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/* @(#)w_jn.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 jn(int n, double x), yn(int n, double x)

 * floating point Bessel's function of the 1st and 2nd kind

 * of order n

 *

 * Special cases:

 *      y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;

 *      y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.

 * Note 2. About jn(n,x), yn(n,x)

 *      For n=0, j0(x) is called,

 *      for n=1, j1(x) is called,

 *      for n<x, forward recursion us used starting

 *      from values of j0(x) and j1(x).

 *      for n>x, a continued fraction approximation to

 *      j(n,x)/j(n-1,x) is evaluated and then backward

 *      recursion is used starting from a supposed value

 *      for j(n,x). The resulting value of j(0,x) is

 *      compared with the actual value to correct the

 *      supposed value of j(n,x).

 *

 *      yn(n,x) is similar in all respects, except

 *      that forward recursion is used for all

 *      values of n>1.

 *

 */

#include "fdlibm.h"

#include <errno.h>

#ifndef _DOUBLE_IS_32BITS

#ifdef __STDC__

        double jn(int n, double x)      /* wrapper jn */

#else

        double jn(n,x)                  /* wrapper jn */

        double x; int n;

#endif

{

#ifdef _IEEE_LIBM

        return jn(n,x);

#else

        double z;

        struct exception exc;

        z = jn(n,x);

        if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;

        if(fabs(x)>X_TLOSS) {

            /* jn(|x|>X_TLOSS) */

            exc.type = TLOSS;

            exc.name = "jn";

            exc.err = 0;

            exc.arg1 = n;

            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 yn(int n, double x)      /* wrapper yn */

#else

        double yn(n,x)                  /* wrapper yn */

        double x; int n;

#endif

{

#ifdef _IEEE_LIBM

        return yn(n,x);

#else

        double z;

        struct exception exc;

        z = yn(n,x);

        if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;

        if(x <= 0.0){

            /* yn(n,0) = -inf or yn(x<0) = NaN */

#ifndef HUGE_VAL 

#define HUGE_VAL inf

            double inf = 0.0;

            SET_HIGH_WORD(inf,0x7ff00000);      /* set inf to infinite */

#endif

            exc.type = DOMAIN;  /* should be SING for IEEE */

            exc.name = "yn";

            exc.err = 0;

            exc.arg1 = n;

            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) {

            /* yn(x>X_TLOSS) */

            exc.type = TLOSS;

            exc.name = "yn";

            exc.err = 0;

            exc.arg1 = n;

            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) */