[thirdparty/glibc.git] / math / s_catanhl.c

/* Return arc hyperbole tangent for long double value.
   Copyright (C) 1997-2015 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <http://www.gnu.org/licenses/>.  */

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

/* To avoid spurious overflows, use this definition to treat IBM long
   double as approximating an IEEE-style format.  */
#if LDBL_MANT_DIG == 106
# undef LDBL_EPSILON
# define LDBL_EPSILON 0x1p-106L
#endif

__complex__ long double
__catanhl (__complex__ long double x)
{
  __complex__ long double res;
  int rcls = fpclassify (__real__ x);
  int icls = fpclassify (__imag__ x);

  if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
    {
      if (icls == FP_INFINITE)
	{
	  __real__ res = __copysignl (0.0, __real__ x);
	  __imag__ res = __copysignl (M_PI_2l, __imag__ x);
	}
      else if (rcls == FP_INFINITE || rcls == FP_ZERO)
	{
	  __real__ res = __copysignl (0.0, __real__ x);
	  if (icls >= FP_ZERO)
	    __imag__ res = __copysignl (M_PI_2l, __imag__ x);
	  else
	    __imag__ res = __nanl ("");
	}
      else
	{
	  __real__ res = __nanl ("");
	  __imag__ res = __nanl ("");
	}
    }
  else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
    {
      res = x;
    }
  else
    {
      if (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON
	  || fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON)
	{
	  __imag__ res = __copysignl (M_PI_2l, __imag__ x);
	  if (fabsl (__imag__ x) <= 1.0L)
	    __real__ res = 1.0L / __real__ x;
	  else if (fabsl (__real__ x) <= 1.0L)
	    __real__ res = __real__ x / __imag__ x / __imag__ x;
	  else
	    {
	      long double h = __ieee754_hypotl (__real__ x / 2.0L,
						__imag__ x / 2.0L);
	      __real__ res = __real__ x / h / h / 4.0L;
	    }
	}
      else
	{
	  if (fabsl (__real__ x) == 1.0L
	      && fabsl (__imag__ x) < LDBL_EPSILON * LDBL_EPSILON)
	    __real__ res = (__copysignl (0.5L, __real__ x)
			    * (M_LN2l - __ieee754_logl (fabsl (__imag__ x))));
	  else
	    {
	      long double i2 = 0.0;
	      if (fabsl (__imag__ x) >= LDBL_EPSILON * LDBL_EPSILON)
		i2 = __imag__ x * __imag__ x;

	      long double num = 1.0L + __real__ x;
	      num = i2 + num * num;

	      long double den = 1.0L - __real__ x;
	      den = i2 + den * den;

	      long double f = num / den;
	      if (f < 0.5L)
		__real__ res = 0.25L * __ieee754_logl (f);
	      else
		{
		  num = 4.0L * __real__ x;
		  __real__ res = 0.25L * __log1pl (num / den);
		}
	    }

	  long double absx, absy, den;

	  absx = fabsl (__real__ x);
	  absy = fabsl (__imag__ x);
	  if (absx < absy)
	    {
	      long double t = absx;
	      absx = absy;
	      absy = t;
	    }

	  if (absy < LDBL_EPSILON / 2.0L)
	    {
	      den = (1.0L - absx) * (1.0L + absx);
	      if (den == -0.0L)
		den = 0.0L;
	    }
	  else if (absx >= 1.0L)
	    den = (1.0L - absx) * (1.0L + absx) - absy * absy;
	  else if (absx >= 0.75L || absy >= 0.5L)
	    den = -__x2y2m1l (absx, absy);
	  else
	    den = (1.0L - absx) * (1.0L + absx) - absy * absy;

	  __imag__ res = 0.5L * __ieee754_atan2l (2.0L * __imag__ x, den);
	}

      if (fabsl (__real__ res) < LDBL_MIN)
	{
	  volatile long double force_underflow = __real__ res * __real__ res;
	  (void) force_underflow;
	}
      if (fabsl (__imag__ res) < LDBL_MIN)
	{
	  volatile long double force_underflow = __imag__ res * __imag__ res;
	  (void) force_underflow;
	}
    }

  return res;
}
weak_alias (__catanhl, catanhl)
Commit	Line	Data
63551311	1	/* Return arc hyperbole tangent for long double value.
b168057a	2	Copyright (C) 1997-2015 Free Software Foundation, Inc.
63551311 UD	3	This file is part of the GNU C Library.
	4	Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
	5
	6	The GNU C Library is free software; you can redistribute it and/or
41bdb6e2 AJ	7	modify it under the terms of the GNU Lesser General Public
	8	License as published by the Free Software Foundation; either
	9	version 2.1 of the License, or (at your option) any later version.
63551311 UD	10
	11	The GNU C Library is distributed in the hope that it will be useful,
	12	but WITHOUT ANY WARRANTY; without even the implied warranty of
	13	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
41bdb6e2	14	Lesser General Public License for more details.
63551311	15
41bdb6e2	16	You should have received a copy of the GNU Lesser General Public
59ba27a6 PE	17	License along with the GNU C Library; if not, see
59ba27a6 PE	18	<http://www.gnu.org/licenses/>. */
63551311 UD	19
	20	#include <complex.h>
	21	#include <math.h>
9277c064	22	#include <math_private.h>
9457fd95	23	#include <float.h>
63551311	24
5b4217d7 JM	25	/* To avoid spurious overflows, use this definition to treat IBM long
	26	double as approximating an IEEE-style format. */
	27	#if LDBL_MANT_DIG == 106
	28	# undef LDBL_EPSILON
	29	# define LDBL_EPSILON 0x1p-106L
	30	#endif
	31
63551311 UD	32	__complex__ long double
	33	__catanhl (__complex__ long double x)
	34	{
	35	__complex__ long double res;
	36	int rcls = fpclassify (__real__ x);
	37	int icls = fpclassify (__imag__ x);
	38
a1ffb40e	39	if (__glibc_unlikely (rcls <= FP_INFINITE \|\| icls <= FP_INFINITE))
63551311 UD	40	{
	41	if (icls == FP_INFINITE)
	42	{
	43	__real__ res = __copysignl (0.0, __real__ x);
0a614877	44	__imag__ res = __copysignl (M_PI_2l, __imag__ x);
63551311 UD	45	}
	46	else if (rcls == FP_INFINITE \|\| rcls == FP_ZERO)
	47	{
	48	__real__ res = __copysignl (0.0, __real__ x);
	49	if (icls >= FP_ZERO)
0a614877	50	__imag__ res = __copysignl (M_PI_2l, __imag__ x);
63551311 UD	51	else
	52	__imag__ res = __nanl ("");
	53	}
	54	else
	55	{
	56	__real__ res = __nanl ("");
	57	__imag__ res = __nanl ("");
	58	}
	59	}
a1ffb40e	60	else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
63551311 UD	61	{
	62	res = x;
	63	}
	64	else
	65	{
5b4217d7 JM	66	if (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON
	67	\|\| fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON)
	68	{
	69	__imag__ res = __copysignl (M_PI_2l, __imag__ x);
	70	if (fabsl (__imag__ x) <= 1.0L)
	71	__real__ res = 1.0L / __real__ x;
	72	else if (fabsl (__real__ x) <= 1.0L)
	73	__real__ res = __real__ x / __imag__ x / __imag__ x;
	74	else
	75	{
	76	long double h = __ieee754_hypotl (__real__ x / 2.0L,
	77	__imag__ x / 2.0L);
	78	__real__ res = __real__ x / h / h / 4.0L;
	79	}
	80	}
	81	else
	82	{
10de07f5 JM	83	if (fabsl (__real__ x) == 1.0L
	84	&& fabsl (__imag__ x) < LDBL_EPSILON * LDBL_EPSILON)
	85	__real__ res = (__copysignl (0.5L, __real__ x)
	86	* (M_LN2l - __ieee754_logl (fabsl (__imag__ x))));
5b4217d7 JM	87	else
5b4217d7 JM	88	{
10de07f5 JM	89	long double i2 = 0.0;
	90	if (fabsl (__imag__ x) >= LDBL_EPSILON * LDBL_EPSILON)
	91	i2 = __imag__ x * __imag__ x;
	92
	93	long double num = 1.0L + __real__ x;
	94	num = i2 + num * num;
	95
	96	long double den = 1.0L - __real__ x;
	97	den = i2 + den * den;
	98
	99	long double f = num / den;
	100	if (f < 0.5L)
	101	__real__ res = 0.25L * __ieee754_logl (f);
	102	else
	103	{
	104	num = 4.0L * __real__ x;
	105	__real__ res = 0.25L * __log1pl (num / den);
	106	}
5b4217d7	107	}
63551311	108
10de07f5	109	long double absx, absy, den;
caf84319 JM	110
	111	absx = fabsl (__real__ x);
	112	absy = fabsl (__imag__ x);
	113	if (absx < absy)
	114	{
	115	long double t = absx;
	116	absx = absy;
	117	absy = t;
	118	}
	119
10de07f5	120	if (absy < LDBL_EPSILON / 2.0L)
a84e78c8 JM	121	{
	122	den = (1.0L - absx) * (1.0L + absx);
	123	if (den == -0.0L)
	124	den = 0.0L;
	125	}
10de07f5 JM	126	else if (absx >= 1.0L)
10de07f5 JM	127	den = (1.0L - absx) * (1.0L + absx) - absy * absy;
caf84319 JM	128	else if (absx >= 0.75L \|\| absy >= 0.5L)
	129	den = -__x2y2m1l (absx, absy);
	130	else
	131	den = (1.0L - absx) * (1.0L + absx) - absy * absy;
63551311	132
5b4217d7 JM	133	__imag__ res = 0.5L * __ieee754_atan2l (2.0L * __imag__ x, den);
5b4217d7 JM	134	}
9457fd95 JM	135
	136	if (fabsl (__real__ res) < LDBL_MIN)
	137	{
	138	volatile long double force_underflow = __real__ res * __real__ res;
	139	(void) force_underflow;
	140	}
	141	if (fabsl (__imag__ res) < LDBL_MIN)
	142	{
	143	volatile long double force_underflow = __imag__ res * __imag__ res;
	144	(void) force_underflow;
	145	}
63551311 UD	146	}
	147
	148	return res;
	149	}
	150	weak_alias (__catanhl, catanhl)