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/* @(#)z_asine.c 1.0 98/08/13 */
/******************************************************************
* The following routines are coded directly from the algorithms
* and coefficients given in "Software Manual for the Elementary
* Functions" by William J. Cody, Jr. and William Waite, Prentice
* Hall, 1980.
******************************************************************/
/*
FUNCTION
<<asin>>, <<asinf>>, <<acos>>, <<acosf>>, <<asine>>, <<asinef>>---arc sine or cosine
INDEX
asin
INDEX
asinf
INDEX
acos
INDEX
acosf
INDEX
asine
INDEX
asinef
ANSI_SYNOPSIS
#include <math.h>
double asine(double <[x]>);
float asinef(float <[x]>);
double asin(double <[x]>);
float asinf(float <[x]>);
double acos(double <[x]>);
float acosf(float <[x]>);
TRAD_SYNOPSIS
#include <math.h>
double asine(<[x]>);
double <[x]>;
float asinef(<[x]>);
float <[x]>;
double asin(<[x]>)
double <[x]>;
float asinf(<[x]>)
float <[x]>;
double acos(<[x]>)
double <[x]>;
float acosf(<[x]>)
float <[x]>;
DESCRIPTION
<<asin>> computes the inverse sine or cosine of the argument <[x]>.
Arguments to <<asin>> and <<acos>> must be in the range @minus{}1 to 1.
<<asinf>> and <<acosf>> are identical to <<asin>> and <<acos>>, other
than taking and returning floats.
RETURNS
@ifnottex
<<asin>> and <<acos>> return values in radians, in the range of -pi/2 to pi/2.
@end ifnottex
@tex
<<asin>> and <<acos>> return values in radians, in the range of $-\pi/2$ to $\pi/2$.
@end tex
If <[x]> is not in the range @minus{}1 to 1, <<asin>> and <<asinf>>
return NaN (not a number), set the global variable <<errno>> to
<<EDOM>>, and issue a <<DOMAIN error>> message.
*/
/******************************************************************
* Arcsine
*
* Input:
* x - floating point value
* acosine - indicates acos calculation
*
* Output:
* Arcsine of x.
*
* Description:
* This routine calculates arcsine / arccosine.
*
*****************************************************************/
#include "fdlibm.h"
#include "zmath.h"
#ifndef _DOUBLE_IS_32BITS
static const double p[] = { -0.27368494524164255994e+2,
0.57208227877891731407e+2,
-0.39688862997404877339e+2,
0.10152522233806463645e+2,
-0.69674573447350646411 };
static const double q[] = { -0.16421096714498560795e+3,
0.41714430248260412556e+3,
-0.38186303361750149284e+3,
0.15095270841030604719e+3,
-0.23823859153670238830e+2 };
static const double a[] = { 0.0, 0.78539816339744830962 };
static const double b[] = { 1.57079632679489661923, 0.78539816339744830962 };
double
_DEFUN (asine, (double, int),
double x _AND
int acosine)
{
int flag, i;
int branch = 0;
double g, res, R, P, Q, y;
/* Check for special values. */
i = numtest (x);
if (i == NAN || i == INF)
{
errno = EDOM;
if (i == NAN)
return (x);
else
return (z_infinity.d);
}
y = fabs (x);
flag = acosine;
if (y > 0.5)
{
i = 1 - flag;
/* Check for range error. */
if (y > 1.0)
{
errno = ERANGE;
return (z_notanum.d);
}
g = (1 - y) / 2.0;
y = -2 * sqrt (g);
branch = 1;
}
else
{
i = flag;
if (y < z_rooteps)
res = y;
else
g = y * y;
}
if (y >= z_rooteps || branch == 1)
{
/* Calculate the Taylor series. */
P = ((((p[4] * g + p[3]) * g + p[2]) * g + p[1]) * g + p[0]) * g;
Q = ((((g + q[4]) * g + q[3]) * g + q[2]) * g + q[1]) * g + q[0];
R = P / Q;
res = y + y * R;
}
/* Calculate asine or acose. */
if (flag == 0)
{
res = (a[i] + res) + a[i];
if (x < 0.0)
res = -res;
}
else
{
if (x < 0.0)
res = (b[i] + res) + b[i];
else
res = (a[i] - res) + a[i];
}
return (res);
}
#endif /* _DOUBLE_IS_32BITS */
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