mirror of
https://github.com/ZDoom/Raze.git
synced 2024-11-16 01:11:44 +00:00
417 lines
7.8 KiB
C
417 lines
7.8 KiB
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(x)
|
||
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( y, x )
|
||
#else
|
||
double c_atan2( x, y )
|
||
#endif
|
||
double x, y;
|
||
{
|
||
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 );
|
||
}
|