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