newlib/newlib/libm/math/w_j0.c

/* @(#)w_j0.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/*
FUNCTION
<<jN>>, <<jNf>>, <<yN>>, <<yNf>>---Bessel functions 

INDEX
j0
INDEX
j0f
INDEX
j1
INDEX
j1f
INDEX
jn
INDEX
jnf
INDEX
y0
INDEX
y0f
INDEX
y1
INDEX
y1f
INDEX
yn
INDEX
ynf

ANSI_SYNOPSIS
#include <math.h>
double j0(double <[x]>);
float j0f(float <[x]>);
double j1(double <[x]>);
float j1f(float <[x]>);
double jn(int <[n]>, double <[x]>);
float jnf(int <[n]>, float <[x]>);
double y0(double <[x]>);
float y0f(float <[x]>);
double y1(double <[x]>);
float y1f(float <[x]>);
double yn(int <[n]>, double <[x]>);
float ynf(int <[n]>, float <[x]>);

TRAD_SYNOPSIS
#include <math.h>

double j0(<[x]>)
double <[x]>;
float j0f(<[x]>)
float <[x]>;
double j1(<[x]>)
double <[x]>;
float j1f(<[x]>)
float <[x]>;
double jn(<[n]>, <[x]>)
int <[n]>;
double <[x]>;
float jnf(<[n]>, <[x]>)
int <[n]>;
float <[x]>;

double y0(<[x]>)
double <[x]>;
float y0f(<[x]>)
float <[x]>;
double y1(<[x]>)
double <[x]>;
float y1f(<[x]>)
float <[x]>;
double yn(<[n]>, <[x]>)
int <[n]>;
double <[x]>;
float ynf(<[n]>, <[x]>)
int <[n]>;
float <[x]>;

DESCRIPTION
The Bessel functions are a family of functions that solve the
differential equation 
@ifnottex
.  2               2    2
. x  y'' + xy' + (x  - p )y  = 0
@end ifnottex
@tex
$$x^2{d^2y\over dx^2} + x{dy\over dx} + (x^2-p^2)y = 0$$
@end tex
These functions have many applications in engineering and physics.

<<jn>> calculates the Bessel function of the first kind of order
<[n]>.  <<j0>> and <<j1>> are special cases for order 0 and order
1 respectively.

Similarly, <<yn>> calculates the Bessel function of the second kind of
order <[n]>, and <<y0>> and <<y1>> are special cases for order 0 and
1.

<<jnf>>, <<j0f>>, <<j1f>>, <<ynf>>, <<y0f>>, and <<y1f>> perform the
same calculations, but on <<float>> rather than <<double>> values.

RETURNS
The value of each Bessel function at <[x]> is returned.

PORTABILITY
None of the Bessel functions are in ANSI C.
*/

/*
 * wrapper j0(double x), y0(double x)
 */

#include "fdlibm.h"
#include <errno.h>

#ifndef _DOUBLE_IS_32BITS

#ifdef __STDC__
	double j0(double x)		/* wrapper j0 */
#else
	double j0(x)			/* wrapper j0 */
	double x;
#endif
{
#ifdef _IEEE_LIBM
	return __ieee754_j0(x);
#else
	struct exception exc;
	double z = __ieee754_j0(x);
	if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
	if(fabs(x)>X_TLOSS) {
	    /* j0(|x|>X_TLOSS) */
            exc.type = TLOSS;
            exc.name = "j0";
	    exc.err = 0;
	    exc.arg1 = exc.arg2 = x;
            exc.retval = 0.0;
            if (_LIB_VERSION == _POSIX_)
               errno = ERANGE;
            else if (!matherr(&exc)) {
               errno = ERANGE;
            }        
	    if (exc.err != 0)
	       errno = exc.err;
            return exc.retval; 
	} else
	    return z;
#endif
}

#ifdef __STDC__
	double y0(double x)		/* wrapper y0 */
#else
	double y0(x)			/* wrapper y0 */
	double x;
#endif
{
#ifdef _IEEE_LIBM
	return __ieee754_y0(x);
#else
	double z;
	struct exception exc;
	z = __ieee754_y0(x);
	if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
        if(x <= 0.0){
#ifndef HUGE_VAL 
#define HUGE_VAL inf
	    double inf = 0.0;

	    SET_HIGH_WORD(inf,0x7ff00000);	/* set inf to infinite */
#endif
	    /* y0(0) = -inf or y0(x<0) = NaN */
	    exc.type = DOMAIN;	/* should be SING for IEEE y0(0) */
	    exc.name = "y0";
	    exc.err = 0;
	    exc.arg1 = exc.arg2 = x;
	    if (_LIB_VERSION == _SVID_)
	       exc.retval = -HUGE;
	    else
	       exc.retval = -HUGE_VAL;
	    if (_LIB_VERSION == _POSIX_)
	       errno = EDOM;
	    else if (!matherr(&exc)) {
	       errno = EDOM;
	    }
	    if (exc.err != 0)
	       errno = exc.err;
            return exc.retval; 
        }
	if(x>X_TLOSS) {
	    /* y0(x>X_TLOSS) */
            exc.type = TLOSS;
            exc.name = "y0";
	    exc.err = 0;
	    exc.arg1 = exc.arg2 = x;
            exc.retval = 0.0;
            if (_LIB_VERSION == _POSIX_)
               errno = ERANGE;
            else if (!matherr(&exc)) {
               errno = ERANGE;
            }        
	    if (exc.err != 0)
	       errno = exc.err;
	    return exc.retval; 
	} else
	    return z;
#endif
}

#endif /* defined(_DOUBLE_IS_32BITS) */