(y) + i cosh(x) sin(y).
*
* Exceptional values are noted in the comments within the source code.
* These values and the return value were taken from n1124.pdf.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <math.h>
#include "math_private.h"
double complex
csinh(double complex z)
{
double x, y;
int32_t hx, hy, ix, iy, lx, ly;
x = creal(z);
y = cimag(z);
EXTRACT_WORDS(hx, lx, x);
EXTRACT_WORDS(hy, ly, y);
ix = 0x7fffffff & hx;
iy = 0x7fffffff & hy;
/* Handle the nearly-non-exceptional cases where x and y are finite. */
if (ix < 0x7ff00000 && iy < 0x7ff00000) {
if ((iy | ly) == 0)
return (cpack(sinh(x), y));
/* XXX We don't handle |x| > DBL_MAX ln(2) yet. */
return (cpack(sinh(x) * cos(y), cosh(x) * sin(y)));
}
/*
* sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN.
* The sign of 0 in the result is unspecified. Choice = normally
* the same as dNaN. Raise the invalid floating-point exception.
*
* sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN).
* The sign of 0 in the result is unspecified. Choice = normally
* the same as d(NaN).
*/
if ((ix | lx) == 0 && iy >= 0x7ff00000)
return (cpack(copysign(0, x * (y - y)), y - y));
/*
* sinh(+-Inf +- I 0) = +-Inf + I (+-)(+-)0.
*
* sinh(NaN +- I 0) = d(NaN) + I +-0.
*/
if ((iy | ly) == 0 && ix >= 0x7ff00000) {
if (((hx & 0xfffff) | lx) == 0)
return (cpack(x, copysign(0, x) * y));
return (cpack(x, copysign(0, y)));
}
/*
* sinh(x +- I Inf) = dNaN + I dNaN.
* Raise the invalid floating-point exception for finite nonzero x.
*
* sinh(x + I NaN) = d(NaN) + I d(NaN).
* Optionally raises the invalid floating-point exception for finite
* nonzero x. Choice = don't raise (except for signaling NaNs).
*/
if (ix < 0x7ff00000 && iy >= 0x7ff00000)
return (cpack(y - y, x * (y - y)));
/*
* sinh(+-Inf + I NaN) = +-Inf + I d(NaN).
* The sign of Inf in the result is unspecified. Choice = normally
* the same as d(NaN).
*
* sinh(+-Inf +- I Inf) = +Inf + I dNaN.
* The sign of Inf in the result is unspecified. Choice = always +.
* Raise the invalid floating-point exception.
*
* sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y)
*/
if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
if (iy >= 0x7ff00000)
return (cpack(x * x, x * (y - y)));
return (cpack(x * cos(y), INFINITY * sin(y)));
}
/*
* sinh(NaN + I NaN) = d(NaN) + I d(NaN).
*
* sinh(NaN +- I Inf) = d(NaN) + I d(NaN).
* Optionally raises the invalid floating-point exception.
* Choice = raise.
*
* sinh(NaN + I y) = d(NaN) + I d(NaN).
* Optionally raises the invalid floating-point exception for finite
* nonzero y. Choice = don't raise (except for signaling NaNs).
*/
return (cpack((x * x) * (y - y), (x + x) * (y - y)));
}
double complex
csin(double complex z)
{
/* csin(z) = -I * csinh(I * z) */
z = csinh(cpack(-cimag(z), creal(z)));
return (cpack(cimag(z), -creal(z)));
}

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/*-
* Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
* 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 unmodified, 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 ``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 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.
*/
/*
* Hyperbolic sine of a complex argument z. See s_csinh.c for details.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <math.h>
#include "math_private.h"
float complex
csinhf(float complex z)
{
float x, y;
int32_t hx, hy, ix, iy;
x = crealf(z);
y = cimagf(z);
GET_FLOAT_WORD(hx, x);
GET_FLOAT_WORD(hy, y);
ix = 0x7fffffff & hx;
iy = 0x7fffffff & hy;
if (ix < 0x7f800000 && iy < 0x7f800000) {
if (iy == 0)
return (cpackf(sinhf(x), y));
/* XXX We don't handle |x| > FLT_MAX ln(2) yet. */
return (cpackf(sinhf(x) * cosf(y), coshf(x) * sinf(y)));
}
if (ix == 0 && iy >= 0x7f800000)
return (cpackf(copysignf(0, x * (y - y)), y - y));
if (iy == 0 && ix >= 0x7f800000) {
if ((hx & 0x7fffff) == 0)
return (cpackf(x, copysignf(0, x) * y));
return (cpackf(x, copysignf(0, y)));
}
if (ix < 0x7f800000 && iy >= 0x7f800000)
return (cpackf(y - y, x * (y - y)));
if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) {
if (iy >= 0x7f800000)
return (cpackf(x * x, x * (y - y)));
return (cpackf(x * cosf(y), INFINITY * sinf(y)));
}
return (cpackf((x * x) * (y - y), (x + x) * (y - y)));
}
float complex
csinf(float complex z)
{
z = csinhf(cpackf(-cimagf(z), crealf(z)));
return (cpackf(cimagf(z), -crealf(z)));
}

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/*-
* Copyright (c) 2011 David Schultz
* 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 unmodified, 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 ``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 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.
*/
/*
* Hyperbolic tangent of a complex argument z = x + i y.
*
* The algorithm is from:
*
* W. Kahan. Branch Cuts for Complex Elementary Functions or Much
* Ado About Nothing's Sign Bit. In The State of the Art in
* Numerical Analysis, pp. 165 ff. Iserles and Powell, eds., 1987.
*
* Method:
*
* Let t = tan(x)
* beta = 1/cos^2(y)
* s = sinh(x)
* rho = cosh(x)
*
* We have:
*
* tanh(z) = sinh(z) / cosh(z)
*
* sinh(x) cos(y) + i cosh(x) sin(y)
* = ---------------------------------
* cosh(x) cos(y) + i sinh(x) sin(y)
*
* cosh(x) sinh(x) / cos^2(y) + i tan(y)
* = -------------------------------------
* 1 + sinh^2(x) / cos^2(y)
*
* beta rho s + i t
* = ----------------
* 1 + beta s^2
*
* Modifications:
*
* I omitted the original algorithm's handling of overflow in tan(x) after
* verifying with nearpi.c that this can't happen in IEEE single or double
* precision. I also handle large x differently.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <math.h>
#include "math_private.h"
double complex
ctanh(double complex z)
{
double x, y;
double t, beta, s, rho, denom;
uint32_t hx, ix, lx;
x = creal(z);
y = cimag(z);
EXTRACT_WORDS(hx, lx, x);
ix = hx & 0x7fffffff;
/*
* ctanh(NaN + i 0) = NaN + i 0
*
* ctanh(NaN + i y) = NaN + i NaN for y != 0
*
* The imaginary part has the sign of x*sin(2*y), but there's no
* special effort to get this right.
*
* ctanh(+-Inf +- i Inf) = +-1 +- 0
*
* ctanh(+-Inf + i y) = +-1 + 0 sin(2y) for y finite
*
* The imaginary part of the sign is unspecified. This special
* case is only needed to avoid a spurious invalid exception when
* y is infinite.
*/
if (ix >= 0x7ff00000) {
if ((ix & 0xfffff) | lx) /* x is NaN */
return (cpack(x, (y == 0 ? y : x * y)));
SET_HIGH_WORD(x, hx - 0x40000000); /* x = copysign(1, x) */
return (cpack(x, copysign(0, isinf(y) ? y : sin(y) * cos(y))));
}
/*
* ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the
* approximation sinh^2(huge) ~= exp(2*huge) / 4.
* We use a modified formula to avoid spurious overflow.
*/
if (ix >= 0x40360000) { /* x >= 22 */
double exp_mx = exp(-fabs(x));
return (cpack(copysign(1, x),
4 * sin(y) * cos(y) * exp_mx * exp_mx));
}
/* Kahan's algorithm */
t = tan(y);
beta = 1.0 + t * t; /* = 1 / cos^2(y) */
s = sinh(x);
rho = sqrt(1 + s * s); /* = cosh(x) */
denom = 1 + beta * s * s;
return (cpack((beta * rho * s) / denom, t / denom));
}
double complex
ctan(double complex z)
{
/* ctan(z) = -I * ctanh(I * z) */
z = ctanh(cpack(-cimag(z), creal(z)));
return (cpack(cimag(z), -creal(z)));
}

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/*-
* Copyright (c) 2011 David Schultz
* 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 unmodified, 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 ``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 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.
*/
/*
* Hyperbolic tangent of a complex argument z. See s_ctanh.c for details.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <complex.h>
#include <math.h>
#include "math_private.h"
float complex
ctanhf(float complex z)
{
float x, y;
float t, beta, s, rho, denom;
uint32_t hx, ix;
x = crealf(z);
y = cimagf(z);
GET_FLOAT_WORD(hx, x);
ix = hx & 0x7fffffff;
if (ix >= 0x7f800000) {
if (ix & 0x7fffff)
return (cpackf(x, (y == 0 ? y : x * y)));
SET_FLOAT_WORD(x, hx - 0x40000000);
return (cpackf(x,
copysignf(0, isinf(y) ? y : sinf(y) * cosf(y))));
}
if (ix >= 0x41300000) { /* x >= 11 */
float exp_mx = expf(-fabsf(x));
return (cpackf(copysignf(1, x),
4 * sinf(y) * cosf(y) * exp_mx * exp_mx));
}
t = tanf(y);
beta = 1.0 + t * t;
s = sinhf(x);
rho = sqrtf(1 + s * s);
denom = 1 + beta * s * s;
return (cpackf((beta * rho * s) / denom, t / denom));
}
float complex
ctanf(float complex z)
{
z = ctanhf(cpackf(-cimagf(z), crealf(z)));
return (cpackf(cimagf(z), -crealf(z)));
}