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/* asinf.c
*
* Inverse circular sine
*
*
*
* SYNOPSIS:
*
* float x, y, asinf();
*
* y = asinf( x );
*
*
*
* DESCRIPTION:
*
* Returns radian angle between -pi/2 and +pi/2 whose sine is x.
*
* A polynomial of the form x + x**3 P(x**2)
* is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
* transformed by the identity
*
* asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -1, 1 100000 2.5e-7 5.0e-8
*
*
* ERROR MESSAGES:
*
* message condition value returned
* asinf domain |x| > 1 0.0
*
*/
/* acosf()
*
* Inverse circular cosine
*
*
*
* SYNOPSIS:
*
* float x, y, acosf();
*
* y = acosf( x );
*
*
*
* DESCRIPTION:
*
* Returns radian angle between -pi/2 and +pi/2 whose cosine
* is x.
*
* Analytically, acos(x) = pi/2 - asin(x). However if |x| is
* near 1, there is cancellation error in subtracting asin(x)
* from pi/2. Hence if x < -0.5,
*
* acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
*
* or if x > +0.5,
*
* acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -1, 1 100000 1.4e-7 4.2e-8
*
*
* ERROR MESSAGES:
*
* message condition value returned
* acosf domain |x| > 1 0.0
*/
/* asin.c */
/*
Cephes Math Library Release 2.2: June, 1992
Copyright 1984, 1987, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
/* Single precision circular arcsine
* test interval: [-0.5, +0.5]
* trials: 10000
* peak relative error: 6.7e-8
* rms relative error: 2.5e-8
*/
#include <math.h>
extern float PIF, PIO2F;
float sqrtf( float );
float asinf( float xx )
{
float a, x, z;
int sign, flag;
x = xx;
if( x > 0 )
{
sign = 1;
a = x;
}
else
{
sign = -1;
a = -x;
}
if( a > 1.0 )
{
mtherr( "asinf", DOMAIN );
return( 0.0 );
}
if( a < 1.0e-4 )
{
z = a;
goto done;
}
if( a > 0.5 )
{
z = 0.5 * (1.0 - a);
x = sqrtf( z );
flag = 1;
}
else
{
x = a;
z = x * x;
flag = 0;
}
z =
(((( 4.2163199048E-2 * z
+ 2.4181311049E-2) * z
+ 4.5470025998E-2) * z
+ 7.4953002686E-2) * z
+ 1.6666752422E-1) * z * x
+ x;
if( flag != 0 )
{
z = z + z;
z = PIO2F - z;
}
done:
if( sign < 0 )
z = -z;
return( z );
}
float acosf( float x )
{
if( x < -1.0 )
goto domerr;
if( x < -0.5)
return( PIF - 2.0 * asinf( sqrtf(0.5*(1.0+x)) ) );
if( x > 1.0 )
{
domerr: mtherr( "acosf", DOMAIN );
return( 0.0 );
}
if( x > 0.5 )
return( 2.0 * asinf( sqrtf(0.5*(1.0-x) ) ) );
return( PIO2F - asinf(x) );
}
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