/*
 * $Id: math_kernel_tan.c,v 1.4 2006-01-08 12:04:23 obarthel Exp $
 *
 * :ts=4
 *
 * Portable ISO 'C' (1994) runtime library for the Amiga computer
 * Copyright (c) 2002-2015 by Olaf Barthel <obarthel (at) gmx.net>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 *   - Redistributions of source code must retain the above copyright
 *     notice, this list of conditions and the following disclaimer.
 *
 *   - Neither the name of Olaf Barthel nor the names of contributors
 *     may be used to endorse or promote products derived from this
 *     software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 *
 *
 * PowerPC math library based in part on work by Sun Microsystems
 * 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.
 */

#ifndef _MATH_HEADERS_H
#include "math_headers.h"
#endif /* _MATH_HEADERS_H */

/****************************************************************************/

#if defined(FLOATING_POINT_SUPPORT) && defined(PPC_FLOATING_POINT_SUPPORT)

/****************************************************************************/

static const double 
one   =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pio4  =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
pio4lo=  3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
T[] =  {
  3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
  1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
  5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
  2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
  8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
  3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
  1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
  5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
  2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
  7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
  7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
 -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
  2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
};

double __kernel_tan(double x, double y, int iy)
{
	double z,r,v,w,s;
	int ix,hx;
	GET_HIGH_WORD(hx,x);
	ix = hx&0x7fffffff;	/* high word of |x| */
	if(ix<0x3e300000)			/* x < 2**-28 */
	{
		if((int)x==0) {			/* generate inexact */
			unsigned int low;
			GET_LOW_WORD(low,x);
			if(((ix|low)|(iy+1))==0) return one/fabs(x);
			else {
				if (iy == 1)
					return x;
				else {	/* compute -1 / (x+y) carefully */
					double a, t;

					z = w = x + y;
					SET_LOW_WORD(z,0);
					v = y - (z - x);
					t = a = -one / w;
					SET_LOW_WORD(t,0);
					s = one + t * z;
					return t + a * (s + t * v);
				}
			}
		}
	}
	if(ix>=0x3FE59428) { 			/* |x|>=0.6744 */
	    if(hx<0) {x = -x; y = -y;}
	    z = pio4-x;
	    w = pio4lo-y;
	    x = z+w; y = 0.0;
	}
	z	=  x*x;
	w 	=  z*z;
    /* Break x^5*(T[1]+x^2*T[2]+...) into
     *	  x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
     *	  x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
     */
	r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
	v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
	s = z*x;
	r = y + z*(s*(r+v)+y);
	r += T[0]*s;
	w = x+r;
	if(ix>=0x3FE59428) {
	    v = (double)iy;
	    return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
	}
	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 */
	    double a,t;
	    z  = w;
	    SET_LOW_WORD(z,0);
	    v  = r-(z - x); 	/* z+v = r+x */
	    t = a  = -1.0/w;	/* a = -1.0/w */
	    SET_LOW_WORD(t,0);
	    s  = 1.0+t*z;
	    return t+a*(s+t*v);
	}
}

/****************************************************************************/

#endif /* FLOATING_POINT_SUPPORT && PPC_FLOATING_POINT_SUPPORT */