/*

 * ====================================================

 * 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

    <http://www.gnu.org/licenses/>.  */

/* __kernel_tanl( x, y, k )

 * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854

 * Input x is assumed to be bounded by ~pi/4 in magnitude.

 * Input y is the tail of x.

 * Input k indicates whether tan (if k=1) or

 * -1/tan (if k= -1) is returned.

 *

 * Algorithm

 *	1. Since tan(-x) = -tan(x), we need only to consider positive x.

 *	2. if x < 2^-57, return x with inexact if x!=0.

 *	3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)

 *          on [0,0.67433].

 *

 *	   Note: tan(x+y) = tan(x) + tan'(x)*y

 *		          ~ tan(x) + (1+x*x)*y

 *	   Therefore, for better accuracy in computing tan(x+y), let

 *		r = x^3 * R(x^2)

 *	   then

 *		tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))

 *

 *      4. For x in [0.67433,pi/4],  let y = pi/4 - x, then

 *		tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))

 *		       = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))

 */

#include <float.h>

#include <math.h>

#include <math_private.h>

#include <math-underflow.h>

#include <libc-diag.h>

static const long double

  one = 1.0L,

  pio4hi = 7.8539816339744830961566084581987569936977E-1L,

  pio4lo = 2.1679525325309452561992610065108379921906E-35L,

  /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)

     0 <= x <= 0.6743316650390625

     Peak relative error 8.0e-36  */

 TH =  3.333333333333333333333333333333333333333E-1L,

 T0 = -1.813014711743583437742363284336855889393E7L,

 T1 =  1.320767960008972224312740075083259247618E6L,

 T2 = -2.626775478255838182468651821863299023956E4L,

 T3 =  1.764573356488504935415411383687150199315E2L,

 T4 = -3.333267763822178690794678978979803526092E-1L,

 U0 = -1.359761033807687578306772463253710042010E8L,

 U1 =  6.494370630656893175666729313065113194784E7L,

 U2 = -4.180787672237927475505536849168729386782E6L,

 U3 =  8.031643765106170040139966622980914621521E4L,

 U4 = -5.323131271912475695157127875560667378597E2L;

  /* 1.000000000000000000000000000000000000000E0 */

long double

__kernel_tanl (long double x, long double y, int iy)

{

  long double z, r, v, w, s;

  int32_t ix, sign, hx, lx;

  double xhi;

  xhi = ldbl_high (x);

  EXTRACT_WORDS (hx, lx, xhi);

  ix = hx & 0x7fffffff;

  if (ix < 0x3c600000)		/* x < 2**-57 */

    {

      if ((int) x == 0)		/* generate inexact */

	{

	  if ((ix | lx | (iy + 1)) == 0)

	    return one / fabs (x);

	  else if (iy == 1)

	    {

	      math_check_force_underflow (x);

	      return x;

	    }

	  else

	    return -one / x;

	}

    }

  if (ix >= 0x3fe59420) /* |x| >= 0.6743316650390625 */

    {

      if ((hx & 0x80000000) != 0)

	{

	  x = -x;

	  y = -y;

	  sign = -1;

	}

      else

	sign = 1;

      z = pio4hi - x;

      w = pio4lo - y;

      x = z + w;

      y = 0.0;

    }

  z = x * x;

  r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));

  v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));

  r = r / v;

  s = z * x;

  r = y + z * (s * r + y);

  r += TH * s;

  w = x + r;

  if (ix >= 0x3fe59420)

    {

      v = (long double) iy;

      w = (v - 2.0 * (x - (w * w / (w + v) - r)));

      /* SIGN is set for arguments that reach this code, but not

	 otherwise, resulting in warnings that it may be used

	 uninitialized although in the cases where it is used it has

	 always been set.  */

      DIAG_PUSH_NEEDS_COMMENT;

      DIAG_IGNORE_NEEDS_COMMENT (5, "-Wmaybe-uninitialized");

      if (sign < 0)

	w = -w;

      DIAG_POP_NEEDS_COMMENT;

      return w;

    }

  if (iy == 1)

    return w;

  else

    {				/* if allow error up to 2 ulp,

				   simply return -1.0/(x+r) here */

      /*  compute -1.0/(x+r) accurately */

      long double u1, z1;

      u1 = ldbl_high (w);

      v = r - (u1 - x);		/* u1+v = r+x */

      z = -1.0 / w;

      z1 = ldbl_high (z);

      s = 1.0 + z1 * u1;

      return z1 + z * (s + z1 * v);

    }

}