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/* @(#)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
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 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
double z = __ieee754_j0(x);
if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
if(fabs(x)>X_TLOSS) {
/* j0(|x|>X_TLOSS) */
errno = ERANGE;
return 0.0;
} 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;
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 */
errno = EDOM;
return -HUGE_VAL;
}
if(x>X_TLOSS) {
/* y0(x>X_TLOSS) */
errno = ERANGE;
return 0.0;
} else
return z;
#endif
}
#endif /* defined(_DOUBLE_IS_32BITS) */
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