[thirdparty/glibc.git] / sysdeps / ieee754 / ldbl-128ibm / e_acosl.c

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

/*
   Long double expansions are
   Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
   and are incorporated herein by permission of the author.  The author
   reserves the right to distribute this material elsewhere under different
   copying permissions.  These modifications are distributed here under
   the following terms:

    This 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.

    This 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 this library; if not, see
    <https://www.gnu.org/licenses/>.  */

/* __ieee754_acosl(x)
 * Method :
 *      acos(x)  = pi/2 - asin(x)
 *      acos(-x) = pi/2 + asin(x)
 * For |x| <= 0.375
 *      acos(x) = pi/2 - asin(x)
 * Between .375 and .5 the approximation is
 *      acos(0.4375 + x) = acos(0.4375) + x P(x) / Q(x)
 * Between .5 and .625 the approximation is
 *      acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
 * For x > 0.625,
 *      acos(x) = 2 asin(sqrt((1-x)/2))
 *      computed with an extended precision square root in the leading term.
 * For x < -0.625
 *      acos(x) = pi - 2 asin(sqrt((1-|x|)/2))
 *
 * Special cases:
 *      if x is NaN, return x itself;
 *      if |x|>1, return NaN with invalid signal.
 *
 * Functions needed: sqrtl.
 */

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

static const long double
  one = 1.0L,
  pio2_hi = 1.5707963267948966192313216916397514420986L,
  pio2_lo = 4.3359050650618905123985220130216759843812E-35L,

  /* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
     -0.0625 <= x <= 0.0625
     peak relative error 3.3e-35  */

  rS0 =  5.619049346208901520945464704848780243887E0L,
  rS1 = -4.460504162777731472539175700169871920352E1L,
  rS2 =  1.317669505315409261479577040530751477488E2L,
  rS3 = -1.626532582423661989632442410808596009227E2L,
  rS4 =  3.144806644195158614904369445440583873264E1L,
  rS5 =  9.806674443470740708765165604769099559553E1L,
  rS6 = -5.708468492052010816555762842394927806920E1L,
  rS7 = -1.396540499232262112248553357962639431922E1L,
  rS8 =  1.126243289311910363001762058295832610344E1L,
  rS9 =  4.956179821329901954211277873774472383512E-1L,
  rS10 = -3.313227657082367169241333738391762525780E-1L,

  sS0 = -4.645814742084009935700221277307007679325E0L,
  sS1 =  3.879074822457694323970438316317961918430E1L,
  sS2 = -1.221986588013474694623973554726201001066E2L,
  sS3 =  1.658821150347718105012079876756201905822E2L,
  sS4 = -4.804379630977558197953176474426239748977E1L,
  sS5 = -1.004296417397316948114344573811562952793E2L,
  sS6 =  7.530281592861320234941101403870010111138E1L,
  sS7 =  1.270735595411673647119592092304357226607E1L,
  sS8 = -1.815144839646376500705105967064792930282E1L,
  sS9 = -7.821597334910963922204235247786840828217E-2L,
  /* 1.000000000000000000000000000000000000000E0 */

  acosr5625 = 9.7338991014954640492751132535550279812151E-1L,
  pimacosr5625 = 2.1682027434402468335351320579240000860757E0L,

  /* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x)
     -0.0625 <= x <= 0.0625
     peak relative error 2.1e-35  */

  P0 =  2.177690192235413635229046633751390484892E0L,
  P1 = -2.848698225706605746657192566166142909573E1L,
  P2 =  1.040076477655245590871244795403659880304E2L,
  P3 = -1.400087608918906358323551402881238180553E2L,
  P4 =  2.221047917671449176051896400503615543757E1L,
  P5 =  9.643714856395587663736110523917499638702E1L,
  P6 = -5.158406639829833829027457284942389079196E1L,
  P7 = -1.578651828337585944715290382181219741813E1L,
  P8 =  1.093632715903802870546857764647931045906E1L,
  P9 =  5.448925479898460003048760932274085300103E-1L,
  P10 = -3.315886001095605268470690485170092986337E-1L,
  Q0 = -1.958219113487162405143608843774587557016E0L,
  Q1 =  2.614577866876185080678907676023269360520E1L,
  Q2 = -9.990858606464150981009763389881793660938E1L,
  Q3 =  1.443958741356995763628660823395334281596E2L,
  Q4 = -3.206441012484232867657763518369723873129E1L,
  Q5 = -1.048560885341833443564920145642588991492E2L,
  Q6 =  6.745883931909770880159915641984874746358E1L,
  Q7 =  1.806809656342804436118449982647641392951E1L,
  Q8 = -1.770150690652438294290020775359580915464E1L,
  Q9 = -5.659156469628629327045433069052560211164E-1L,
  /* 1.000000000000000000000000000000000000000E0 */

  acosr4375 = 1.1179797320499710475919903296900511518755E0L,
  pimacosr4375 = 2.0236129215398221908706530535894517323217E0L,

  /* asin(x) = x + x^3 pS(x^2) / qS(x^2)
     0 <= x <= 0.5
     peak relative error 1.9e-35  */
  pS0 = -8.358099012470680544198472400254596543711E2L,
  pS1 =  3.674973957689619490312782828051860366493E3L,
  pS2 = -6.730729094812979665807581609853656623219E3L,
  pS3 =  6.643843795209060298375552684423454077633E3L,
  pS4 = -3.817341990928606692235481812252049415993E3L,
  pS5 =  1.284635388402653715636722822195716476156E3L,
  pS6 = -2.410736125231549204856567737329112037867E2L,
  pS7 =  2.219191969382402856557594215833622156220E1L,
  pS8 = -7.249056260830627156600112195061001036533E-1L,
  pS9 =  1.055923570937755300061509030361395604448E-3L,

  qS0 = -5.014859407482408326519083440151745519205E3L,
  qS1 =  2.430653047950480068881028451580393430537E4L,
  qS2 = -4.997904737193653607449250593976069726962E4L,
  qS3 =  5.675712336110456923807959930107347511086E4L,
  qS4 = -3.881523118339661268482937768522572588022E4L,
  qS5 =  1.634202194895541569749717032234510811216E4L,
  qS6 = -4.151452662440709301601820849901296953752E3L,
  qS7 =  5.956050864057192019085175976175695342168E2L,
  qS8 = -4.175375777334867025769346564600396877176E1L;
  /* 1.000000000000000000000000000000000000000E0 */

long double
__ieee754_acosl (long double x)
{
  long double a, z, r, w, p, q, s, t, f2;

  if (__glibc_unlikely (isnan (x)))
    return x + x;
  a = __builtin_fabsl (x);
  if (a == 1.0L)
    {
      if (x > 0.0L)
	return 0.0;		/* acos(1) = 0  */
      else
	return (2.0 * pio2_hi) + (2.0 * pio2_lo);	/* acos(-1)= pi */
    }
  else if (a > 1.0L)
    {
      return (x - x) / (x - x);	/* acos(|x| > 1) is NaN */
    }
  if (a < 0.5L)
    {
      if (a < 0x1p-106L)
	return pio2_hi + pio2_lo;
      if (a < 0.4375L)
	{
	  /* Arcsine of x.  */
	  z = x * x;
	  p = (((((((((pS9 * z
		       + pS8) * z
		      + pS7) * z
		     + pS6) * z
		    + pS5) * z
		   + pS4) * z
		  + pS3) * z
		 + pS2) * z
		+ pS1) * z
	       + pS0) * z;
	  q = (((((((( z
		       + qS8) * z
		     + qS7) * z
		    + qS6) * z
		   + qS5) * z
		  + qS4) * z
		 + qS3) * z
		+ qS2) * z
	       + qS1) * z
	    + qS0;
	  r = x + x * p / q;
	  z = pio2_hi - (r - pio2_lo);
	  return z;
	}
      /* .4375 <= |x| < .5 */
      t = a - 0.4375L;
      p = ((((((((((P10 * t
		    + P9) * t
		   + P8) * t
		  + P7) * t
		 + P6) * t
		+ P5) * t
	       + P4) * t
	      + P3) * t
	     + P2) * t
	    + P1) * t
	   + P0) * t;

      q = (((((((((t
		   + Q9) * t
		  + Q8) * t
		 + Q7) * t
		+ Q6) * t
	       + Q5) * t
	      + Q4) * t
	     + Q3) * t
	    + Q2) * t
	   + Q1) * t
	+ Q0;
      r = p / q;
      if (x < 0.0L)
	r = pimacosr4375 - r;
      else
	r = acosr4375 + r;
      return r;
    }
  else if (a < 0.625L)
    {
      t = a - 0.5625L;
      p = ((((((((((rS10 * t
		    + rS9) * t
		   + rS8) * t
		  + rS7) * t
		 + rS6) * t
		+ rS5) * t
	       + rS4) * t
	      + rS3) * t
	     + rS2) * t
	    + rS1) * t
	   + rS0) * t;

      q = (((((((((t
		   + sS9) * t
		  + sS8) * t
		 + sS7) * t
		+ sS6) * t
	       + sS5) * t
	      + sS4) * t
	     + sS3) * t
	    + sS2) * t
	   + sS1) * t
	+ sS0;
      if (x < 0.0L)
	r = pimacosr5625 - p / q;
      else
	r = acosr5625 + p / q;
      return r;
    }
  else
    {				/* |x| >= .625 */
      double shi, slo;

      z = (one - a) * 0.5;
      s = sqrtl (z);
      /* Compute an extended precision square root from
	 the Newton iteration  s -> 0.5 * (s + z / s).
	 The change w from s to the improved value is
	    w = 0.5 * (s + z / s) - s  = (s^2 + z)/2s - s = (z - s^2)/2s.
	  Express s = f1 + f2 where f1 * f1 is exactly representable.
	  w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s .
	  s + w has extended precision.  */
      ldbl_unpack (s, &shi, &slo);
      a = shi;
      f2 = slo;
      w = z - a * a;
      w = w - 2.0 * a * f2;
      w = w - f2 * f2;
      w = w / (2.0 * s);
      /* Arcsine of s.  */
      p = (((((((((pS9 * z
		   + pS8) * z
		  + pS7) * z
		 + pS6) * z
		+ pS5) * z
	       + pS4) * z
	      + pS3) * z
	     + pS2) * z
	    + pS1) * z
	   + pS0) * z;
      q = (((((((( z
		   + qS8) * z
		 + qS7) * z
		+ qS6) * z
	       + qS5) * z
	      + qS4) * z
	     + qS3) * z
	    + qS2) * z
	   + qS1) * z
	+ qS0;
      r = s + (w + s * p / q);

      if (x < 0.0L)
	w = pio2_hi + (pio2_lo - r);
      else
	w = r;
      return 2.0 * w;
    }
}
strong_alias (__ieee754_acosl, __acosl_finite)
Commit	Line	Data
f964490f RM	1	/*
	2	* ====================================================
	3	* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
	4	*
	5	* Developed at SunPro, a Sun Microsystems, Inc. business.
	6	* Permission to use, copy, modify, and distribute this
	7	* software is freely granted, provided that this notice
	8	* is preserved.
	9	* ====================================================
	10	*/
	11
	12	/*
	13	Long double expansions are
	14	Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
	15	and are incorporated herein by permission of the author. The author
	16	reserves the right to distribute this material elsewhere under different
	17	copying permissions. These modifications are distributed here under
	18	the following terms:
	19
	20	This library is free software; you can redistribute it and/or
	21	modify it under the terms of the GNU Lesser General Public
	22	License as published by the Free Software Foundation; either
	23	version 2.1 of the License, or (at your option) any later version.
	24
	25	This library is distributed in the hope that it will be useful,
	26	but WITHOUT ANY WARRANTY; without even the implied warranty of
	27	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
	28	Lesser General Public License for more details.
	29
	30	You should have received a copy of the GNU Lesser General Public
59ba27a6	31	License along with this library; if not, see
5a82c748	32	<https://www.gnu.org/licenses/>. */
f964490f RM	33
	34	/* __ieee754_acosl(x)
	35	* Method :
	36	* acos(x) = pi/2 - asin(x)
	37	* acos(-x) = pi/2 + asin(x)
	38	* For \|x\| <= 0.375
	39	* acos(x) = pi/2 - asin(x)
	40	* Between .375 and .5 the approximation is
	41	* acos(0.4375 + x) = acos(0.4375) + x P(x) / Q(x)
	42	* Between .5 and .625 the approximation is
	43	* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
	44	* For x > 0.625,
	45	* acos(x) = 2 asin(sqrt((1-x)/2))
	46	* computed with an extended precision square root in the leading term.
	47	* For x < -0.625
	48	* acos(x) = pi - 2 asin(sqrt((1-\|x\|)/2))
	49	*
	50	* Special cases:
	51	* if x is NaN, return x itself;
	52	* if \|x\|>1, return NaN with invalid signal.
	53	*
f67a8147	54	* Functions needed: sqrtl.
f964490f RM	55	*/
f964490f RM	56
1ed0291c RH	57	#include <math.h>
1ed0291c RH	58	#include <math_private.h>
f964490f	59
f964490f	60	static const long double
f964490f RM	61	one = 1.0L,
	62	pio2_hi = 1.5707963267948966192313216916397514420986L,
	63	pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
	64
	65	/* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
	66	-0.0625 <= x <= 0.0625
	67	peak relative error 3.3e-35 */
	68
	69	rS0 = 5.619049346208901520945464704848780243887E0L,
	70	rS1 = -4.460504162777731472539175700169871920352E1L,
	71	rS2 = 1.317669505315409261479577040530751477488E2L,
	72	rS3 = -1.626532582423661989632442410808596009227E2L,
	73	rS4 = 3.144806644195158614904369445440583873264E1L,
	74	rS5 = 9.806674443470740708765165604769099559553E1L,
	75	rS6 = -5.708468492052010816555762842394927806920E1L,
	76	rS7 = -1.396540499232262112248553357962639431922E1L,
	77	rS8 = 1.126243289311910363001762058295832610344E1L,
	78	rS9 = 4.956179821329901954211277873774472383512E-1L,
	79	rS10 = -3.313227657082367169241333738391762525780E-1L,
	80
	81	sS0 = -4.645814742084009935700221277307007679325E0L,
	82	sS1 = 3.879074822457694323970438316317961918430E1L,
	83	sS2 = -1.221986588013474694623973554726201001066E2L,
	84	sS3 = 1.658821150347718105012079876756201905822E2L,
	85	sS4 = -4.804379630977558197953176474426239748977E1L,
	86	sS5 = -1.004296417397316948114344573811562952793E2L,
	87	sS6 = 7.530281592861320234941101403870010111138E1L,
	88	sS7 = 1.270735595411673647119592092304357226607E1L,
	89	sS8 = -1.815144839646376500705105967064792930282E1L,
	90	sS9 = -7.821597334910963922204235247786840828217E-2L,
	91	/* 1.000000000000000000000000000000000000000E0 */
	92
	93	acosr5625 = 9.7338991014954640492751132535550279812151E-1L,
	94	pimacosr5625 = 2.1682027434402468335351320579240000860757E0L,
	95
	96	/* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x)
	97	-0.0625 <= x <= 0.0625
	98	peak relative error 2.1e-35 */
	99
	100	P0 = 2.177690192235413635229046633751390484892E0L,
	101	P1 = -2.848698225706605746657192566166142909573E1L,
	102	P2 = 1.040076477655245590871244795403659880304E2L,
	103	P3 = -1.400087608918906358323551402881238180553E2L,
	104	P4 = 2.221047917671449176051896400503615543757E1L,
	105	P5 = 9.643714856395587663736110523917499638702E1L,
	106	P6 = -5.158406639829833829027457284942389079196E1L,
	107	P7 = -1.578651828337585944715290382181219741813E1L,
	108	P8 = 1.093632715903802870546857764647931045906E1L,
	109	P9 = 5.448925479898460003048760932274085300103E-1L,
	110	P10 = -3.315886001095605268470690485170092986337E-1L,
	111	Q0 = -1.958219113487162405143608843774587557016E0L,
	112	Q1 = 2.614577866876185080678907676023269360520E1L,
	113	Q2 = -9.990858606464150981009763389881793660938E1L,
	114	Q3 = 1.443958741356995763628660823395334281596E2L,
	115	Q4 = -3.206441012484232867657763518369723873129E1L,
	116	Q5 = -1.048560885341833443564920145642588991492E2L,
	117	Q6 = 6.745883931909770880159915641984874746358E1L,
	118	Q7 = 1.806809656342804436118449982647641392951E1L,
	119	Q8 = -1.770150690652438294290020775359580915464E1L,
	120	Q9 = -5.659156469628629327045433069052560211164E-1L,
	121	/* 1.000000000000000000000000000000000000000E0 */
	122
	123	acosr4375 = 1.1179797320499710475919903296900511518755E0L,
	124	pimacosr4375 = 2.0236129215398221908706530535894517323217E0L,
125
126	/* asin(x) = x + x^3 pS(x^2) / qS(x^2)
127	0 <= x <= 0.5
128	peak relative error 1.9e-35 */
129	pS0 = -8.358099012470680544198472400254596543711E2L,
130	pS1 = 3.674973957689619490312782828051860366493E3L,
131	pS2 = -6.730729094812979665807581609853656623219E3L,
132	pS3 = 6.643843795209060298375552684423454077633E3L,
133	pS4 = -3.817341990928606692235481812252049415993E3L,
134	pS5 = 1.284635388402653715636722822195716476156E3L,
135	pS6 = -2.410736125231549204856567737329112037867E2L,
136	pS7 = 2.219191969382402856557594215833622156220E1L,
137	pS8 = -7.249056260830627156600112195061001036533E-1L,
138	pS9 = 1.055923570937755300061509030361395604448E-3L,
139
140	qS0 = -5.014859407482408326519083440151745519205E3L,
141	qS1 = 2.430653047950480068881028451580393430537E4L,
142	qS2 = -4.997904737193653607449250593976069726962E4L,
143	qS3 = 5.675712336110456923807959930107347511086E4L,
144	qS4 = -3.881523118339661268482937768522572588022E4L,
145	qS5 = 1.634202194895541569749717032234510811216E4L,
146	qS6 = -4.151452662440709301601820849901296953752E3L,
147	qS7 = 5.956050864057192019085175976175695342168E2L,
148	qS8 = -4.175375777334867025769346564600396877176E1L;
149	/* 1.000000000000000000000000000000000000000E0 */
150
f964490f RM	151	long double
f964490f RM	152	__ieee754_acosl (long double x)
f964490f	153	{
4ebd120c	154	long double a, z, r, w, p, q, s, t, f2;
f964490f	155
d81f90cc	156	if (__glibc_unlikely (isnan (x)))
6f10289e	157	return x + x;
4ebd120c AM	158	a = __builtin_fabsl (x);
4ebd120c AM	159	if (a == 1.0L)
31dc8730 AZ	160	{
	161	if (x > 0.0L)
	162	return 0.0; /* acos(1) = 0 */
	163	else
	164	return (2.0 * pio2_hi) + (2.0 * pio2_lo); /* acos(-1)= pi */
	165	}
4ebd120c	166	else if (a > 1.0L)
f964490f	167	{
f964490f RM	168	return (x - x) / (x - x); /* acos(\|x\| > 1) is NaN */
f964490f RM	169	}
4ebd120c	170	if (a < 0.5L)
f964490f	171	{
1d9ab20c	172	if (a < 0x1p-106L)
f964490f	173	return pio2_hi + pio2_lo;
4ebd120c	174	if (a < 0.4375L)
f964490f RM	175	{
	176	/* Arcsine of x. */
	177	z = x * x;
	178	p = (((((((((pS9 * z
	179	+ pS8) * z
	180	+ pS7) * z
	181	+ pS6) * z
	182	+ pS5) * z
	183	+ pS4) * z
	184	+ pS3) * z
	185	+ pS2) * z
	186	+ pS1) * z
	187	+ pS0) * z;
	188	q = (((((((( z
	189	+ qS8) * z
	190	+ qS7) * z
	191	+ qS6) * z
	192	+ qS5) * z
	193	+ qS4) * z
	194	+ qS3) * z
	195	+ qS2) * z
	196	+ qS1) * z
	197	+ qS0;
	198	r = x + x * p / q;
	199	z = pio2_hi - (r - pio2_lo);
	200	return z;
	201	}
	202	/* .4375 <= \|x\| < .5 */
4ebd120c	203	t = a - 0.4375L;
f964490f RM	204	p = ((((((((((P10 * t
	205	+ P9) * t
	206	+ P8) * t
	207	+ P7) * t
	208	+ P6) * t
	209	+ P5) * t
	210	+ P4) * t
	211	+ P3) * t
	212	+ P2) * t
	213	+ P1) * t
	214	+ P0) * t;
	215
	216	q = (((((((((t
	217	+ Q9) * t
	218	+ Q8) * t
	219	+ Q7) * t
	220	+ Q6) * t
	221	+ Q5) * t
	222	+ Q4) * t
	223	+ Q3) * t
	224	+ Q2) * t
	225	+ Q1) * t
	226	+ Q0;
	227	r = p / q;
31dc8730	228	if (x < 0.0L)
f964490f RM	229	r = pimacosr4375 - r;
	230	else
	231	r = acosr4375 + r;
	232	return r;
	233	}
4ebd120c	234	else if (a < 0.625L)
f964490f	235	{
4ebd120c	236	t = a - 0.5625L;
f964490f RM	237	p = ((((((((((rS10 * t
	238	+ rS9) * t
	239	+ rS8) * t
	240	+ rS7) * t
	241	+ rS6) * t
	242	+ rS5) * t
	243	+ rS4) * t
	244	+ rS3) * t
	245	+ rS2) * t
	246	+ rS1) * t
	247	+ rS0) * t;
	248
	249	q = (((((((((t
	250	+ sS9) * t
	251	+ sS8) * t
	252	+ sS7) * t
	253	+ sS6) * t
	254	+ sS5) * t
	255	+ sS4) * t
	256	+ sS3) * t
	257	+ sS2) * t
	258	+ sS1) * t
	259	+ sS0;
31dc8730	260	if (x < 0.0L)
f964490f RM	261	r = pimacosr5625 - p / q;
	262	else
	263	r = acosr5625 + p / q;
	264	return r;
	265	}
	266	else
	267	{ /* \|x\| >= .625 */
4ebd120c AM	268	double shi, slo;
	269
	270	z = (one - a) * 0.5;
f67a8147	271	s = sqrtl (z);
f964490f RM	272	/* Compute an extended precision square root from
f964490f RM	273	the Newton iteration s -> 0.5 * (s + z / s).
0ac5ae23	274	The change w from s to the improved value is
f964490f	275	w = 0.5 * (s + z / s) - s = (s^2 + z)/2s - s = (z - s^2)/2s.
0ac5ae23	276	Express s = f1 + f2 where f1 * f1 is exactly representable.
f964490f	277	w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s .
0ac5ae23	278	s + w has extended precision. */
4ebd120c AM	279	ldbl_unpack (s, &shi, &slo);
	280	a = shi;
	281	f2 = slo;
	282	w = z - a * a;
	283	w = w - 2.0 * a * f2;
f964490f RM	284	w = w - f2 * f2;
	285	w = w / (2.0 * s);
	286	/* Arcsine of s. */
	287	p = (((((((((pS9 * z
	288	+ pS8) * z
	289	+ pS7) * z
	290	+ pS6) * z
	291	+ pS5) * z
	292	+ pS4) * z
	293	+ pS3) * z
	294	+ pS2) * z
	295	+ pS1) * z
	296	+ pS0) * z;
	297	q = (((((((( z
	298	+ qS8) * z
	299	+ qS7) * z
	300	+ qS6) * z
	301	+ qS5) * z
	302	+ qS4) * z
	303	+ qS3) * z
	304	+ qS2) * z
	305	+ qS1) * z
	306	+ qS0;
	307	r = s + (w + s * p / q);
	308
31dc8730	309	if (x < 0.0L)
f964490f RM	310	w = pio2_hi + (pio2_lo - r);
	311	else
	312	w = r;
	313	return 2.0 * w;
	314	}
	315	}
0ac5ae23	316	strong_alias (__ieee754_acosl, __acosl_finite)