mirror of https://github.com/mkerrisk/man-pages
236 lines
5.6 KiB
Groff
236 lines
5.6 KiB
Groff
.\" Copyright 1993 David Metcalfe (david@prism.demon.co.uk)
|
|
.\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
|
|
.\" <mtk.manpages@gmail.com>
|
|
.\"
|
|
.\" Permission is granted to make and distribute verbatim copies of this
|
|
.\" manual provided the copyright notice and this permission notice are
|
|
.\" preserved on all copies.
|
|
.\"
|
|
.\" Permission is granted to copy and distribute modified versions of this
|
|
.\" manual under the conditions for verbatim copying, provided that the
|
|
.\" entire resulting derived work is distributed under the terms of a
|
|
.\" permission notice identical to this one.
|
|
.\"
|
|
.\" Since the Linux kernel and libraries are constantly changing, this
|
|
.\" manual page may be incorrect or out-of-date. The author(s) assume no
|
|
.\" responsibility for errors or omissions, or for damages resulting from
|
|
.\" the use of the information contained herein. The author(s) may not
|
|
.\" have taken the same level of care in the production of this manual,
|
|
.\" which is licensed free of charge, as they might when working
|
|
.\" professionally.
|
|
.\"
|
|
.\" Formatted or processed versions of this manual, if unaccompanied by
|
|
.\" the source, must acknowledge the copyright and authors of this work.
|
|
.\"
|
|
.\" References consulted:
|
|
.\" Linux libc source code
|
|
.\" Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)
|
|
.\" 386BSD man pages
|
|
.\" Modified Sat Jul 24 19:08:17 1993 by Rik Faith (faith@cs.unc.edu)
|
|
.\" Modified 2002-08-25, aeb
|
|
.\" Modified 2004-11-12 as per suggestion by Fabian Kreutz/AEB
|
|
.\" 2008-07-24, mtk, created this page, based on material from j0.3.
|
|
.\"
|
|
.TH Y0 3 2008-08-10 "" "Linux Programmer's Manual"
|
|
.SH NAME
|
|
y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl \-
|
|
Bessel functions of the second kind
|
|
.SH SYNOPSIS
|
|
.nf
|
|
.B #include <math.h>
|
|
.sp
|
|
.BI "double y0(double " x );
|
|
.br
|
|
.BI "double y1(double " x );
|
|
.br
|
|
.BI "double yn(int " n ", double " x );
|
|
.sp
|
|
.BI "float y0f(float " x );
|
|
.br
|
|
.BI "float y1f(float " x );
|
|
.br
|
|
.BI "float ynf(int " n ", float " x );
|
|
.sp
|
|
.BI "long double y0l(long double " x );
|
|
.br
|
|
.BI "long double y1l(long double " x );
|
|
.br
|
|
.BI "long double ynl(int " n ", long double " x );
|
|
.fi
|
|
.sp
|
|
Link with \fI\-lm\fP.
|
|
.sp
|
|
.in -4n
|
|
Feature Test Macro Requirements for glibc (see
|
|
.BR feature_test_macros (7)):
|
|
.in
|
|
.sp
|
|
.ad l
|
|
.BR y0 (),
|
|
.BR y1 (),
|
|
.BR yn ():
|
|
_SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE
|
|
.br
|
|
.BR y0f (),
|
|
.BR y0l (),
|
|
.BR y1f (),
|
|
.BR y1l (),
|
|
.BR ynf (),
|
|
.BR ynl ():
|
|
_SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE\ >=\ 600
|
|
.\" Also seems to work: -std=c99 -D_XOPEN_SOURCE
|
|
.ad b
|
|
.SH DESCRIPTION
|
|
.PP
|
|
The
|
|
.BR y0 ()
|
|
and
|
|
.BR y1 ()
|
|
functions return Bessel functions of \fIx\fP
|
|
of the second kind of orders 0 and 1, respectively.
|
|
The
|
|
.BR yn ()
|
|
function
|
|
returns the Bessel function of \fIx\fP of the second kind of order \fIn\fP.
|
|
.PP
|
|
The value of \fIx\fP must be positive.
|
|
.PP
|
|
The
|
|
.BR y0f ()
|
|
etc. and
|
|
.BR y0l ()
|
|
etc. functions are versions that take and return
|
|
.I float
|
|
and
|
|
.I "long double"
|
|
values, respectively.
|
|
.SH RETURN VALUE
|
|
On success, these functions return the appropriate
|
|
Bessel value of the second kind for
|
|
.IR x .
|
|
|
|
If
|
|
.I x
|
|
is a NaN, a NaN is returned.
|
|
|
|
If
|
|
.I x
|
|
is negative,
|
|
a domain error occurs,
|
|
and the functions return
|
|
.RB - HUGE_VAL ,
|
|
.RB - HUGE_VALF ,
|
|
or
|
|
.RB - HUGE_VALL ,
|
|
respectively.
|
|
(POSIX.1-2001 also allows a NaN return for this case.)
|
|
|
|
If
|
|
.I x
|
|
is 0.0,
|
|
a pole error occurs,
|
|
and the functions return
|
|
.RB - HUGE_VAL ,
|
|
.RB - HUGE_VALF ,
|
|
or
|
|
.RB - HUGE_VALL ,
|
|
respectively.
|
|
|
|
If the result underflows,
|
|
a range error occurs,
|
|
and the functions return 0.0
|
|
|
|
If the result overflows,
|
|
a range error occurs,
|
|
and the functions return
|
|
.RB - HUGE_VAL ,
|
|
.RB - HUGE_VALF ,
|
|
or
|
|
.RB - HUGE_VALL ,
|
|
respectively.
|
|
(POSIX.1-2001 also allows a 0.0 return for this case.)
|
|
.SH ERRORS
|
|
See
|
|
.BR math_error (7)
|
|
for information on how to determine whether an error has occurred
|
|
when calling these functions.
|
|
.PP
|
|
The following errors can occur:
|
|
.TP
|
|
Domain error: \fIx\fP is negative
|
|
.I errno
|
|
is set to
|
|
.BR EDOM .
|
|
An invalid floating-point exception
|
|
.RB ( FE_INVALID )
|
|
is raised.
|
|
.TP
|
|
Pole error: \fIx\fP is 0.0
|
|
.\" Before POSIX.1-2001 TC2, this was (inconsistently) specified
|
|
.\" as a range error.
|
|
.I errno
|
|
is set to
|
|
.\" FIXME . y0(0.0) gives EDOM
|
|
.BR ERANGE
|
|
(but see BUGS).
|
|
No
|
|
.B FE_DIVBYZERO
|
|
exception is returned by
|
|
.BR fetestexcept (3)
|
|
for this case.
|
|
.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808
|
|
.TP
|
|
Range error: result underflow
|
|
.\" e.g., y0(1e33) on glibc 2.8/x86-32
|
|
.I errno
|
|
is set to
|
|
.BR ERANGE .
|
|
.\" An underflow floating-point exception
|
|
.\" .RB ( FE_UNDERFLOW )
|
|
.\" is raised.
|
|
.\" FIXME . Is it intentional that these functions do not use FE_*?
|
|
.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6806
|
|
No
|
|
.B FE_UNDERFLOW
|
|
exception is returned by
|
|
.BR fetestexcept (3)
|
|
for this case.
|
|
.TP
|
|
Range error: result overflow
|
|
.\" e.g., yn(10, 1e-40) on glibc 2.8/x86-32
|
|
.\" .I errno
|
|
.\" is set to
|
|
.\" .BR ERANGE .
|
|
.I errno
|
|
is not set for this case.
|
|
.\" FIXME . Is it intentional that errno is not set?
|
|
.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808
|
|
An overflow floating-point exception
|
|
.RB ( FE_OVERFLOW )
|
|
is raised.
|
|
.SH "CONFORMING TO"
|
|
The functions returning
|
|
.I double
|
|
conform to SVr4, 4.3BSD,
|
|
POSIX.1-2001.
|
|
The others are nonstandard functions that also exist on the BSDs.
|
|
.SH BUGS
|
|
On a pole error, these functions set
|
|
.I errno
|
|
to
|
|
.BR EDOM ,
|
|
instead of
|
|
.BR ERANGE
|
|
as POSIX.1-2004 requires.
|
|
.\" FIXME .
|
|
.\" Bug raised: http://sourceware.org/bugzilla/show_bug.cgi?id=6807
|
|
|
|
In glibc version 2.3.2 and earlier,
|
|
.\" FIXME . Actually, 2.3.2 is the earliest test result I have; so yet
|
|
.\" to confirm if this error occurs only in 2.3.2.
|
|
these functions do not raise an invalid floating-point exception
|
|
.RB ( FE_INVALID )
|
|
when a domain error occurs.
|
|
.SH SEE ALSO
|
|
.BR j0 (3)
|