/*
 * $Id: math_atan.c,v 1.5 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)

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

#if defined(IEEE_FLOATING_POINT_SUPPORT)

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

#if defined(__GNUC__)

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

#if defined(SMALL_DATA)
#define A4(x) "a4@(" #x ":W)"
#elif defined(SMALL_DATA32)
#define A4(x) "a4@(" #x ":L)"
#else
#define A4(x) #x
#endif /* SMALL_DATA */

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

extern double __atan(double x);

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

asm(

"	.text\n"
"	.even\n"

"	.globl	_MathIeeeDoubTransBase\n"
"	.globl	___atan\n"

"___atan:\n"

"	movel	a6,sp@-\n"
"	movel	"A4(_MathIeeeDoubTransBase)",a6\n"
"	moveml	sp@(8),d0/d1\n"
"	jsr		a6@(-30:W)\n"
"	movel	sp@+,a6\n"
"	rts\n"

);

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

#else

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

INLINE STATIC const double
__atan(double x)
{
	double result;

	result = IEEEDPAtan(x);

	return(result);
}

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

#endif /* __GNUC__ */

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

#endif /* IEEE_FLOATING_POINT_SUPPORT */

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

#if defined(M68881_FLOATING_POINT_SUPPORT)

INLINE STATIC const double
__atan(double x)
{
	double result;

	__asm ("fatan%.x %1,%0"
	       : "=f" (result)
	       : "f" (x));

	return(result);
}

#endif /* M68881_FLOATING_POINT_SUPPORT */

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

#if defined(PPC_FLOATING_POINT_SUPPORT)

static const double atanhi[] = {
  4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
  7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
  9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
  1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
};

static const double atanlo[] = {
  2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
  3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
  1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
  6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
};

static const double aT[] = {
  3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
  1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
  9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
  6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
  4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
  1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
};

static const double 
one   = 1.0,
huge   = 1.0e300;

INLINE STATIC double
__atan(double x)
{
	double w,s1,s2,z;
	int ix,hx,id;

	GET_HIGH_WORD(hx,x);

	ix = hx&0x7fffffff;

	if(ix>=0x44100000)         	              /* if |x| >= 2^66 */
	{
	    unsigned int low;

	    GET_LOW_WORD(low,x);

	    if(ix>0x7ff00000|| (ix==0x7ff00000&&(low!=0)))
			return x+x;		                 /* NaN */

	    if(hx>0) 
			return  atanhi[3]+atanlo[3];
	    else
			return -atanhi[3]-atanlo[3];
	} 

	if (ix < 0x3fdc0000) 	                 /* |x| < 0.4375 */
	{
	    if (ix < 0x3e200000)         	     /* |x| < 2^-29 */
		{
			if(huge+x>one) 
				return x;	                 /* raise inexact */
	    }
	    id = -1;
	} 
	else 
	{
		x = fabs(x);
		if (ix < 0x3ff30000) 		        /* |x| < 1.1875 */
		{
			if (ix < 0x3fe60000)     	    /* 7/16 <=|x|<11/16 */
			{
				id = 0; 
				x = (2.0*x-one)/(2.0+x); 
			}
			else                            /* 11/16<=|x|< 19/16 */
			{
				id = 1; 
				x  = (x-one)/(x+one); 
			}
		} 
		else 
		{
			if (ix < 0x40038000)   	        /* |x| < 2.4375 */
			{
				id = 2; 
				x  = (x-1.5)/(one+1.5*x);
			}
			else 			                /* 2.4375 <= |x| < 2^66 */
			{
				id = 3; 
				x  = -1.0/x;
			}
		}
	}

    /* end of argument reduction */
	z = x*x;
	w = z*z;

    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));

	if (id<0) 
	{
		return x - x*(s1+s2);
	}
	else 
	{
	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
	    return (hx<0)? -z:z;
	}
}

#endif /* PPC_FLOATIN_POINT_SUPPORT */


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

double
atan(double x)
{
	double result;

	result = __atan(x);

	return(result);
}

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

#endif /* FLOATING_POINT_SUPPORT */