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/* atanf.c
*
* Inverse circular tangent
* (arctangent)
*
*
*
* SYNOPSIS:
*
* float x, y, atanf();
*
* y = atanf( x );
*
*
*
* DESCRIPTION:
*
* Returns radian angle between -pi/2 and +pi/2 whose tangent
* is x.
*
* Range reduction is from four intervals into the interval
* from zero to tan( pi/8 ). A polynomial approximates
* the function in this basic interval.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10, 10 100000 1.9e-7 4.1e-8
*
*/
/* atan2f()
*
* Quadrant correct inverse circular tangent
*
*
*
* SYNOPSIS:
*
* float x, y, z, atan2f();
*
* z = atan2f( 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 100000 1.9e-7 4.1e-8
* See atan.c.
*
*/
/* atan.c */
/*
Cephes Math Library Release 2.2: June, 1992
Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
/* Single precision circular arcsine
* test interval: [-tan(pi/8), +tan(pi/8)]
* trials: 10000
* peak relative error: 7.7e-8
* rms relative error: 2.9e-8
*/
#include <math.h>
extern float PIF, PIO2F, PIO4F;
float atanf( float xx )
{
float x, y, z;
int sign;
x = xx;
/* make argument positive and save the sign */
if( xx < 0.0 )
{
sign = -1;
x = -xx;
}
else
{
sign = 1;
x = xx;
}
/* range reduction */
if( x > 2.414213562373095 ) /* tan 3pi/8 */
{
y = PIO2F;
x = -( 1.0/x );
}
else if( x > 0.4142135623730950 ) /* tan pi/8 */
{
y = PIO4F;
x = (x-1.0)/(x+1.0);
}
else
y = 0.0;
z = x * x;
y +=
((( 8.05374449538e-2 * z
- 1.38776856032E-1) * z
+ 1.99777106478E-1) * z
- 3.33329491539E-1) * z * x
+ x;
if( sign < 0 )
y = -y;
return( y );
}
float atan2f( float y, float x )
{
float z, w;
int code;
code = 0;
if( x < 0.0 )
code = 2;
if( y < 0.0 )
code |= 1;
if( x == 0.0 )
{
if( code & 1 )
{
#if ANSIC
return( -PIO2F );
#else
return( 3.0*PIO2F );
#endif
}
if( y == 0.0 )
return( 0.0 );
return( PIO2F );
}
if( y == 0.0 )
{
if( code & 2 )
return( PIF );
return( 0.0 );
}
switch( code )
{
default:
#if ANSIC
case 0:
case 1: w = 0.0; break;
case 2: w = PIF; break;
case 3: w = -PIF; break;
#else
case 0: w = 0.0; break;
case 1: w = 2.0 * PIF; break;
case 2:
case 3: w = PIF; break;
#endif
}
z = atanf( y/x );
return( w + z );
}
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