raze/source/common/thirdparty/math/atan.c

/*							atan.c
 *
 *	Inverse circular tangent
 *      (arctangent)
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, atan();
 *
 * y = atan( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns radian angle between -pi/2 and +pi/2 whose tangent
 * is x.
 *
 * Range reduction is from three intervals into the interval
 * from zero to 0.66.  The approximant uses a rational
 * function of degree 4/5 of the form x + x**3 P(x)/Q(x).
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       -10, 10     50000       2.4e-17     8.3e-18
 *    IEEE      -10, 10      10^6       1.8e-16     5.0e-17
 *
 */
/*							atan2()
 *
 *	Quadrant correct inverse circular tangent
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, z, atan2();
 *
 * z = atan2( y, x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns radian angle whose tangent is y/x.
 * Define compile time symbol ANSIC = 1 for ANSI standard,
 * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
 * 0 to 2PI, args (x,y).
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      -10, 10      10^6       2.5e-16     6.9e-17
 * See atan.c.
 *
 */

/*							atan.c */


/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice,
   this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions and the following disclaimer in the
   documentation and/or other materials provided with the distribution.
3. Neither the name of the <ORGANIZATION> nor the names of its
   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.
*/


#include "mconf.h"

/* arctan(x)  = x + x^3 P(x^2)/Q(x^2)
   0 <= x <= 0.66
   Peak relative error = 2.6e-18  */
#ifdef UNK
static double P[5] = {
-8.750608600031904122785E-1,
-1.615753718733365076637E1,
-7.500855792314704667340E1,
-1.228866684490136173410E2,
-6.485021904942025371773E1,
};
static double Q[5] = {
/* 1.000000000000000000000E0, */
 2.485846490142306297962E1,
 1.650270098316988542046E2,
 4.328810604912902668951E2,
 4.853903996359136964868E2,
 1.945506571482613964425E2,
};

/* tan( 3*pi/8 ) */
static double T3P8 = 2.41421356237309504880;
#endif

#ifdef DEC
static short P[20] = {
0140140,0001775,0007671,0026242,
0141201,0041242,0155534,0001715,
0141626,0002141,0132100,0011625,
0141765,0142771,0064055,0150453,
0141601,0131517,0164507,0062164,
};
static short Q[20] = {
/* 0040200,0000000,0000000,0000000, */
0041306,0157042,0154243,0000742,
0042045,0003352,0016707,0150452,
0042330,0070306,0113425,0170730,
0042362,0130770,0116602,0047520,
0042102,0106367,0156753,0013541,
};

/* tan( 3*pi/8 ) = 2.41421356237309504880 */
static unsigned short T3P8A[] = {040432,0101171,0114774,0167462,};
#define T3P8 *(double *)T3P8A
#endif

#ifdef IBMPC
static short P[20] = {
0x2594,0xa1f7,0x007f,0xbfec,
0x807a,0x5b6b,0x2854,0xc030,
0x0273,0x3688,0xc08c,0xc052,
0xba25,0x2d05,0xb8bf,0xc05e,
0xec8e,0xfd28,0x3669,0xc050,
};
static short Q[20] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0x603c,0x5b14,0xdbc4,0x4038,
0xfa25,0x43b8,0xa0dd,0x4064,
0xbe3b,0xd2e2,0x0e18,0x407b,
0x49ea,0x13b0,0x563f,0x407e,
0x62ec,0xfbbd,0x519e,0x4068,
};

/* tan( 3*pi/8 ) = 2.41421356237309504880 */
static unsigned short T3P8A[] = {0x9de6,0x333f,0x504f,0x4003};
#define T3P8 *(double *)T3P8A
#endif

#ifdef MIEEE
static short P[20] = {
0xbfec,0x007f,0xa1f7,0x2594,
0xc030,0x2854,0x5b6b,0x807a,
0xc052,0xc08c,0x3688,0x0273,
0xc05e,0xb8bf,0x2d05,0xba25,
0xc050,0x3669,0xfd28,0xec8e,
};
static short Q[20] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0x4038,0xdbc4,0x5b14,0x603c,
0x4064,0xa0dd,0x43b8,0xfa25,
0x407b,0x0e18,0xd2e2,0xbe3b,
0x407e,0x563f,0x13b0,0x49ea,
0x4068,0x519e,0xfbbd,0x62ec,
};

/* tan( 3*pi/8 ) = 2.41421356237309504880 */
static unsigned short T3P8A[] = {
0x4003,0x504f,0x333f,0x9de6
};
#define T3P8 *(double *)T3P8A
#endif

#ifdef ANSIPROT
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double atan ( double );
extern double fabs ( double );
extern int signbit ( double );
extern int isnan ( double );
#else
double polevl(), p1evl(), atan(), fabs();
int signbit(), isnan();
#endif
extern double PI, PIO2, PIO4, INFINITY, NEGZERO, MAXNUM;

/* pi/2 = PIO2 + MOREBITS.  */
#ifdef DEC
#define MOREBITS 5.721188726109831840122E-18
#else
#define MOREBITS 6.123233995736765886130E-17
#endif


double c_atan(double x)
{
double y, z;
short sign, flag;

#ifdef MINUSZERO
if( x == 0.0 )
	return(x);
#endif
#ifdef INFINITIES
if(x == INFINITY)
	return(PIO2);
if(x == -INFINITY)
	return(-PIO2);
#endif
/* make argument positive and save the sign */
sign = 1;
if( x < 0.0 )
	{
	sign = -1;
	x = -x;
	}
/* range reduction */
flag = 0;
if( x > T3P8 )
	{
	y = PIO2;
	flag = 1;
	x = -( 1.0/x );
	}
else if( x <= 0.66 )
	{
	y = 0.0;
	}
else
	{
	y = PIO4;
	flag = 2;
	x = (x-1.0)/(x+1.0);
	}
z = x * x;
z = z * polevl( z, P, 4 ) / p1evl( z, Q, 5 );
z = x * z + x;
if( flag == 2 )
	z += 0.5 * MOREBITS;
else if( flag == 1 )
	z += MOREBITS;
y = y + z;
if( sign < 0 )
	y = -y;
return(y);
}

/*							atan2	*/

#ifdef ANSIC
double c_atan2(double y, double x)
#else
double c_atan2(double x, double y)
#endif
{
double z, w;
short code;

code = 0;

#ifdef NANS
if( isnan(x) )
	return(x);
if( isnan(y) )
	return(y);
#endif
#ifdef MINUSZERO
if( y == 0.0 )
	{
	if( signbit(y) )
		{
		if( x > 0.0 )
			z = y;
		else if( x < 0.0 )
			z = -PI;
		else
			{
			if( signbit(x) )
				z = -PI;
			else
				z = y;
			}
		}
	else /* y is +0 */
		{
		if( x == 0.0 )
			{
			if( signbit(x) )
				z = PI;
			else
				z = 0.0;
			}
		else if( x > 0.0 )
			z = 0.0;
		else
			z = PI;
		}
	return z;
	}
if( x == 0.0 )
	{
	if( y > 0.0 )
		z = PIO2;
	else
		z = -PIO2;
	return z;
	}
#endif /* MINUSZERO */
#ifdef INFINITIES
if( x == INFINITY )
	{
	if( y == INFINITY )
		z = 0.25 * PI;
	else if( y == -INFINITY )
		z = -0.25 * PI;
	else if( y < 0.0 )
		z = NEGZERO;
	else
		z = 0.0;
	return z;
	}
if( x == -INFINITY )
	{
	if( y == INFINITY )
		z = 0.75 * PI;
	else if( y <= -INFINITY )
		z = -0.75 * PI;
	else if( y >= 0.0 )
		z = PI;
	else
		z = -PI;
	return z;
	}
if( y == INFINITY )
	return( PIO2 );
if( y == -INFINITY )
	return( -PIO2 );
#endif

if( x < 0.0 )
	code = 2;
if( y < 0.0 )
	code |= 1;

#ifdef INFINITIES
if( x == 0.0 )
#else
if( fabs(x) <= (fabs(y) / MAXNUM) )
#endif
	{
	if( code & 1 )
		{
#if ANSIC
		return( -PIO2 );
#else
		return( 3.0*PIO2 );
#endif
		}
	if( y == 0.0 )
		return( 0.0 );
	return( PIO2 );
	}

if( y == 0.0 )
	{
	if( code & 2 )
		return( PI );
	return( 0.0 );
	}


switch( code )
	{
#if ANSIC
	default:
	case 0:
	case 1: w = 0.0; break;
	case 2: w = PI; break;
	case 3: w = -PI; break;
#else
	default:
	case 0: w = 0.0; break;
	case 1: w = 2.0 * PI; break;
	case 2:
	case 3: w = PI; break;
#endif
	}

z = w + c_atan( y/x );
#ifdef MINUSZERO
if( z == 0.0 && y < 0 )
	z = NEGZERO;
#endif
return( z );
}