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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
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]>);
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) */
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