|
|
/* @(#)w_jn.c 5.1 93/09/24 */
|
/* @(#)w_jn.c 5.1 93/09/24 */
|
/*
|
/*
|
* ====================================================
|
* ====================================================
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
*
|
*
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
* Permission to use, copy, modify, and distribute this
|
* Permission to use, copy, modify, and distribute this
|
* software is freely granted, provided that this notice
|
* software is freely granted, provided that this notice
|
* is preserved.
|
* is preserved.
|
* ====================================================
|
* ====================================================
|
*/
|
*/
|
|
|
/*
|
/*
|
FUNCTION
|
FUNCTION
|
<<jN>>, <<jNf>>, <<yN>>, <<yNf>>---Bessel functions
|
<<jN>>, <<jNf>>, <<yN>>, <<yNf>>---Bessel functions
|
|
|
INDEX
|
INDEX
|
j0
|
j0
|
INDEX
|
INDEX
|
j0f
|
j0f
|
INDEX
|
INDEX
|
j1
|
j1
|
INDEX
|
INDEX
|
j1f
|
j1f
|
INDEX
|
INDEX
|
jn
|
jn
|
INDEX
|
INDEX
|
jnf
|
jnf
|
INDEX
|
INDEX
|
y0
|
y0
|
INDEX
|
INDEX
|
y0f
|
y0f
|
INDEX
|
INDEX
|
y1
|
y1
|
INDEX
|
INDEX
|
y1f
|
y1f
|
INDEX
|
INDEX
|
yn
|
yn
|
INDEX
|
INDEX
|
ynf
|
ynf
|
|
|
ANSI_SYNOPSIS
|
ANSI_SYNOPSIS
|
#include <math.h>
|
#include <math.h>
|
double j0(double <[x]>);
|
double j0(double <[x]>);
|
float j0f(float <[x]>);
|
float j0f(float <[x]>);
|
double j1(double <[x]>);
|
double j1(double <[x]>);
|
float j1f(float <[x]>);
|
float j1f(float <[x]>);
|
double jn(int <[n]>, double <[x]>);
|
double jn(int <[n]>, double <[x]>);
|
float jnf(int <[n]>, float <[x]>);
|
float jnf(int <[n]>, float <[x]>);
|
double y0(double <[x]>);
|
double y0(double <[x]>);
|
float y0f(float <[x]>);
|
float y0f(float <[x]>);
|
double y1(double <[x]>);
|
double y1(double <[x]>);
|
float y1f(float <[x]>);
|
float y1f(float <[x]>);
|
double yn(int <[n]>, double <[x]>);
|
double yn(int <[n]>, double <[x]>);
|
float ynf(int <[n]>, float <[x]>);
|
float ynf(int <[n]>, float <[x]>);
|
|
|
TRAD_SYNOPSIS
|
TRAD_SYNOPSIS
|
#include <math.h>
|
#include <math.h>
|
|
|
double j0(<[x]>)
|
double j0(<[x]>)
|
double <[x]>;
|
double <[x]>;
|
float j0f(<[x]>)
|
float j0f(<[x]>)
|
float <[x]>;
|
float <[x]>;
|
double j1(<[x]>)
|
double j1(<[x]>)
|
double <[x]>;
|
double <[x]>;
|
float j1f(<[x]>)
|
float j1f(<[x]>)
|
float <[x]>;
|
float <[x]>;
|
double jn(<[n]>, <[x]>)
|
double jn(<[n]>, <[x]>)
|
int <[n]>;
|
int <[n]>;
|
double <[x]>;
|
double <[x]>;
|
float jnf(<[n]>, <[x]>)
|
float jnf(<[n]>, <[x]>)
|
int <[n]>;
|
int <[n]>;
|
float <[x]>;
|
float <[x]>;
|
|
|
double y0(<[x]>)
|
double y0(<[x]>)
|
double <[x]>;
|
double <[x]>;
|
float y0f(<[x]>)
|
float y0f(<[x]>)
|
float <[x]>;
|
float <[x]>;
|
double y1(<[x]>)
|
double y1(<[x]>)
|
double <[x]>;
|
double <[x]>;
|
float y1f(<[x]>)
|
float y1f(<[x]>)
|
float <[x]>;
|
float <[x]>;
|
double yn(<[n]>, <[x]>)
|
double yn(<[n]>, <[x]>)
|
int <[n]>;
|
int <[n]>;
|
double <[x]>;
|
double <[x]>;
|
float ynf(<[n]>, <[x]>)
|
float ynf(<[n]>, <[x]>)
|
int <[n]>;
|
int <[n]>;
|
float <[x]>;
|
float <[x]>;
|
|
|
DESCRIPTION
|
DESCRIPTION
|
The Bessel functions are a family of functions that solve the
|
The Bessel functions are a family of functions that solve the
|
differential equation
|
differential equation
|
@ifnottex
|
@ifnottex
|
. 2 2 2
|
. 2 2 2
|
. x y'' + xy' + (x - p )y = 0
|
. x y'' + xy' + (x - p )y = 0
|
@end ifnottex
|
@end ifnottex
|
@tex
|
@tex
|
$$x^2{d^2y\over dx^2} + x{dy\over dx} + (x^2-p^2)y = 0$$
|
$$x^2{d^2y\over dx^2} + x{dy\over dx} + (x^2-p^2)y = 0$$
|
@end tex
|
@end tex
|
These functions have many applications in engineering and physics.
|
These functions have many applications in engineering and physics.
|
|
|
<<jn>> calculates the Bessel function of the first kind of order
|
<<jn>> calculates the Bessel function of the first kind of order
|
<[n]>. <<j0>> and <<j1>> are special cases for order 0 and order
|
<[n]>. <<j0>> and <<j1>> are special cases for order 0 and order
|
1 respectively.
|
1 respectively.
|
|
|
Similarly, <<yn>> calculates the Bessel function of the second kind of
|
Similarly, <<yn>> calculates the Bessel function of the second kind of
|
order <[n]>, and <<y0>> and <<y1>> are special cases for order 0 and
|
order <[n]>, and <<y0>> and <<y1>> are special cases for order 0 and
|
1.
|
1.
|
|
|
<<jnf>>, <<j0f>>, <<j1f>>, <<ynf>>, <<y0f>>, and <<y1f>> perform the
|
<<jnf>>, <<j0f>>, <<j1f>>, <<ynf>>, <<y0f>>, and <<y1f>> perform the
|
same calculations, but on <<float>> rather than <<double>> values.
|
same calculations, but on <<float>> rather than <<double>> values.
|
|
|
RETURNS
|
RETURNS
|
The value of each Bessel function at <[x]> is returned.
|
The value of each Bessel function at <[x]> is returned.
|
|
|
PORTABILITY
|
PORTABILITY
|
None of the Bessel functions are in ANSI C.
|
None of the Bessel functions are in ANSI C.
|
*/
|
*/
|
|
|
/*
|
/*
|
* wrapper jn(int n, double x), yn(int n, double x)
|
* wrapper jn(int n, double x), yn(int n, double x)
|
* floating point Bessel's function of the 1st and 2nd kind
|
* floating point Bessel's function of the 1st and 2nd kind
|
* of order n
|
* of order n
|
*
|
*
|
* Special cases:
|
* Special cases:
|
* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
|
* 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.
|
* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
|
* Note 2. About jn(n,x), yn(n,x)
|
* Note 2. About jn(n,x), yn(n,x)
|
* For n=0, j0(x) is called,
|
* For n=0, j0(x) is called,
|
* for n=1, j1(x) is called,
|
* for n=1, j1(x) is called,
|
* for n<x, forward recursion us used starting
|
* for n<x, forward recursion us used starting
|
* from values of j0(x) and j1(x).
|
* from values of j0(x) and j1(x).
|
* for n>x, a continued fraction approximation to
|
* for n>x, a continued fraction approximation to
|
* j(n,x)/j(n-1,x) is evaluated and then backward
|
* j(n,x)/j(n-1,x) is evaluated and then backward
|
* recursion is used starting from a supposed value
|
* recursion is used starting from a supposed value
|
* for j(n,x). The resulting value of j(0,x) is
|
* for j(n,x). The resulting value of j(0,x) is
|
* compared with the actual value to correct the
|
* compared with the actual value to correct the
|
* supposed value of j(n,x).
|
* supposed value of j(n,x).
|
*
|
*
|
* yn(n,x) is similar in all respects, except
|
* yn(n,x) is similar in all respects, except
|
* that forward recursion is used for all
|
* that forward recursion is used for all
|
* values of n>1.
|
* values of n>1.
|
*
|
*
|
*/
|
*/
|
|
|
#include "fdlibm.h"
|
#include "fdlibm.h"
|
#include <errno.h>
|
#include <errno.h>
|
|
|
#ifndef _DOUBLE_IS_32BITS
|
#ifndef _DOUBLE_IS_32BITS
|
|
|
#ifdef __STDC__
|
#ifdef __STDC__
|
double jn(int n, double x) /* wrapper jn */
|
double jn(int n, double x) /* wrapper jn */
|
#else
|
#else
|
double jn(n,x) /* wrapper jn */
|
double jn(n,x) /* wrapper jn */
|
double x; int n;
|
double x; int n;
|
#endif
|
#endif
|
{
|
{
|
#ifdef _IEEE_LIBM
|
#ifdef _IEEE_LIBM
|
return jn(n,x);
|
return jn(n,x);
|
#else
|
#else
|
double z;
|
double z;
|
struct exception exc;
|
struct exception exc;
|
z = jn(n,x);
|
z = jn(n,x);
|
if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
|
if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
|
if(fabs(x)>X_TLOSS) {
|
if(fabs(x)>X_TLOSS) {
|
/* jn(|x|>X_TLOSS) */
|
/* jn(|x|>X_TLOSS) */
|
exc.type = TLOSS;
|
exc.type = TLOSS;
|
exc.name = "jn";
|
exc.name = "jn";
|
exc.err = 0;
|
exc.err = 0;
|
exc.arg1 = n;
|
exc.arg1 = n;
|
exc.arg2 = x;
|
exc.arg2 = x;
|
exc.retval = 0.0;
|
exc.retval = 0.0;
|
if (_LIB_VERSION == _POSIX_)
|
if (_LIB_VERSION == _POSIX_)
|
errno = ERANGE;
|
errno = ERANGE;
|
else if (!matherr(&exc)) {
|
else if (!matherr(&exc)) {
|
errno = ERANGE;
|
errno = ERANGE;
|
}
|
}
|
if (exc.err != 0)
|
if (exc.err != 0)
|
errno = exc.err;
|
errno = exc.err;
|
return exc.retval;
|
return exc.retval;
|
} else
|
} else
|
return z;
|
return z;
|
#endif
|
#endif
|
}
|
}
|
|
|
#ifdef __STDC__
|
#ifdef __STDC__
|
double yn(int n, double x) /* wrapper yn */
|
double yn(int n, double x) /* wrapper yn */
|
#else
|
#else
|
double yn(n,x) /* wrapper yn */
|
double yn(n,x) /* wrapper yn */
|
double x; int n;
|
double x; int n;
|
#endif
|
#endif
|
{
|
{
|
#ifdef _IEEE_LIBM
|
#ifdef _IEEE_LIBM
|
return yn(n,x);
|
return yn(n,x);
|
#else
|
#else
|
double z;
|
double z;
|
struct exception exc;
|
struct exception exc;
|
z = yn(n,x);
|
z = yn(n,x);
|
if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
|
if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z;
|
if(x <= 0.0){
|
if(x <= 0.0){
|
/* yn(n,0) = -inf or yn(x<0) = NaN */
|
/* yn(n,0) = -inf or yn(x<0) = NaN */
|
#ifndef HUGE_VAL
|
#ifndef HUGE_VAL
|
#define HUGE_VAL inf
|
#define HUGE_VAL inf
|
double inf = 0.0;
|
double inf = 0.0;
|
|
|
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
|
SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */
|
#endif
|
#endif
|
exc.type = DOMAIN; /* should be SING for IEEE */
|
exc.type = DOMAIN; /* should be SING for IEEE */
|
exc.name = "yn";
|
exc.name = "yn";
|
exc.err = 0;
|
exc.err = 0;
|
exc.arg1 = n;
|
exc.arg1 = n;
|
exc.arg2 = x;
|
exc.arg2 = x;
|
if (_LIB_VERSION == _SVID_)
|
if (_LIB_VERSION == _SVID_)
|
exc.retval = -HUGE;
|
exc.retval = -HUGE;
|
else
|
else
|
exc.retval = -HUGE_VAL;
|
exc.retval = -HUGE_VAL;
|
if (_LIB_VERSION == _POSIX_)
|
if (_LIB_VERSION == _POSIX_)
|
errno = EDOM;
|
errno = EDOM;
|
else if (!matherr(&exc)) {
|
else if (!matherr(&exc)) {
|
errno = EDOM;
|
errno = EDOM;
|
}
|
}
|
if (exc.err != 0)
|
if (exc.err != 0)
|
errno = exc.err;
|
errno = exc.err;
|
return exc.retval;
|
return exc.retval;
|
}
|
}
|
if(x>X_TLOSS) {
|
if(x>X_TLOSS) {
|
/* yn(x>X_TLOSS) */
|
/* yn(x>X_TLOSS) */
|
exc.type = TLOSS;
|
exc.type = TLOSS;
|
exc.name = "yn";
|
exc.name = "yn";
|
exc.err = 0;
|
exc.err = 0;
|
exc.arg1 = n;
|
exc.arg1 = n;
|
exc.arg2 = x;
|
exc.arg2 = x;
|
exc.retval = 0.0;
|
exc.retval = 0.0;
|
if (_LIB_VERSION == _POSIX_)
|
if (_LIB_VERSION == _POSIX_)
|
errno = ERANGE;
|
errno = ERANGE;
|
else if (!matherr(&exc)) {
|
else if (!matherr(&exc)) {
|
errno = ERANGE;
|
errno = ERANGE;
|
}
|
}
|
if (exc.err != 0)
|
if (exc.err != 0)
|
errno = exc.err;
|
errno = exc.err;
|
return exc.retval;
|
return exc.retval;
|
} else
|
} else
|
return z;
|
return z;
|
#endif
|
#endif
|
}
|
}
|
|
|
#endif /* defined(_DOUBLE_IS_32BITS) */
|
#endif /* defined(_DOUBLE_IS_32BITS) */
|
|
|
