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