text: /*
   * IBM Accurate Mathematical Library
   * written by International Business Machines Corp.
   * Copyright (C) 2001-2016 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 <http://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 <math.h>
  #include <math_private.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, t7, t8, t9, t10, u, u2, u3,
  	 v, vv, w, ww, y, yy, z, zz;
  #ifndef DLA_FMS
    double t4, t5, t6;
  #endif
    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, t1, t2, t3, t4, t5);	/* 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, t3, t4, t5, t6, t7, t8);
  	      ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
  	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  	      ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
  	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  	      ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
  	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  	      MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7,
  		    t8);
  	      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, t3, t4, t5, t6, t7, t8);
  	  ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
  	  MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  	  ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
  	  MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  	  ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
  	  MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  	  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, t3, t4, t5, t6, t7);
  	  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, t5, t6, t7, t8, t9,
  		t10);
  	  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, t3, t4, t5, t6, t7, t8);
  	  ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
  	  MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  	  ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
  	  MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  	  ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
  	  MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  	  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, t3, t4, t5, t6, t7);
  
  	      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, t5, t6, t7, t8,
  		    t9, t10);
  	      MUL2 (w, ww, w, ww, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
  
  	      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, t3, t4, t5, t6, t7, t8);
  	      ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
  	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  	      ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
  	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  	      ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
  	      MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
  	      MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
  	      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 */
  }
  
  #ifdef NO_LONG_DOUBLE
  weak_alias (atan, atanl)
  #endif
  