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Add various complex math routines from OpenBSD.

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This commit is contained in:
Viral B. Shah 2014-12-05 00:13:36 +05:30
parent f876e59885
commit da782e78d9
37 changed files with 3005 additions and 0 deletions
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30
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/* $OpenBSD: s_cabs.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */
/*
* Copyright (c) 2008 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.
*/
#include <complex.h>
#include <float.h>
#include <math.h>
double
cabs(double complex z)
{
return hypot(__real__ z, __imag__ z);
}
#if LDBL_MANT_DIG == DBL_MANT_DIG
__strong_alias(cabsl, cabs);
#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */

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/* $OpenBSD: s_cabsf.c,v 1.1 2008/09/07 20:36:09 martynas Exp $ */
/*
* Copyright (c) 2008 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.
*/
#include <complex.h>
#include <math.h>
float
cabsf(float complex z)
{
return hypotf(__real__ z, __imag__ z);
}

26
src/s_cabsl.c Normal file
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/* $OpenBSD: s_cabsl.c,v 1.1 2011/07/08 19:25:31 martynas 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.
*/
#include <complex.h>
#include <math.h>
long double
cabsl(long double complex z)
{
return hypotl(__real__ z, __imag__ z);
}

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/* $OpenBSD: s_cacos.c,v 1.6 2013/07/03 04:46:36 espie 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.
*/
/* cacos()
*
* Complex circular arc cosine
*
*
*
* SYNOPSIS:
*
* double complex cacos();
* double complex z, w;
*
* w = cacos (z);
*
*
*
* DESCRIPTION:
*
*
* w = arccos z = PI/2 - arcsin z.
*
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 5200 1.6e-15 2.8e-16
* IEEE -10,+10 30000 1.8e-14 2.2e-15
*/
#include <complex.h>
#include <float.h>
#include <math.h>
double complex
cacos(double complex z)
{
double complex w;
w = casin (z);
w = (M_PI_2 - creal (w)) - cimag (w) * I;
return (w);
}
#if LDBL_MANT_DIG == DBL_MANT_DIG
__strong_alias(cacosl, cacos);
#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */

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/* $OpenBSD: s_cacosf.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.
*/
/* cacosf()
*
* Complex circular arc cosine
*
*
*
* SYNOPSIS:
*
* void cacosf();
* cmplxf z, w;
*
* cacosf( &z, &w );
*
*
*
* DESCRIPTION:
*
*
* w = arccos z = PI/2 - arcsin z.
*
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 9.2e-6 1.2e-6
*
*/
#include <complex.h>
#include <math.h>
float complex
cacosf(float complex z)
{
float complex w;
w = casinf( z );
w = ((float)M_PI_2 - crealf (w)) - cimagf (w) * I;
return (w);
}

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/* $OpenBSD: s_cacosh.c,v 1.6 2013/07/03 04:46:36 espie 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.
*/
/* cacosh
*
* Complex inverse hyperbolic cosine
*
*
*
* SYNOPSIS:
*
* double complex cacosh();
* double complex z, w;
*
* w = cacosh (z);
*
*
*
* DESCRIPTION:
*
* acosh z = i acos z .
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 1.6e-14 2.1e-15
*
*/
#include <complex.h>
#include <float.h>
#include <math.h>
double complex
cacosh(double complex z)
{
double complex w;
w = I * cacos (z);
return (w);
}
#if LDBL_MANT_DIG == DBL_MANT_DIG
__strong_alias(cacoshl, cacosh);
#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */

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/* $OpenBSD: s_cacoshf.c,v 1.1 2008/09/07 20:36:09 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.
*/
/* cacoshf
*
* Complex inverse hyperbolic cosine
*
*
*
* SYNOPSIS:
*
* float complex cacoshf();
* float complex z, w;
*
* w = cacoshf (z);
*
*
*
* DESCRIPTION:
*
* acosh z = i acos z .
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 1.6e-14 2.1e-15
*
*/
#include <complex.h>
#include <math.h>
float complex
cacoshf(float complex z)
{
float complex w;
w = I * cacosf (z);
return (w);
}

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/* $OpenBSD: s_cacoshl.c,v 1.1 2011/07/08 19:25:31 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.
*/
/* cacoshl
*
* Complex inverse hyperbolic cosine
*
*
*
* SYNOPSIS:
*
* long double complex cacoshl();
* long double complex z, w;
*
* w = cacoshl (z);
*
*
*
* DESCRIPTION:
*
* acosh z = i acos z .
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 1.6e-14 2.1e-15
*
*/
#include <complex.h>
#include <math.h>
long double complex
cacoshl(long double complex z)
{
long double complex w;
w = I * cacosl(z);
return (w);
}

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/* $OpenBSD: s_cacosl.c,v 1.3 2011/07/20 21:02:51 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.
*/
/* cacosl()
*
* Complex circular arc cosine
*
*
*
* SYNOPSIS:
*
* long double complex cacosl();
* long double complex z, w;
*
* w = cacosl( z );
*
*
*
* DESCRIPTION:
*
*
* w = arccos z = PI/2 - arcsin z.
*
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 5200 1.6e-15 2.8e-16
* IEEE -10,+10 30000 1.8e-14 2.2e-15
*/
#include <complex.h>
#include <math.h>
static const long double PIO2L = 1.570796326794896619231321691639751442098585L;
long double complex
cacosl(long double complex z)
{
long double complex w;
w = casinl(z);
w = (PIO2L - creall(w)) - cimagl(w) * I;
return (w);
}

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/* $OpenBSD: s_casin.c,v 1.6 2013/07/03 04:46:36 espie 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.
*/
/* casin()
*
* Complex circular arc sine
*
*
*
* SYNOPSIS:
*
* double complex casin();
* double complex z, w;
*
* w = casin (z);
*
*
*
* DESCRIPTION:
*
* Inverse complex sine:
*
* 2
* w = -i clog( iz + csqrt( 1 - z ) ).
*
* casin(z) = -i casinh(iz)
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 10100 2.1e-15 3.4e-16
* IEEE -10,+10 30000 2.2e-14 2.7e-15
* Larger relative error can be observed for z near zero.
* Also tested by csin(casin(z)) = z.
*/
#include <complex.h>
#include <float.h>
#include <math.h>
double complex
casin(double complex z)
{
double complex w;
static double complex ca, ct, zz, z2;
double x, y;
x = creal (z);
y = cimag (z);
if (y == 0.0) {
if (fabs(x) > 1.0) {
w = M_PI_2 + 0.0 * I;
/*mtherr ("casin", DOMAIN);*/
}
else {
w = asin (x) + 0.0 * I;
}
return (w);
}
/* Power series expansion */
/*
b = cabs(z);
if( b < 0.125 ) {
z2.r = (x - y) * (x + y);
z2.i = 2.0 * x * y;
cn = 1.0;
n = 1.0;
ca.r = x;
ca.i = y;
sum.r = x;
sum.i = y;
do {
ct.r = z2.r * ca.r - z2.i * ca.i;
ct.i = z2.r * ca.i + z2.i * ca.r;
ca.r = ct.r;
ca.i = ct.i;
cn *= n;
n += 1.0;
cn /= n;
n += 1.0;
b = cn/n;
ct.r *= b;
ct.i *= b;
sum.r += ct.r;
sum.i += ct.i;
b = fabs(ct.r) + fabs(ct.i);
}
while( b > MACHEP );
w->r = sum.r;
w->i = sum.i;
return;
}
*/
ca = x + y * I;
ct = ca * I;
/* sqrt( 1 - z*z) */
/* cmul( &ca, &ca, &zz ) */
/*x * x - y * y */
zz = (x - y) * (x + y) + (2.0 * x * y) * I;
zz = 1.0 - creal(zz) - cimag(zz) * I;
z2 = csqrt (zz);
zz = ct + z2;
zz = clog (zz);
/* multiply by 1/i = -i */
w = zz * (-1.0 * I);
return (w);
}
#if LDBL_MANT_DIG == DBL_MANT_DIG
__strong_alias(casinl, casin);
#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */

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/* $OpenBSD: s_casinf.c,v 1.3 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.
*/
/* casinf()
*
* Complex circular arc sine
*
*
*
* SYNOPSIS:
*
* void casinf();
* cmplxf z, w;
*
* casinf( &z, &w );
*
*
*
* DESCRIPTION:
*
* Inverse complex sine:
*
* 2
* w = -i clog( iz + csqrt( 1 - z ) ).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 1.1e-5 1.5e-6
* Larger relative error can be observed for z near zero.
*
*/
#include <complex.h>
#include <math.h>
float complex
casinf(float complex z)
{
float complex w;
float x, y;
static float complex ca, ct, zz, z2;
/*
float cn, n;
static float a, b, s, t, u, v, y2;
static cmplxf sum;
*/
x = crealf(z);
y = cimagf(z);
if(y == 0.0f) {
if(fabsf(x) > 1.0f) {
w = (float)M_PI_2 + 0.0f * I;
/*mtherr( "casinf", DOMAIN );*/
}
else {
w = asinf (x) + 0.0f * I;
}
return (w);
}
/* Power series expansion */
/*
b = cabsf(z);
if(b < 0.125) {
z2.r = (x - y) * (x + y);
z2.i = 2.0 * x * y;
cn = 1.0;
n = 1.0;
ca.r = x;
ca.i = y;
sum.r = x;
sum.i = y;
do {
ct.r = z2.r * ca.r - z2.i * ca.i;
ct.i = z2.r * ca.i + z2.i * ca.r;
ca.r = ct.r;
ca.i = ct.i;
cn *= n;
n += 1.0;
cn /= n;
n += 1.0;
b = cn/n;
ct.r *= b;
ct.i *= b;
sum.r += ct.r;
sum.i += ct.i;
b = fabsf(ct.r) + fabsf(ct.i);
}
while(b > MACHEPF);
w->r = sum.r;
w->i = sum.i;
return;
}
*/
ca = x + y * I;
ct = ca * I; /* iz */
/* sqrt( 1 - z*z) */
/* cmul( &ca, &ca, &zz ) */
/*x * x - y * y */
zz = (x - y) * (x + y) + (2.0f * x * y) * I;
zz = 1.0f - crealf(zz) - cimagf(zz) * I;
z2 = csqrtf (zz);
zz = ct + z2;
zz = clogf (zz);
/* multiply by 1/i = -i */
w = zz * (-1.0f * I);
return (w);
}

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/* $OpenBSD: s_casinh.c,v 1.6 2013/07/03 04:46:36 espie 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.
*/
/* casinh
*
* Complex inverse hyperbolic sine
*
*
*
* SYNOPSIS:
*
* double complex casinh();
* double complex z, w;
*
* w = casinh (z);
*
*
*
* DESCRIPTION:
*
* casinh z = -i casin iz .
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 1.8e-14 2.6e-15
*
*/
#include <complex.h>
#include <float.h>
#include <math.h>
double complex
casinh(double complex z)
{
double complex w;
w = -1.0 * I * casin (z * I);
return (w);
}
#if LDBL_MANT_DIG == DBL_MANT_DIG
__strong_alias(casinhl, casinh);
#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */

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/* $OpenBSD: s_casinhf.c,v 1.1 2008/09/07 20:36:09 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.
*/
/* casinhf
*
* Complex inverse hyperbolic sine
*
*
*
* SYNOPSIS:
*
* float complex casinhf();
* float complex z, w;
*
* w = casinhf (z);
*
*
*
* DESCRIPTION:
*
* casinh z = -i casin iz .
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 1.8e-14 2.6e-15
*
*/
#include <complex.h>
#include <math.h>
float complex
casinhf(float complex z)
{
float complex w;
w = -1.0f * I * casinf (z * I);
return (w);
}

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/* $OpenBSD: s_casinhl.c,v 1.1 2011/07/08 19:25:31 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.
*/
/* casinhl
*
* Complex inverse hyperbolic sine
*
*
*
* SYNOPSIS:
*
* long double complex casinhf();
* long double complex z, w;
*
* w = casinhl (z);
*
*
*
* DESCRIPTION:
*
* casinh z = -i casin iz .
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 1.8e-14 2.6e-15
*
*/
#include <complex.h>
#include <math.h>
long double complex
casinhl(long double complex z)
{
long double complex w;
w = -1.0L * I * casinl(z * I);
return (w);
}

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/* $OpenBSD: s_casinl.c,v 1.3 2011/07/20 21:02:51 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.
*/
/* casinl()
*
* Complex circular arc sine
*
*
*
* SYNOPSIS:
*
* long double complex casinl();
* long double complex z, w;
*
* w = casinl( z );
*
*
*
* DESCRIPTION:
*
* Inverse complex sine:
*
* 2
* w = -i clog( iz + csqrt( 1 - z ) ).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 10100 2.1e-15 3.4e-16
* IEEE -10,+10 30000 2.2e-14 2.7e-15
* Larger relative error can be observed for z near zero.
* Also tested by csin(casin(z)) = z.
*/
#include <complex.h>
#include <float.h>
#include <math.h>
#if LDBL_MANT_DIG == 64
static const long double MACHEPL= 5.42101086242752217003726400434970855712890625E-20L;
#elif LDBL_MANT_DIG == 113
static const long double MACHEPL = 9.629649721936179265279889712924636592690508e-35L;
#endif
static const long double PIO2L = 1.570796326794896619231321691639751442098585L;
long double complex
casinl(long double complex z)
{
long double complex w;
long double x, y, b;
static long double complex ca, ct, zz, z2;
x = creall(z);
y = cimagl(z);
if (y == 0.0L) {
if (fabsl(x) > 1.0L) {
w = PIO2L + 0.0L * I;
/*mtherr( "casinl", DOMAIN );*/
}
else {
w = asinl(x) + 0.0L * I;
}
return (w);
}
/* Power series expansion */
b = cabsl(z);
if (b < 0.125L) {
long double complex sum;
long double n, cn;
z2 = (x - y) * (x + y) + (2.0L * x * y) * I;
cn = 1.0L;
n = 1.0L;
ca = x + y * I;
sum = x + y * I;
do {
ct = z2 * ca;
ca = ct;
cn *= n;
n += 1.0L;
cn /= n;
n += 1.0L;
b = cn/n;
ct *= b;
sum += ct;
b = cabsl(ct);
}
while (b > MACHEPL);
w = sum;
return w;
}
ca = x + y * I;
ct = ca * I; /* iz */
/* sqrt(1 - z*z) */
/* cmul(&ca, &ca, &zz) */
/* x * x - y * y */
zz = (x - y) * (x + y) + (2.0L * x * y) * I;
zz = 1.0L - creall(zz) - cimagl(zz) * I;
z2 = csqrtl(zz);
zz = ct + z2;
zz = clogl(zz);
/* multiply by 1/i = -i */
w = zz * (-1.0L * I);
return (w);
}

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/* $OpenBSD: s_catan.c,v 1.6 2013/07/03 04:46:36 espie 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.
*/
/* catan()
*
* Complex circular arc tangent
*
*
*
* SYNOPSIS:
*
* double complex catan();
* double complex z, w;
*
* w = catan (z);
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
* 1 ( 2x )
* Re w = - arctan(-----------) + k PI
* 2 ( 2 2)
* (1 - x - y )
*
* ( 2 2)
* 1 (x + (y+1) )
* Im w = - log(------------)
* 4 ( 2 2)
* (x + (y-1) )
*
* Where k is an arbitrary integer.
*
* catan(z) = -i catanh(iz).
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 5900 1.3e-16 7.8e-18
* IEEE -10,+10 30000 2.3e-15 8.5e-17
* The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
* had peak relative error 1.5e-16, rms relative error
* 2.9e-17. See also clog().
*/
#include <complex.h>
#include <float.h>
#include <math.h>
#define MAXNUM 1.0e308
static const double DP1 = 3.14159265160560607910E0;
static const double DP2 = 1.98418714791870343106E-9;
static const double DP3 = 1.14423774522196636802E-17;
static double
_redupi(double x)
{
double t;
long i;
t = x/M_PI;
if(t >= 0.0)
t += 0.5;
else
t -= 0.5;
i = t; /* the multiple */
t = i;
t = ((x - t * DP1) - t * DP2) - t * DP3;
return (t);
}
double complex
catan(double complex z)
{
double complex w;
double a, t, x, x2, y;
x = creal (z);
y = cimag (z);
if ((x == 0.0) && (y > 1.0))
goto ovrf;
x2 = x * x;
a = 1.0 - x2 - (y * y);
if (a == 0.0)
goto ovrf;
t = 0.5 * atan2 (2.0 * x, a);
w = _redupi (t);
t = y - 1.0;
a = x2 + (t * t);
if (a == 0.0)
goto ovrf;
t = y + 1.0;
a = (x2 + (t * t))/a;
w = w + (0.25 * log (a)) * I;
return (w);
ovrf:
/*mtherr ("catan", OVERFLOW);*/
w = MAXNUM + MAXNUM * I;
return (w);
}
#if LDBL_MANT_DIG == DBL_MANT_DIG
__strong_alias(catanl, catan);
#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */

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/* $OpenBSD: s_catanf.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.
*/
/* catanf()
*
* Complex circular arc tangent
*
*
*
* SYNOPSIS:
*
* float complex catanf();
* float complex z, w;
*
* w = catanf( z );
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
* 1 ( 2x )
* Re w = - arctan(-----------) + k PI
* 2 ( 2 2)
* (1 - x - y )
*
* ( 2 2)
* 1 (x + (y+1) )
* Im w = - log(------------)
* 4 ( 2 2)
* (x + (y-1) )
*
* Where k is an arbitrary integer.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 2.3e-6 5.2e-8
*
*/
#include <complex.h>
#include <math.h>
#define MAXNUMF 1.0e38F
static const double DP1 = 3.140625;
static const double DP2 = 9.67502593994140625E-4;
static const double DP3 = 1.509957990978376432E-7;
static float
_redupif(float xx)
{
float x, t;
long i;
x = xx;
t = x/(float)M_PI;
if(t >= 0.0)
t += 0.5;
else
t -= 0.5;
i = t; /* the multiple */
t = i;
t = ((x - t * DP1) - t * DP2) - t * DP3;
return(t);
}
float complex
catanf(float complex z)
{
float complex w;
float a, t, x, x2, y;
x = crealf(z);
y = cimagf(z);
if((x == 0.0f) && (y > 1.0f))
goto ovrf;
x2 = x * x;
a = 1.0f - x2 - (y * y);
if (a == 0.0f)
goto ovrf;
t = 0.5f * atan2f(2.0f * x, a);
w = _redupif(t);
t = y - 1.0f;
a = x2 + (t * t);
if(a == 0.0f)
goto ovrf;
t = y + 1.0f;
a = (x2 + (t * t))/a;
w = w + (0.25f * logf (a)) * I;
return (w);
ovrf:
/*mtherr( "catanf", OVERFLOW );*/
w = MAXNUMF + MAXNUMF * I;
return (w);
}

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/* $OpenBSD: s_catanh.c,v 1.6 2013/07/03 04:46:36 espie 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.
*/
/* catanh
*
* Complex inverse hyperbolic tangent
*
*
*
* SYNOPSIS:
*
* double complex catanh();
* double complex z, w;
*
* w = catanh (z);
*
*
*
* DESCRIPTION:
*
* Inverse tanh, equal to -i catan (iz);
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 2.3e-16 6.2e-17
*
*/
#include <complex.h>
#include <float.h>
#include <math.h>
double complex
catanh(double complex z)
{
double complex w;
w = -1.0 * I * catan (z * I);
return (w);
}
#if LDBL_MANT_DIG == DBL_MANT_DIG
__strong_alias(catanhl, catanh);
#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */

55
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/* $OpenBSD: s_catanhf.c,v 1.1 2008/09/07 20:36:09 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.
*/
/* catanhf
*
* Complex inverse hyperbolic tangent
*
*
*
* SYNOPSIS:
*
* float complex catanhf();
* float complex z, w;
*
* w = catanhf (z);
*
*
*
* DESCRIPTION:
*
* Inverse tanh, equal to -i catan (iz);
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 2.3e-16 6.2e-17
*
*/
#include <complex.h>
#include <math.h>
float complex
catanhf(float complex z)
{
float complex w;
w = -1.0f * I * catanf (z * I);
return (w);
}

56
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/* $OpenBSD: s_catanhl.c,v 1.1 2011/07/08 19:25:31 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.
*/
/* catanhl
*
* Complex inverse hyperbolic tangent
*
*
*
* SYNOPSIS:
*
* long double complex catanhl();
* long double complex z, w;
*
* w = catanhl (z);
*
*
*
* DESCRIPTION:
*
* Inverse tanh, equal to -i catan (iz);
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 2.3e-16 6.2e-17
*
*/
#include <complex.h>
#include <math.h>
long double complex
catanhl(long double complex z)
{
long double complex w;
w = -1.0L * I * catanl(z * I);
return (w);
}

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/* $OpenBSD: s_catanl.c,v 1.3 2011/07/20 21:02:51 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.
*/
/* catanl()
*
* Complex circular arc tangent
*
*
*
* SYNOPSIS:
*
* long double complex catanl();
* long double complex z, w;
*
* w = catanl( z );
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
* 1 ( 2x )
* Re w = - arctan(-----------) + k PI
* 2 ( 2 2)
* (1 - x - y )
*
* ( 2 2)
* 1 (x + (y+1) )
* Im w = - log(------------)
* 4 ( 2 2)
* (x + (y-1) )
*
* Where k is an arbitrary integer.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 5900 1.3e-16 7.8e-18
* IEEE -10,+10 30000 2.3e-15 8.5e-17
* The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
* had peak relative error 1.5e-16, rms relative error
* 2.9e-17. See also clog().
*/
#include <complex.h>
#include <float.h>
#include <math.h>
static const long double PIL = 3.141592653589793238462643383279502884197169L;
static const long double DP1 = 3.14159265358979323829596852490908531763125L;
static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
static long double
redupil(long double x)
{
long double t;
long i;
t = x / PIL;
if (t >= 0.0L)
t += 0.5L;
else
t -= 0.5L;
i = t; /* the multiple */
t = i;
t = ((x - t * DP1) - t * DP2) - t * DP3;
return (t);
}
long double complex
catanl(long double complex z)
{
long double complex w;
long double a, t, x, x2, y;
x = creall(z);
y = cimagl(z);
if ((x == 0.0L) && (y > 1.0L))
goto ovrf;
x2 = x * x;
a = 1.0L - x2 - (y * y);
if (a == 0.0L)
goto ovrf;
t = atan2l(2.0L * x, a) * 0.5L;
w = redupil(t);
t = y - 1.0L;
a = x2 + (t * t);
if (a == 0.0L)
goto ovrf;
t = y + 1.0L;
a = (x2 + (t * t)) / a;
w = w + (0.25L * logl(a)) * I;
return (w);
ovrf:
/*mtherr( "catanl", OVERFLOW );*/
w = LDBL_MAX + LDBL_MAX * I;
return (w);
}

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/* $OpenBSD: s_ccos.c,v 1.6 2013/07/03 04:46:36 espie 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.
*/
/* ccos()
*
* Complex circular cosine
*
*
*
* SYNOPSIS:
*
* double complex ccos();
* double complex z, w;
*
* w = ccos (z);
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
*
* w = cos x cosh y - i sin x sinh y.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 8400 4.5e-17 1.3e-17
* IEEE -10,+10 30000 3.8e-16 1.0e-16
*/
#include <complex.h>
#include <float.h>
#include <math.h>
/* calculate cosh and sinh */
static void
_cchsh(double x, double *c, double *s)
{
double e, ei;
if (fabs(x) <= 0.5) {
*c = cosh(x);
*s = sinh(x);
}
else {
e = exp(x);
ei = 0.5/e;
e = 0.5 * e;
*s = e - ei;
*c = e + ei;
}
}
double complex
ccos(double complex z)
{
double complex w;
double ch, sh;
_cchsh( cimag(z), &ch, &sh );
w = cos(creal (z)) * ch - (sin (creal (z)) * sh) * I;
return (w);
}
#if LDBL_MANT_DIG == DBL_MANT_DIG
__strong_alias(ccosl, ccos);
#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */

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/* $OpenBSD: s_ccosf.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.
*/
/* ccosf()
*
* Complex circular cosine
*
*
*
* SYNOPSIS:
*
* void ccosf();
* cmplxf z, w;
*
* ccosf( &z, &w );
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
*
* w = cos x cosh y - i sin x sinh y.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 1.8e-7 5.5e-8
*/
#include <complex.h>
#include <math.h>
/* calculate cosh and sinh */
static void
_cchshf(float xx, float *c, float *s)
{
float x, e, ei;
x = xx;
if(fabsf(x) <= 0.5f) {
*c = coshf(x);
*s = sinhf(x);
}
else {
e = expf(x);
ei = 0.5f/e;
e = 0.5f * e;
*s = e - ei;
*c = e + ei;
}
}
float complex
ccosf(float complex z)
{
float complex w;
float ch, sh;
_cchshf( cimagf(z), &ch, &sh );
w = cosf( crealf(z) ) * ch + ( -sinf( crealf(z) ) * sh) * I;
return (w);
}

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/* $OpenBSD: s_ccoshl.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.
*/
/* ccoshl
*
* Complex hyperbolic cosine
*
*
*
* SYNOPSIS:
*
* long double complex ccoshl();
* long double complex z, w;
*
* w = ccoshl (z);
*
*
*
* DESCRIPTION:
*
* ccosh(z) = cosh x cos y + i sinh x sin y .
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 2.9e-16 8.1e-17
*
*/
#include <complex.h>
#include <math.h>
long double complex
ccoshl(long double complex z)
{
long double complex w;
long double x, y;
x = creall(z);
y = cimagl(z);
w = coshl(x) * cosl(y) + (sinhl(x) * sinl(y)) * I;
return (w);
}

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/* $OpenBSD: s_ccosl.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.
*/
/* ccosl()
*
* Complex circular cosine
*
*
*
* SYNOPSIS:
*
* long double complex ccosl();
* long double complex z, w;
*
* w = ccosl( z );
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
*
* w = cos x cosh y - i sin x sinh y.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 8400 4.5e-17 1.3e-17
* IEEE -10,+10 30000 3.8e-16 1.0e-16
*/
#include <complex.h>
#include <math.h>
static void
cchshl(long double x, long double *c, long double *s)
{
long double e, ei;
if(fabsl(x) <= 0.5L) {
*c = coshl(x);
*s = sinhl(x);
} else {
e = expl(x);
ei = 0.5L/e;
e = 0.5L * e;
*s = e - ei;
*c = e + ei;
}
}
long double complex
ccosl(long double complex z)
{
long double complex w;
long double ch, sh;
cchshl(cimagl(z), &ch, &sh);
w = cosl(creall(z)) * ch + (-sinl(creall(z)) * sh) * I;
return (w);
}

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/* $OpenBSD: s_cexpl.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.
*/
/* cexpl()
*
* Complex exponential function
*
*
*
* SYNOPSIS:
*
* long double complex cexpl();
* long double complex z, w;
*
* w = cexpl( z );
*
*
*
* DESCRIPTION:
*
* Returns the exponential of the complex argument z
* into the complex result w.
*
* If
* z = x + iy,
* r = exp(x),
*
* then
*
* w = r cos y + i r sin y.
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 8700 3.7e-17 1.1e-17
* IEEE -10,+10 30000 3.0e-16 8.7e-17
*
*/
#include <complex.h>
#include <math.h>
long double complex
cexpl(long double complex z)
{
long double complex w;
long double r;
r = expl(creall(z));
w = r * cosl(cimagl(z)) + (r * sinl(cimagl(z))) * I;
return (w);
}

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/* $OpenBSD: s_clog.c,v 1.6 2013/07/03 04:46:36 espie 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);
}
#if LDBL_MANT_DIG == DBL_MANT_DIG
__strong_alias(clogl, clog);
#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */

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/* $OpenBSD: s_clogf.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.
*/
/* 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);
}

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/* $OpenBSD: s_clogl.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.
*/
/* 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);
}

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/* $OpenBSD: s_csin.c,v 1.6 2013/07/03 04:46:36 espie 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.
*/
/* csin()
*
* Complex circular sine
*
*
*
* SYNOPSIS:
*
* double complex csin();
* double complex z, w;
*
* w = csin (z);
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
*
* w = sin x cosh y + i cos x sinh y.
*
* csin(z) = -i csinh(iz).
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 8400 5.3e-17 1.3e-17
* IEEE -10,+10 30000 3.8e-16 1.0e-16
* Also tested by csin(casin(z)) = z.
*
*/
#include <complex.h>
#include <float.h>
#include <math.h>
/* calculate cosh and sinh */
static void
cchsh(double x, double *c, double *s)
{
double e, ei;
if (fabs(x) <= 0.5) {
*c = cosh(x);
*s = sinh(x);
}
else {
e = exp(x);
ei = 0.5/e;
e = 0.5 * e;
*s = e - ei;
*c = e + ei;
}
}
double complex
csin(double complex z)
{
double complex w;
double ch, sh;
cchsh( cimag (z), &ch, &sh );
w = sin (creal(z)) * ch + (cos (creal(z)) * sh) * I;
return (w);
}
#if LDBL_MANT_DIG == DBL_MANT_DIG
__strong_alias(csinl, csin);
#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */

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/* $OpenBSD: s_csinf.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.
*/
/* csinf()
*
* Complex circular sine
*
*
*
* SYNOPSIS:
*
* void csinf();
* cmplxf z, w;
*
* csinf( &z, &w );
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
*
* w = sin x cosh y + i cos x sinh y.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 1.9e-7 5.5e-8
*
*/
#include <complex.h>
#include <math.h>
/* calculate cosh and sinh */
static void
cchshf(float xx, float *c, float *s)
{
float x, e, ei;
x = xx;
if(fabsf(x) <= 0.5f) {
*c = coshf(x);
*s = sinhf(x);
}
else {
e = expf(x);
ei = 0.5f/e;
e = 0.5f * e;
*s = e - ei;
*c = e + ei;
}
}
float complex
csinf(float complex z)
{
float complex w;
float ch, sh;
cchshf(cimagf(z), &ch, &sh);
w = sinf(crealf(z)) * ch + (cosf(crealf(z)) * sh) * I;
return (w);
}

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/* $OpenBSD: s_csinhl.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.
*/
/* csinhl
*
* Complex hyperbolic sine
*
*
*
* SYNOPSIS:
*
* long double complex csinhl();
* long double complex z, w;
*
* w = csinhl (z);
*
* DESCRIPTION:
*
* csinh z = (cexp(z) - cexp(-z))/2
* = sinh x * cos y + i cosh x * sin y .
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 3.1e-16 8.2e-17
*
*/
#include <complex.h>
#include <math.h>
long double complex
csinhl(long double complex z)
{
long double complex w;
long double x, y;
x = creall(z);
y = cimagl(z);
w = sinhl(x) * cosl(y) + (coshl(x) * sinl(y)) * I;
return (w);
}

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/* $OpenBSD: s_csinl.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.
*/
/* csinl()
*
* Complex circular sine
*
*
*
* SYNOPSIS:
*
* long double complex csinl();
* long double complex z, w;
*
* w = csinl( z );
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
*
* w = sin x cosh y + i cos x sinh y.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 8400 5.3e-17 1.3e-17
* IEEE -10,+10 30000 3.8e-16 1.0e-16
* Also tested by csin(casin(z)) = z.
*
*/
#include <complex.h>
#include <math.h>
static void
cchshl(long double x, long double *c, long double *s)
{
long double e, ei;
if(fabsl(x) <= 0.5L) {
*c = coshl(x);
*s = sinhl(x);
} else {
e = expl(x);
ei = 0.5L/e;
e = 0.5L * e;
*s = e - ei;
*c = e + ei;
}
}
long double complex
csinl(long double complex z)
{
long double complex w;
long double ch, sh;
cchshl(cimagl(z), &ch, &sh);
w = sinl(creall(z)) * ch + (cosl(creall(z)) * sh) * I;
return (w);
}

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/* $OpenBSD: s_ctan.c,v 1.6 2013/07/03 04:46:36 espie 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.
*/
/* ctan()
*
* Complex circular tangent
*
*
*
* SYNOPSIS:
*
* double complex ctan();
* double complex z, w;
*
* w = ctan (z);
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
*
* sin 2x + i sinh 2y
* w = --------------------.
* cos 2x + cosh 2y
*
* On the real axis the denominator is zero at odd multiples
* of PI/2. The denominator is evaluated by its Taylor
* series near these points.
*
* ctan(z) = -i ctanh(iz).
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 5200 7.1e-17 1.6e-17
* IEEE -10,+10 30000 7.2e-16 1.2e-16
* Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
*/
#include <complex.h>
#include <float.h>
#include <math.h>
#define MACHEP 1.1e-16
#define MAXNUM 1.0e308
static const double DP1 = 3.14159265160560607910E0;
static const double DP2 = 1.98418714791870343106E-9;
static const double DP3 = 1.14423774522196636802E-17;
static double
_redupi(double x)
{
double t;
long i;
t = x/M_PI;
if (t >= 0.0)
t += 0.5;
else
t -= 0.5;
i = t; /* the multiple */
t = i;
t = ((x - t * DP1) - t * DP2) - t * DP3;
return (t);
}
/* Taylor series expansion for cosh(2y) - cos(2x) */
static double
_ctans(double complex z)
{
double f, x, x2, y, y2, rn, t;
double d;
x = fabs (2.0 * creal (z));
y = fabs (2.0 * cimag(z));
x = _redupi(x);
x = x * x;
y = y * y;
x2 = 1.0;
y2 = 1.0;
f = 1.0;
rn = 0.0;
d = 0.0;
do {
rn += 1.0;
f *= rn;
rn += 1.0;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 + x2;
t /= f;
d += t;
rn += 1.0;
f *= rn;
rn += 1.0;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 - x2;
t /= f;
d += t;
}
while (fabs(t/d) > MACHEP)
;
return (d);
}
double complex
ctan(double complex z)
{
double complex w;
double d;
d = cos (2.0 * creal (z)) + cosh (2.0 * cimag (z));
if (fabs(d) < 0.25)
d = _ctans (z);
if (d == 0.0) {
/*mtherr ("ctan", OVERFLOW);*/
w = MAXNUM + MAXNUM * I;
return (w);
}
w = sin (2.0 * creal(z)) / d + (sinh (2.0 * cimag(z)) / d) * I;
return (w);
}
#if LDBL_MANT_DIG == DBL_MANT_DIG
__strong_alias(ctanl, ctan);
#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */

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/* $OpenBSD: s_ctanf.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.
*/
/* ctanf()
*
* Complex circular tangent
*
*
*
* SYNOPSIS:
*
* void ctanf();
* cmplxf z, w;
*
* ctanf( &z, &w );
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
*
* sin 2x + i sinh 2y
* w = --------------------.
* cos 2x + cosh 2y
*
* On the real axis the denominator is zero at odd multiples
* of PI/2. The denominator is evaluated by its Taylor
* series near these points.
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 3.3e-7 5.1e-8
*/
#include <complex.h>
#include <math.h>
#define MACHEPF 3.0e-8
#define MAXNUMF 1.0e38f
static const double DP1 = 3.140625;
static const double DP2 = 9.67502593994140625E-4;
static const double DP3 = 1.509957990978376432E-7;
static float
_redupif(float xx)
{
float x, t;
long i;
x = xx;
t = x/(float)M_PI;
if(t >= 0.0)
t += 0.5;
else
t -= 0.5;
i = t; /* the multiple */
t = i;
t = ((x - t * DP1) - t * DP2) - t * DP3;
return(t);
}
/* Taylor series expansion for cosh(2y) - cos(2x) */
static float
_ctansf(float complex z)
{
float f, x, x2, y, y2, rn, t, d;
x = fabsf(2.0f * crealf(z));
y = fabsf(2.0f * cimagf(z));
x = _redupif(x);
x = x * x;
y = y * y;
x2 = 1.0f;
y2 = 1.0f;
f = 1.0f;
rn = 0.0f;
d = 0.0f;
do {
rn += 1.0f;
f *= rn;
rn += 1.0f;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 + x2;
t /= f;
d += t;
rn += 1.0f;
f *= rn;
rn += 1.0f;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 - x2;
t /= f;
d += t;
}
while (fabsf(t/d) > MACHEPF)
;
return(d);
}
float complex
ctanf(float complex z)
{
float complex w;
float d;
d = cosf( 2.0f * crealf(z) ) + coshf( 2.0f * cimagf(z) );
if(fabsf(d) < 0.25f)
d = _ctansf(z);
if (d == 0.0f) {
/*mtherr( "ctanf", OVERFLOW );*/
w = MAXNUMF + MAXNUMF * I;
return (w);
}
w = sinf (2.0f * crealf(z)) / d + (sinhf (2.0f * cimagf(z)) / d) * I;
return (w);
}

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/* $OpenBSD: s_ctanhl.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.
*/
/* ctanhl
*
* Complex hyperbolic tangent
*
*
*
* SYNOPSIS:
*
* long double complex ctanhl();
* long double complex z, w;
*
* w = ctanhl (z);
*
*
*
* DESCRIPTION:
*
* tanh z = (sinh 2x + i sin 2y) / (cosh 2x + cos 2y) .
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 1.7e-14 2.4e-16
*
*/
#include <complex.h>
#include <math.h>
long double complex
ctanhl(long double complex z)
{
long double complex w;
long double x, y, d;
x = creall(z);
y = cimagl(z);
d = coshl(2.0L * x) + cosl(2.0L * y);
w = sinhl(2.0L * x) / d + (sinl(2.0L * y) / d) * I;
return (w);
}

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/* $OpenBSD: s_ctanl.c,v 1.3 2011/07/20 21:02:51 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.
*/
/* ctanl()
*
* Complex circular tangent
*
*
*
* SYNOPSIS:
*
* long double complex ctanl();
* long double complex z, w;
*
* w = ctanl( z );
*
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
*
* sin 2x + i sinh 2y
* w = --------------------.
* cos 2x + cosh 2y
*
* On the real axis the denominator is zero at odd multiples
* of PI/2. The denominator is evaluated by its Taylor
* series near these points.
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC -10,+10 5200 7.1e-17 1.6e-17
* IEEE -10,+10 30000 7.2e-16 1.2e-16
* Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
*/
#include <complex.h>
#include <float.h>
#include <math.h>
#if LDBL_MANT_DIG == 64
static const long double MACHEPL= 5.42101086242752217003726400434970855712890625E-20L;
#elif LDBL_MANT_DIG == 113
static const long double MACHEPL = 9.629649721936179265279889712924636592690508e-35L;
#endif
static const long double PIL = 3.141592653589793238462643383279502884197169L;
static const long double DP1 = 3.14159265358979323829596852490908531763125L;
static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
static long double
redupil(long double x)
{
long double t;
long i;
t = x / PIL;
if (t >= 0.0L)
t += 0.5L;
else
t -= 0.5L;
i = t; /* the multiple */
t = i;
t = ((x - t * DP1) - t * DP2) - t * DP3;
return (t);
}
static long double
ctansl(long double complex z)
{
long double f, x, x2, y, y2, rn, t;
long double d;
x = fabsl(2.0L * creall(z));
y = fabsl(2.0L * cimagl(z));
x = redupil(x);
x = x * x;
y = y * y;
x2 = 1.0L;
y2 = 1.0L;
f = 1.0L;
rn = 0.0L;
d = 0.0L;
do {
rn += 1.0L;
f *= rn;
rn += 1.0L;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 + x2;
t /= f;
d += t;
rn += 1.0L;
f *= rn;
rn += 1.0L;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 - x2;
t /= f;
d += t;
}
while (fabsl(t/d) > MACHEPL);
return(d);
}
long double complex
ctanl(long double complex z)
{
long double complex w;
long double d, x, y;
x = creall(z);
y = cimagl(z);
d = cosl(2.0L * x) + coshl(2.0L * y);
if (fabsl(d) < 0.25L) {
d = fabsl(d);
d = ctansl(z);
}
if (d == 0.0L) {
/*mtherr( "ctan", OVERFLOW );*/
w = LDBL_MAX + LDBL_MAX * I;
return (w);
}
w = sinl(2.0L * x) / d + (sinhl(2.0L * y) / d) * I;
return (w);
}