[thirdparty/glibc.git] / sysdeps / ieee754 / dbl-64 / s_atan.c

/*
 * IBM Accurate Mathematical Library
 * written by International Business Machines Corp.
 * Copyright (C) 2001-2021 Free Software Foundation, Inc.
 *
 * This program 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 program 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 program; if not, see <https://www.gnu.org/licenses/>.
 */
/************************************************************************/
/*  MODULE_NAME: atnat.c                                                */
/*                                                                      */
/*  FUNCTIONS:  uatan                                                   */
/*              atanMp                                                  */
/*              signArctan                                              */
/*                                                                      */
/*                                                                      */
/*  FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat.h                 */
/*                mpatan.c mpatan2.c mpsqrt.c                           */
/*                uatan.tbl                                             */
/*                                                                      */
/* An ultimate atan() routine. Given an IEEE double machine number x    */
/* it computes the correctly rounded (to nearest) value of atan(x).     */
/*                                                                      */
/* Assumption: Machine arithmetic operations are performed in           */
/* round to nearest mode of IEEE 754 standard.                          */
/*                                                                      */
/************************************************************************/

#include <dla.h>
#include "mpa.h"
#include "MathLib.h"
#include "uatan.tbl"
#include "atnat.h"
#include <fenv.h>
#include <float.h>
#include <libm-alias-double.h>
#include <math.h>
#include <fenv_private.h>
#include <math-underflow.h>
#include <stap-probe.h>

void __mpatan (mp_no *, mp_no *, int);	/* see definition in mpatan.c */
static double atanMp (double, const int[]);

  /* Fix the sign of y and return */
static double
__signArctan (double x, double y)
{
  return copysign (y, x);
}


/* An ultimate atan() routine. Given an IEEE double machine number x,    */
/* routine computes the correctly rounded (to nearest) value of atan(x). */
double
__atan (double x)
{
  double cor, s1, ss1, s2, ss2, t1, t2, t3, t4, u, u2, u3,
	 v, vv, w, ww, y, yy, z, zz;
  int i, ux, dx;
  static const int pr[M] = { 6, 8, 10, 32 };
  number num;

  num.d = x;
  ux = num.i[HIGH_HALF];
  dx = num.i[LOW_HALF];

  /* x=NaN */
  if (((ux & 0x7ff00000) == 0x7ff00000)
      && (((ux & 0x000fffff) | dx) != 0x00000000))
    return x + x;

  /* Regular values of x, including denormals +-0 and +-INF */
  SET_RESTORE_ROUND (FE_TONEAREST);
  u = (x < 0) ? -x : x;
  if (u < C)
    {
      if (u < B)
	{
	  if (u < A)
	    {
	      math_check_force_underflow_nonneg (u);
	      return x;
	    }
	  else
	    {			/* A <= u < B */
	      v = x * x;
	      yy = d11.d + v * d13.d;
	      yy = d9.d + v * yy;
	      yy = d7.d + v * yy;
	      yy = d5.d + v * yy;
	      yy = d3.d + v * yy;
	      yy *= x * v;

	      if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x))
		return y;

	      EMULV (x, x, v, vv);	/* v+vv=x^2 */

	      s1 = f17.d + v * f19.d;
	      s1 = f15.d + v * s1;
	      s1 = f13.d + v * s1;
	      s1 = f11.d + v * s1;
	      s1 *= v;

	      ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
	      ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
	      ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
	      ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
	      MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2);
	      ADD2 (x, 0, s2, ss2, s1, ss1, t1, t2);
	      if ((y = s1 + (ss1 - U5 * s1)) == s1 + (ss1 + U5 * s1))
		return y;

	      return atanMp (x, pr);
	    }
	}
      else
	{			/* B <= u < C */
	  i = (TWO52 + TWO8 * u) - TWO52;
	  i -= 16;
	  z = u - cij[i][0].d;
	  yy = cij[i][5].d + z * cij[i][6].d;
	  yy = cij[i][4].d + z * yy;
	  yy = cij[i][3].d + z * yy;
	  yy = cij[i][2].d + z * yy;
	  yy *= z;

	  t1 = cij[i][1].d;
	  if (i < 112)
	    {
	      if (i < 48)
		u2 = U21;	/* u < 1/4        */
	      else
		u2 = U22;
	    }			/* 1/4 <= u < 1/2 */
	  else
	    {
	      if (i < 176)
		u2 = U23;	/* 1/2 <= u < 3/4 */
	      else
		u2 = U24;
	    }			/* 3/4 <= u <= 1  */
	  if ((y = t1 + (yy - u2 * t1)) == t1 + (yy + u2 * t1))
	    return __signArctan (x, y);

	  z = u - hij[i][0].d;

	  s1 = hij[i][14].d + z * hij[i][15].d;
	  s1 = hij[i][13].d + z * s1;
	  s1 = hij[i][12].d + z * s1;
	  s1 = hij[i][11].d + z * s1;
	  s1 *= z;

	  ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
	  MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
	  ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
	  ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
	  ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
	  ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
	  if ((y = s2 + (ss2 - U6 * s2)) == s2 + (ss2 + U6 * s2))
	    return __signArctan (x, y);

	  return atanMp (x, pr);
	}
    }
  else
    {
      if (u < D)
	{			/* C <= u < D */
	  w = 1 / u;
	  EMULV (w, u, t1, t2);
	  ww = w * ((1 - t1) - t2);
	  i = (TWO52 + TWO8 * w) - TWO52;
	  i -= 16;
	  z = (w - cij[i][0].d) + ww;

	  yy = cij[i][5].d + z * cij[i][6].d;
	  yy = cij[i][4].d + z * yy;
	  yy = cij[i][3].d + z * yy;
	  yy = cij[i][2].d + z * yy;
	  yy = HPI1 - z * yy;

	  t1 = HPI - cij[i][1].d;
	  if (i < 112)
	    u3 = U31;           /* w <  1/2 */
	  else
	    u3 = U32;           /* w >= 1/2 */
	  if ((y = t1 + (yy - u3)) == t1 + (yy + u3))
	    return __signArctan (x, y);

	  DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4);
	  t1 = w - hij[i][0].d;
	  EADD (t1, ww, z, zz);

	  s1 = hij[i][14].d + z * hij[i][15].d;
	  s1 = hij[i][13].d + z * s1;
	  s1 = hij[i][12].d + z * s1;
	  s1 = hij[i][11].d + z * s1;
	  s1 *= z;

	  ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
	  MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
	  ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
	  ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
	  ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
	  MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
	  ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
	  SUB2 (HPI, HPI1, s2, ss2, s1, ss1, t1, t2);
	  if ((y = s1 + (ss1 - U7)) == s1 + (ss1 + U7))
	    return __signArctan (x, y);

	  return atanMp (x, pr);
	}
      else
	{
	  if (u < E)
	    {                   /* D <= u < E */
	      w = 1 / u;
	      v = w * w;
	      EMULV (w, u, t1, t2);

	      yy = d11.d + v * d13.d;
	      yy = d9.d + v * yy;
	      yy = d7.d + v * yy;
	      yy = d5.d + v * yy;
	      yy = d3.d + v * yy;
	      yy *= w * v;

	      ww = w * ((1 - t1) - t2);
	      ESUB (HPI, w, t3, cor);
	      yy = ((HPI1 + cor) - ww) - yy;
	      if ((y = t3 + (yy - U4)) == t3 + (yy + U4))
		return __signArctan (x, y);

	      DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4);
	      MUL2 (w, ww, w, ww, v, vv, t1, t2);

	      s1 = f17.d + v * f19.d;
	      s1 = f15.d + v * s1;
	      s1 = f13.d + v * s1;
	      s1 = f11.d + v * s1;
	      s1 *= v;

	      ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
	      ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
	      ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
	      ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
	      MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2);
	      ADD2 (w, ww, s2, ss2, s1, ss1, t1, t2);
	      SUB2 (HPI, HPI1, s1, ss1, s2, ss2, t1, t2);

	      if ((y = s2 + (ss2 - U8)) == s2 + (ss2 + U8))
		return __signArctan (x, y);

	      return atanMp (x, pr);
	    }
	  else
	    {
	      /* u >= E */
	      if (x > 0)
		return HPI;
	      else
		return MHPI;
	    }
	}
    }
}

 /* Final stages. Compute atan(x) by multiple precision arithmetic */
static double
atanMp (double x, const int pr[])
{
  mp_no mpx, mpy, mpy2, mperr, mpt1, mpy1;
  double y1, y2;
  int i, p;

  for (i = 0; i < M; i++)
    {
      p = pr[i];
      __dbl_mp (x, &mpx, p);
      __mpatan (&mpx, &mpy, p);
      __dbl_mp (u9[i].d, &mpt1, p);
      __mul (&mpy, &mpt1, &mperr, p);
      __add (&mpy, &mperr, &mpy1, p);
      __sub (&mpy, &mperr, &mpy2, p);
      __mp_dbl (&mpy1, &y1, p);
      __mp_dbl (&mpy2, &y2, p);
      if (y1 == y2)
	{
	  LIBC_PROBE (slowatan, 3, &p, &x, &y1);
	  return y1;
	}
    }
  LIBC_PROBE (slowatan_inexact, 3, &p, &x, &y1);
  return y1;			/*if impossible to do exact computing */
}

#ifndef __atan
libm_alias_double (__atan, atan)
#endif
Commit	Line	Data
f7eac6eb	1	/*
e4d82761	2	* IBM Accurate Mathematical Library
aeb25823	3	* written by International Business Machines Corp.
2b778ceb	4	* Copyright (C) 2001-2021 Free Software Foundation, Inc.
f7eac6eb	5	*
e4d82761 UD	6	* This program is free software; you can redistribute it and/or modify
e4d82761 UD	7	* it under the terms of the GNU Lesser General Public License as published by
cc7375ce	8	* the Free Software Foundation; either version 2.1 of the License, or
e4d82761	9	* (at your option) any later version.
f7eac6eb	10	*
e4d82761 UD	11	* This program 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
c6c6dd48	14	* GNU Lesser General Public License for more details.
f7eac6eb	15	*
e4d82761	16	* You should have received a copy of the GNU Lesser General Public License
5a82c748	17	* along with this program; if not, see <https://www.gnu.org/licenses/>.
f7eac6eb	18	*/
e4d82761 UD	19	/************************************************************************/
	20	/* MODULE_NAME: atnat.c */
	21	/* */
	22	/* FUNCTIONS: uatan */
	23	/* atanMp */
	24	/* signArctan */
	25	/* */
	26	/* */
	27	/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat.h */
	28	/* mpatan.c mpatan2.c mpsqrt.c */
	29	/* uatan.tbl */
	30	/* */
	31	/* An ultimate atan() routine. Given an IEEE double machine number x */
	32	/* it computes the correctly rounded (to nearest) value of atan(x). */
	33	/* */
	34	/* Assumption: Machine arithmetic operations are performed in */
	35	/* round to nearest mode of IEEE 754 standard. */
	36	/* */
	37	/************************************************************************/
f7eac6eb	38
c8b3296b	39	#include <dla.h>
e4d82761 UD	40	#include "mpa.h"
	41	#include "MathLib.h"
	42	#include "uatan.tbl"
	43	#include "atnat.h"
ae63c7eb	44	#include <fenv.h>
4629c866	45	#include <float.h>
38722448	46	#include <libm-alias-double.h>
1ed0291c	47	#include <math.h>
70e2ba33	48	#include <fenv_private.h>
8f5b00d3	49	#include <math-underflow.h>
10e1cf6b	50	#include <stap-probe.h>
e4d82761	51
d26dd3eb SP	52	void __mpatan (mp_no , mp_no , int); /* see definition in mpatan.c */
d26dd3eb SP	53	static double atanMp (double, const int[]);
af968f62 UD	54
af968f62 UD	55	/* Fix the sign of y and return */
d26dd3eb SP	56	static double
	57	__signArctan (double x, double y)
	58	{
81dca813	59	return copysign (y, x);
af968f62 UD	60	}
	61
	62
e4d82761 UD	63	/* An ultimate atan() routine. Given an IEEE double machine number x, */
e4d82761 UD	64	/* routine computes the correctly rounded (to nearest) value of atan(x). */
d26dd3eb	65	double
527cd19c	66	__atan (double x)
d26dd3eb	67	{
e93c2643	68	double cor, s1, ss1, s2, ss2, t1, t2, t3, t4, u, u2, u3,
c5d5d574	69	v, vv, w, ww, y, yy, z, zz;
d26dd3eb SP	70	int i, ux, dx;
d26dd3eb SP	71	static const int pr[M] = { 6, 8, 10, 32 };
e4d82761	72	number num;
e4d82761	73
d26dd3eb SP	74	num.d = x;
	75	ux = num.i[HIGH_HALF];
	76	dx = num.i[LOW_HALF];
e4d82761 UD	77
e4d82761 UD	78	/* x=NaN */
d26dd3eb SP	79	if (((ux & 0x7ff00000) == 0x7ff00000)
	80	&& (((ux & 0x000fffff) \| dx) != 0x00000000))
	81	return x + x;
e4d82761 UD	82
e4d82761 UD	83	/* Regular values of x, including denormals +-0 and +-INF */
ae63c7eb	84	SET_RESTORE_ROUND (FE_TONEAREST);
a64d7e0e	85	u = (x < 0) ? -x : x;
d26dd3eb SP	86	if (u < C)
	87	{
	88	if (u < B)
	89	{
	90	if (u < A)
4629c866	91	{
d96164c3	92	math_check_force_underflow_nonneg (u);
4629c866 JM	93	return x;
4629c866 JM	94	}
d26dd3eb SP	95	else
	96	{ /* A <= u < B */
	97	v = x * x;
	98	yy = d11.d + v * d13.d;
	99	yy = d9.d + v * yy;
	100	yy = d7.d + v * yy;
	101	yy = d5.d + v * yy;
	102	yy = d3.d + v * yy;
	103	yy = x v;
	104
	105	if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x))
	106	return y;
	107
e93c2643	108	EMULV (x, x, v, vv); /* v+vv=x^2 */
d26dd3eb SP	109
	110	s1 = f17.d + v * f19.d;
	111	s1 = f15.d + v * s1;
	112	s1 = f13.d + v * s1;
	113	s1 = f11.d + v * s1;
	114	s1 *= v;
	115
a64d7e0e	116	ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
e93c2643	117	MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
d26dd3eb	118	ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
e93c2643	119	MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
d26dd3eb	120	ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
e93c2643	121	MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
d26dd3eb	122	ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
e93c2643 VG	123	MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
e93c2643 VG	124	MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2);
a64d7e0e	125	ADD2 (x, 0, s2, ss2, s1, ss1, t1, t2);
d26dd3eb SP	126	if ((y = s1 + (ss1 - U5 * s1)) == s1 + (ss1 + U5 * s1))
	127	return y;
	128
	129	return atanMp (x, pr);
	130	}
	131	}
	132	else
	133	{ /* B <= u < C */
	134	i = (TWO52 + TWO8 * u) - TWO52;
	135	i -= 16;
	136	z = u - cij[i][0].d;
	137	yy = cij[i][5].d + z * cij[i][6].d;
	138	yy = cij[i][4].d + z * yy;
	139	yy = cij[i][3].d + z * yy;
	140	yy = cij[i][2].d + z * yy;
	141	yy *= z;
	142
	143	t1 = cij[i][1].d;
	144	if (i < 112)
	145	{
	146	if (i < 48)
	147	u2 = U21; /* u < 1/4 */
	148	else
	149	u2 = U22;
	150	} /* 1/4 <= u < 1/2 */
	151	else
	152	{
	153	if (i < 176)
	154	u2 = U23; /* 1/2 <= u < 3/4 */
	155	else
	156	u2 = U24;
	157	} /* 3/4 <= u <= 1 */
	158	if ((y = t1 + (yy - u2 * t1)) == t1 + (yy + u2 * t1))
	159	return __signArctan (x, y);
	160
	161	z = u - hij[i][0].d;
	162
	163	s1 = hij[i][14].d + z * hij[i][15].d;
	164	s1 = hij[i][13].d + z * s1;
	165	s1 = hij[i][12].d + z * s1;
	166	s1 = hij[i][11].d + z * s1;
	167	s1 *= z;
	168
a64d7e0e	169	ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
e93c2643	170	MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
d26dd3eb	171	ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
e93c2643	172	MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
d26dd3eb	173	ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
e93c2643	174	MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
d26dd3eb	175	ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
e93c2643	176	MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
d26dd3eb SP	177	ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
	178	if ((y = s2 + (ss2 - U6 * s2)) == s2 + (ss2 + U6 * s2))
	179	return __signArctan (x, y);
	180
	181	return atanMp (x, pr);
	182	}
e4d82761	183	}
d26dd3eb SP	184	else
	185	{
	186	if (u < D)
	187	{ /* C <= u < D */
c2d94018	188	w = 1 / u;
e93c2643	189	EMULV (w, u, t1, t2);
c2d94018	190	ww = w * ((1 - t1) - t2);
d26dd3eb SP	191	i = (TWO52 + TWO8 * w) - TWO52;
	192	i -= 16;
	193	z = (w - cij[i][0].d) + ww;
	194
	195	yy = cij[i][5].d + z * cij[i][6].d;
	196	yy = cij[i][4].d + z * yy;
	197	yy = cij[i][3].d + z * yy;
	198	yy = cij[i][2].d + z * yy;
c5d5d574	199	yy = HPI1 - z * yy;
f7eac6eb	200
d26dd3eb SP	201	t1 = HPI - cij[i][1].d;
d26dd3eb SP	202	if (i < 112)
c5d5d574	203	u3 = U31; /* w < 1/2 */
d26dd3eb	204	else
c5d5d574	205	u3 = U32; /* w >= 1/2 */
d26dd3eb SP	206	if ((y = t1 + (yy - u3)) == t1 + (yy + u3))
	207	return __signArctan (x, y);
	208
e93c2643	209	DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4);
d26dd3eb SP	210	t1 = w - hij[i][0].d;
	211	EADD (t1, ww, z, zz);
	212
	213	s1 = hij[i][14].d + z * hij[i][15].d;
	214	s1 = hij[i][13].d + z * s1;
	215	s1 = hij[i][12].d + z * s1;
	216	s1 = hij[i][11].d + z * s1;
	217	s1 *= z;
	218
a64d7e0e	219	ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
e93c2643	220	MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
d26dd3eb	221	ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
e93c2643	222	MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
d26dd3eb	223	ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
e93c2643	224	MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
d26dd3eb	225	ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
e93c2643	226	MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
d26dd3eb SP	227	ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
	228	SUB2 (HPI, HPI1, s2, ss2, s1, ss1, t1, t2);
	229	if ((y = s1 + (ss1 - U7)) == s1 + (ss1 + U7))
	230	return __signArctan (x, y);
	231
	232	return atanMp (x, pr);
	233	}
	234	else
	235	{
	236	if (u < E)
c5d5d574	237	{ /* D <= u < E */
c2d94018	238	w = 1 / u;
d26dd3eb	239	v = w * w;
e93c2643	240	EMULV (w, u, t1, t2);
d26dd3eb SP	241
	242	yy = d11.d + v * d13.d;
	243	yy = d9.d + v * yy;
	244	yy = d7.d + v * yy;
	245	yy = d5.d + v * yy;
	246	yy = d3.d + v * yy;
	247	yy = w v;
	248
c2d94018	249	ww = w * ((1 - t1) - t2);
d26dd3eb SP	250	ESUB (HPI, w, t3, cor);
	251	yy = ((HPI1 + cor) - ww) - yy;
	252	if ((y = t3 + (yy - U4)) == t3 + (yy + U4))
	253	return __signArctan (x, y);
	254
e93c2643 VG	255	DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4);
e93c2643 VG	256	MUL2 (w, ww, w, ww, v, vv, t1, t2);
d26dd3eb SP	257
	258	s1 = f17.d + v * f19.d;
	259	s1 = f15.d + v * s1;
	260	s1 = f13.d + v * s1;
	261	s1 = f11.d + v * s1;
	262	s1 *= v;
	263
a64d7e0e	264	ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
e93c2643	265	MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
d26dd3eb	266	ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
e93c2643	267	MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
d26dd3eb	268	ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
e93c2643	269	MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
d26dd3eb	270	ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
e93c2643 VG	271	MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
e93c2643 VG	272	MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2);
d26dd3eb SP	273	ADD2 (w, ww, s2, ss2, s1, ss1, t1, t2);
	274	SUB2 (HPI, HPI1, s1, ss1, s2, ss2, t1, t2);
	275
	276	if ((y = s2 + (ss2 - U8)) == s2 + (ss2 + U8))
	277	return __signArctan (x, y);
	278
	279	return atanMp (x, pr);
	280	}
	281	else
	282	{
	283	/* u >= E */
	284	if (x > 0)
	285	return HPI;
	286	else
	287	return MHPI;
	288	}
	289	}
	290	}
f7eac6eb	291	}
e4d82761	292
e4d82761	293	/* Final stages. Compute atan(x) by multiple precision arithmetic */
d26dd3eb SP	294	static double
	295	atanMp (double x, const int pr[])
	296	{
	297	mp_no mpx, mpy, mpy2, mperr, mpt1, mpy1;
	298	double y1, y2;
	299	int i, p;
	300
	301	for (i = 0; i < M; i++)
	302	{
	303	p = pr[i];
	304	__dbl_mp (x, &mpx, p);
	305	__mpatan (&mpx, &mpy, p);
	306	__dbl_mp (u9[i].d, &mpt1, p);
	307	__mul (&mpy, &mpt1, &mperr, p);
	308	__add (&mpy, &mperr, &mpy1, p);
	309	__sub (&mpy, &mperr, &mpy2, p);
	310	__mp_dbl (&mpy1, &y1, p);
	311	__mp_dbl (&mpy2, &y2, p);
	312	if (y1 == y2)
10e1cf6b SP	313	{
	314	LIBC_PROBE (slowatan, 3, &p, &x, &y1);
	315	return y1;
	316	}
d26dd3eb	317	}
10e1cf6b	318	LIBC_PROBE (slowatan_inexact, 3, &p, &x, &y1);
d26dd3eb	319	return y1; /if impossible to do exact computing /
e4d82761 UD	320	}
e4d82761 UD	321
527cd19c	322	#ifndef __atan
38722448	323	libm_alias_double (__atan, atan)
cccda09f	324	#endif