/*
 * ====================================================
 * 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^-33, 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)))
 */

#ifndef __FDLIBM_H__
#include "fdlibm.h"
#endif


long double __kernel_tanl(long double x, long double y, int iy)
{
	long double z, r, v, w, s;
	long double absx = __ieee754_fabsl(x);
	int sign = 0;

	static const long double one = 1.0L;
	static const long double pio4hi = 0xc.90fdaa22168c235p-4L;
	static const long double pio4lo = -0x3.b399d747f23e32ecp-68L;
	/* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)
	   0 <= x <= 0.6743316650390625
	   Peak relative error 8.0e-36  */
	static const long double TH = 3.333333333333333333333333333333333333333E-1L;
	static const long double T0 = -1.813014711743583437742363284336855889393E7L;
	static const long double T1 = 1.320767960008972224312740075083259247618E6L;
	static const long double T2 = -2.626775478255838182468651821863299023956E4L;
	static const long double T3 = 1.764573356488504935415411383687150199315E2L;
	static const long double T4 = -3.333267763822178690794678978979803526092E-1L;
	static const long double U0 = -1.359761033807687578306772463253710042010E8L;
	static const long double U1 = 6.494370630656893175666729313065113194784E7L;
	static const long double U2 = -4.180787672237927475505536849168729386782E6L;
	static const long double U3 = 8.031643765106170040139966622980914621521E4L;
	static const long double U4 = -5.323131271912475695157127875560667378597E2L;
	/* 1.000000000000000000000000000000000000000E0 */

	if (absx < 0x1p-33L)
	{
		if ((int32_t) x == 0)
		{								/* generate inexact */
			if (x == 0 && iy == -1)
				return one / __ieee754_fabsl(x);
			else
				return (iy == 1) ? x : -one / x;
		}
	}
	if (absx >= 0.6743316650390625L)
	{
		if (signbit(x))
		{
			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 (sign != 0)
	{
		v = (long double) iy;
		w = (v - 2.0 * (x - (w * w / (w + v) - r)));
		if (sign < 0)
			w = -w;
		return w;
	}
	if (iy == 1)
		return w;
	else
		return -1.0 / (x + r);
}
