newlib-cygwin/newlib/libm/mathfp/w_jn.c

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2000-02-18 03:39:52 +08:00
/* @(#)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
2005-10-28 Bob Wilson <bob.wilson@acm.org> * libc/misc/unctrl.c: Replace FUNCTION description. * libc/signal/signal.c: Remove documentation for raise and _raise_r. * libc/stdio/getdelim.c: Fix spelling errors. * libc/stdio/getw.c: Put RETURNS on a separate line. Fix punctuation. * libc/stdio/putw.c: Likewise. * libc/stdlib/a64l.c: Fix formatting, spelling and punctuation in documentation. * libc/stdlib/assert.c: Do not capitalize FUNCTION description. * libc/stdlib/efgcvt.c: Add spaces to FUNCTION description. * libc/stdlib/envlock.c: Use em-dash in FUNCTION description. * libc/stdlib/mlock.c: Likewise. * libc/stdlib/mstats.c: Likewise. * libc/time/tzlock.c: Likewise. * libc/stdlib/rand.c: Use "multi-threaded" and "thread-safe" in NOTES. * libc/stdlib/rand48.c: Remove extra space in FUNCTION description and hyphenate "pseudo-random". * libc/string/bcmp.c: Remove extra blank lines in documentation. * libc/string/strncat.c: Likewise. * libc/string/memchr.c: Remove extra ">" character in documentation. * libc/string/strcspn.c: Use "characters" instead of "chars". * libc/string/strpbrk.c: Likewise. * libc/string/strerror_r.c: Capitalize "GNU". * libc/string/strnlen.c: Likewise. * libc/string/strtok.c: Fix formatting, spelling and punctuation in documentation. Use "multi-threaded" and "thread-safe" in NOTES. * libc/string/wcscat.c: Split PORTABILITY into two paragraphs. * libc/string/wcschr.c: Likewise. * libc/string/wcscmp.c: Likewise. * libc/string/wcscpy.c: Likewise. * libc/string/wcscspn.c: Likewise. * libc/string/wcslen.c: Likewise. * libc/string/wcsncat.c: Likewise. * libc/string/wcsncmp.c: Likewise. * libc/string/wcsncpy.c: Likewise. * libc/string/wcsnlen.c: Likewise. * libc/string/wcspbrk.c: Likewise. * libc/string/wcsrchr.c: Likewise. * libc/string/wcsspn.c: Likewise. * libc/string/wmemchr.c: Likewise. * libc/string/wmemcmp.c: Likewise. * libc/string/wmemcpy.c: Likewise. * libc/string/wmemset.c: Likewise. * libc/string/wmemmove.c: Likewise. Also fix FUNCTION description. * libc/string/wcswidth.c: Formatting and punctuation in documentation. * libc/string/wcwidth.c: Likewise. * libm/common/s_modf.c: Remove extra period from documentation. * libm/math/s_isnan.c: Fix formatting, grammar and punctuation in documentation. * libm/mathfp/s_isnan.c: Likewise. * libm/math/s_ldexp.c: Fix punctuation. * libm/mathfp/s_ldexp.c: Likewise. * libm/math/w_log.c: Likewise. * libm/mathfp/s_logarithm.c: Likewise. * libm/math/w_j0.c: Add spaces to FUNCTION description. * libm/mathfp/w_jn.c: Likewise.
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<<jN>>, <<jNf>>, <<yN>>, <<yNf>>---Bessel functions
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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
2003-10-20 Bob Wilson <bob.wilson@acm.org> * libc/locale/locale.c: Use double quotes in code. * libc/locale/locale.tex: Likewise. * libc/libc.texinfo: Hyphenate "floating-point". * libc/machine/necv70/necv70.tex: Likewise. * libc/stdio/sprintf.c: Likewise. * libc/stdio/sscanf.c: Likewise. * libc/stdlib/atof.c: Likewise. * libc/stdlib/ldtoa.c: Fix comment typo. * libc/stdlib/div.c: Use @ifnottex instead of @ifinfo. * libc/stdlib/ldiv.c: Likewise. * libm/common/s_expm1.c: Likewise. * libm/common/s_ilogb.c: Hyphenate "floating-point". Use "nonzero". * libm/common/s_infinity: Hyphenate "double- and single-precision". * libm/common/s_nan.c: Likewise. Also correct the FUNCTION summary. * libm/common/s_nextafter.c: Fix typo. Hyphenate "double-precision" and "floating-point". * libm/common/s_scalbn.c: Correct the FUNCTION summary. * libm/math/e_pow.c: Fix comment typo. * libm/math/math.tex: Hyphenate "single-precision" and "floating-point". * libm/math/s_asinh.c: Use @ifnottex instead of @ifinfo. * libm/math/s_atan.c: Likewise. * libm/math/s_frexp.c: Likewise. Also use "nonzero". * libm/math/s_isnan.c: Hyphenate "single-precision" and "floating-point". Use "nonzero". * libm/math/s_ldexp.c: Use @ifnottex instead of @ifinfo. * libm/math/w_acos.c: Likewise. * libm/math/w_acosh.c: Likewise. * libm/math/w_asin.c: Likewise. * libm/math/w_atan2.c: Likewise. * libm/math/w_atanh.c: Likewise. * libm/math/w_cosh.c: Likewise. * libm/math/w_exp.c: Likewise. * libm/math/w_exp2.c: Likewise. Add missing @end and missing @tex version of 2^x in the description. * libm/math/w_fmod.c: Use @ifnottex instead of @ifinfo. * libm/math/w_gamma.c: Likewise. * libm/math/w_hypot.c: Likewise. * libm/math/w_j0.c: Likewise. * libm/math/w_sinh.c: Likewise. * libm/math/w_pow.c: Replace "exp1.0nt" with "exponent". * libm/mathfp/mathfp.tex: Hyphenate "single-precision" and "floating-point". * libm/mathfp/e_acosh.c: Use @ifnottex instead of @ifinfo. * libm/mathfp/e_atanh.c: Likewise. * libm/mathfp/e_hypot.c: Likewise. * libm/mathfp/er_lgamma.c: Likewise. * libm/mathfp/s_acos.c: Likewise. * libm/mathfp/s_asine.c: Likewise. * libm/mathfp/s_asinh.c: Likewise. * libm/mathfp/s_atan.c: Likewise. * libm/mathfp/s_atan2.c: Likewise. * libm/mathfp/s_atangent.c: Likewise. * libm/mathfp/s_cosh.c: Likewise. * libm/mathfp/s_exp.c: Likewise. * libm/mathfp/s_fmod.c: Likewise. * libm/mathfp/s_frexp.c: Likewise. Also use "nonzero". * libm/mathfp/s_isnan.c: Hyphenate "single-precision" and "floating-point". Use "nonzero". * libm/math/s_pow.c: Replace "exp1.0nt" with "exponent". * libm/mathfp/s_ldexp.c: Use @ifnottex instead of @ifinfo. * libm/mathfp/s_sineh.c: Likewise. * libm/mathfp/w_jn.c: Likewise.
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@ifnottex
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. 2 2 2
. x y'' + xy' + (x - p )y = 0
2003-10-20 Bob Wilson <bob.wilson@acm.org> * libc/locale/locale.c: Use double quotes in code. * libc/locale/locale.tex: Likewise. * libc/libc.texinfo: Hyphenate "floating-point". * libc/machine/necv70/necv70.tex: Likewise. * libc/stdio/sprintf.c: Likewise. * libc/stdio/sscanf.c: Likewise. * libc/stdlib/atof.c: Likewise. * libc/stdlib/ldtoa.c: Fix comment typo. * libc/stdlib/div.c: Use @ifnottex instead of @ifinfo. * libc/stdlib/ldiv.c: Likewise. * libm/common/s_expm1.c: Likewise. * libm/common/s_ilogb.c: Hyphenate "floating-point". Use "nonzero". * libm/common/s_infinity: Hyphenate "double- and single-precision". * libm/common/s_nan.c: Likewise. Also correct the FUNCTION summary. * libm/common/s_nextafter.c: Fix typo. Hyphenate "double-precision" and "floating-point". * libm/common/s_scalbn.c: Correct the FUNCTION summary. * libm/math/e_pow.c: Fix comment typo. * libm/math/math.tex: Hyphenate "single-precision" and "floating-point". * libm/math/s_asinh.c: Use @ifnottex instead of @ifinfo. * libm/math/s_atan.c: Likewise. * libm/math/s_frexp.c: Likewise. Also use "nonzero". * libm/math/s_isnan.c: Hyphenate "single-precision" and "floating-point". Use "nonzero". * libm/math/s_ldexp.c: Use @ifnottex instead of @ifinfo. * libm/math/w_acos.c: Likewise. * libm/math/w_acosh.c: Likewise. * libm/math/w_asin.c: Likewise. * libm/math/w_atan2.c: Likewise. * libm/math/w_atanh.c: Likewise. * libm/math/w_cosh.c: Likewise. * libm/math/w_exp.c: Likewise. * libm/math/w_exp2.c: Likewise. Add missing @end and missing @tex version of 2^x in the description. * libm/math/w_fmod.c: Use @ifnottex instead of @ifinfo. * libm/math/w_gamma.c: Likewise. * libm/math/w_hypot.c: Likewise. * libm/math/w_j0.c: Likewise. * libm/math/w_sinh.c: Likewise. * libm/math/w_pow.c: Replace "exp1.0nt" with "exponent". * libm/mathfp/mathfp.tex: Hyphenate "single-precision" and "floating-point". * libm/mathfp/e_acosh.c: Use @ifnottex instead of @ifinfo. * libm/mathfp/e_atanh.c: Likewise. * libm/mathfp/e_hypot.c: Likewise. * libm/mathfp/er_lgamma.c: Likewise. * libm/mathfp/s_acos.c: Likewise. * libm/mathfp/s_asine.c: Likewise. * libm/mathfp/s_asinh.c: Likewise. * libm/mathfp/s_atan.c: Likewise. * libm/mathfp/s_atan2.c: Likewise. * libm/mathfp/s_atangent.c: Likewise. * libm/mathfp/s_cosh.c: Likewise. * libm/mathfp/s_exp.c: Likewise. * libm/mathfp/s_fmod.c: Likewise. * libm/mathfp/s_frexp.c: Likewise. Also use "nonzero". * libm/mathfp/s_isnan.c: Hyphenate "single-precision" and "floating-point". Use "nonzero". * libm/math/s_pow.c: Replace "exp1.0nt" with "exponent". * libm/mathfp/s_ldexp.c: Use @ifnottex instead of @ifinfo. * libm/mathfp/s_sineh.c: Likewise. * libm/mathfp/w_jn.c: Likewise.
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@end ifnottex
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@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) */