2008-08-01 05:36:10 +00:00
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.\" Copyright 1993 David Metcalfe (david@prism.demon.co.uk)
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.\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
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.\" <mtk.manpages@gmail.com>
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.\"
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.\" Permission is granted to make and distribute verbatim copies of this
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.\" manual provided the copyright notice and this permission notice are
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.\" preserved on all copies.
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.\"
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.\" Permission is granted to copy and distribute modified versions of this
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.\" manual under the conditions for verbatim copying, provided that the
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.\" entire resulting derived work is distributed under the terms of a
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.\" permission notice identical to this one.
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.\"
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.\" Since the Linux kernel and libraries are constantly changing, this
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.\" manual page may be incorrect or out-of-date. The author(s) assume no
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.\" responsibility for errors or omissions, or for damages resulting from
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.\" the use of the information contained herein. The author(s) may not
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.\" have taken the same level of care in the production of this manual,
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.\" which is licensed free of charge, as they might when working
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.\" professionally.
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.\"
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.\" Formatted or processed versions of this manual, if unaccompanied by
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.\" the source, must acknowledge the copyright and authors of this work.
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.\"
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.\" References consulted:
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.\" Linux libc source code
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.\" Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)
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.\" 386BSD man pages
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.\" Modified Sat Jul 24 19:08:17 1993 by Rik Faith (faith@cs.unc.edu)
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.\" Modified 2002-08-25, aeb
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.\" Modified 2004-11-12 as per suggestion by Fabian Kreutz/AEB
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.\" 2008-07-24, mtk, created this page, based on material from j0.3.
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.\"
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2008-08-10 19:08:31 +00:00
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.TH Y0 3 2008-08-10 "" "Linux Programmer's Manual"
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2008-08-01 05:36:10 +00:00
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.SH NAME
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y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl \-
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Bessel functions of the second kind
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.SH SYNOPSIS
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.nf
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.B #include <math.h>
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.sp
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.BI "double y0(double " x );
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.br
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.BI "double y1(double " x );
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.br
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.BI "double yn(int " n ", double " x );
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.sp
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.BI "float y0f(float " x );
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.br
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.BI "float y1f(float " x );
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.br
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.BI "float ynf(int " n ", float " x );
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.sp
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.BI "long double y0l(long double " x );
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.br
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.BI "long double y1l(long double " x );
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.br
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.BI "long double ynl(int " n ", long double " x );
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.fi
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.sp
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Link with \fI\-lm\fP.
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.sp
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.in -4n
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Feature Test Macro Requirements for glibc (see
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.BR feature_test_macros (7)):
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.in
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.sp
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.ad l
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.BR y0 (),
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.BR y1 (),
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.BR yn ():
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2010-09-19 05:45:06 +00:00
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.RS 4
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2008-08-01 05:36:10 +00:00
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_SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE
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2010-09-19 05:45:06 +00:00
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.RE
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2008-08-01 05:36:10 +00:00
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.br
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.BR y0f (),
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.BR y0l (),
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.BR y1f (),
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.BR y1l (),
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.BR ynf (),
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.BR ynl ():
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2010-09-19 05:45:06 +00:00
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.RS 4
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2008-08-01 05:36:10 +00:00
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_SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE\ >=\ 600
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.\" Also seems to work: -std=c99 -D_XOPEN_SOURCE
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2010-09-19 05:45:06 +00:00
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.RE
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2008-08-01 05:36:10 +00:00
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.ad b
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.SH DESCRIPTION
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.PP
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The
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.BR y0 ()
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and
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.BR y1 ()
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functions return Bessel functions of \fIx\fP
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of the second kind of orders 0 and 1, respectively.
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The
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.BR yn ()
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function
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returns the Bessel function of \fIx\fP of the second kind of order \fIn\fP.
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.PP
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The value of \fIx\fP must be positive.
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.PP
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The
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.BR y0f ()
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etc. and
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.BR y0l ()
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etc. functions are versions that take and return
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.I float
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and
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.I "long double"
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values, respectively.
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.SH RETURN VALUE
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On success, these functions return the appropriate
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Bessel value of the second kind for
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.IR x .
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If
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.I x
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is a NaN, a NaN is returned.
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If
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.I x
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is negative,
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2008-08-04 16:00:58 +00:00
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a domain error occurs,
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2008-08-01 05:36:10 +00:00
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and the functions return
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.RB - HUGE_VAL ,
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.RB - HUGE_VALF ,
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or
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.RB - HUGE_VALL ,
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respectively.
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(POSIX.1-2001 also allows a NaN return for this case.)
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If
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.I x
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is 0.0,
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2008-08-04 16:00:58 +00:00
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a pole error occurs,
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2008-08-01 05:36:10 +00:00
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and the functions return
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.RB - HUGE_VAL ,
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.RB - HUGE_VALF ,
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or
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.RB - HUGE_VALL ,
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respectively.
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If the result underflows,
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2008-08-04 16:00:58 +00:00
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a range error occurs,
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2008-08-01 05:36:10 +00:00
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and the functions return 0.0
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If the result overflows,
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2008-08-04 16:00:58 +00:00
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a range error occurs,
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2008-08-01 05:36:10 +00:00
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and the functions return
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.RB - HUGE_VAL ,
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.RB - HUGE_VALF ,
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or
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.RB - HUGE_VALL ,
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respectively.
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(POSIX.1-2001 also allows a 0.0 return for this case.)
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.SH ERRORS
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See
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.BR math_error (7)
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for information on how to determine whether an error has occurred
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when calling these functions.
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.PP
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The following errors can occur:
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.TP
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Domain error: \fIx\fP is negative
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.I errno
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is set to
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.BR EDOM .
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An invalid floating-point exception
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.RB ( FE_INVALID )
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is raised.
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.TP
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Pole error: \fIx\fP is 0.0
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.\" Before POSIX.1-2001 TC2, this was (inconsistently) specified
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.\" as a range error.
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.I errno
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is set to
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.\" FIXME . y0(0.0) gives EDOM
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2008-08-05 10:33:06 +00:00
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.BR ERANGE
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2008-08-01 05:36:10 +00:00
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(but see BUGS).
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No
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.B FE_DIVBYZERO
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exception is returned by
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.BR fetestexcept (3)
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for this case.
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.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808
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.TP
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Range error: result underflow
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.\" e.g., y0(1e33) on glibc 2.8/x86-32
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.I errno
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is set to
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.BR ERANGE .
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.\" An underflow floating-point exception
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.\" .RB ( FE_UNDERFLOW )
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.\" is raised.
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.\" FIXME . Is it intentional that these functions do not use FE_*?
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.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6806
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No
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.B FE_UNDERFLOW
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exception is returned by
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.BR fetestexcept (3)
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for this case.
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.TP
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Range error: result overflow
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.\" e.g., yn(10, 1e-40) on glibc 2.8/x86-32
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.\" .I errno
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.\" is set to
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.\" .BR ERANGE .
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.I errno
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is not set for this case.
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.\" FIXME . Is it intentional that errno is not set?
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.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808
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An overflow floating-point exception
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.RB ( FE_OVERFLOW )
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is raised.
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.SH "CONFORMING TO"
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The functions returning
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.I double
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conform to SVr4, 4.3BSD,
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POSIX.1-2001.
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accept.2, execve.2, futimesat.2, getresuid.2, getrlimit.2, madvise.2, mq_getsetattr.2, msgctl.2, nice.2, open.2, poll.2, setresuid.2, shmctl.2, sigaction.2, times.2, utimensat.2, __setfpucw.3, atoi.3, endian.3, err.3, euidaccess.3, fenv.3, fopencookie.3, fpurge.3, getgrouplist.3, getutmp.3, j0.3, lgamma.3, netlink.3, pthread_attr_init.3, pthread_attr_setaffinity_np.3, pthread_cleanup_push_defer_np.3, pthread_getattr_np.3, pthread_kill_other_threads_np.3, pthread_setaffinity_np.3, pthread_tryjoin_np.3, pthread_yield.3, random_r.3, readdir.3, rtnetlink.3, scanf.3, setenv.3, significand.3, sigsetops.3, strerror.3, strstr.3, sysv_signal.3, termios.3, timegm.3, unlocked_stdio.3, y0.3, locale.5, bootparam.7, feature_test_macros.7, ip.7, locale.7, pthreads.7, rtld-audit.7, nscd.8: Global fix: s/non-standard/nonstandard/
The tendency in English, as prescribed in style guides like
Chicago MoS, is towards removing hyphens after prefixes
like "non-" etc.
Signed-off-by: Michael Kerrisk <mtk.manpages@gmail.com>
2010-01-16 16:37:52 +00:00
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The others are nonstandard functions that also exist on the BSDs.
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2008-08-01 05:36:10 +00:00
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.SH BUGS
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2008-08-04 06:11:37 +00:00
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On a pole error, these functions set
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2008-08-01 05:36:10 +00:00
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.I errno
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to
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.BR EDOM ,
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instead of
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.BR ERANGE
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as POSIX.1-2004 requires.
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.\" FIXME .
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.\" Bug raised: http://sourceware.org/bugzilla/show_bug.cgi?id=6807
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2008-08-10 19:08:31 +00:00
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In glibc version 2.3.2 and earlier,
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.\" FIXME . Actually, 2.3.2 is the earliest test result I have; so yet
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.\" to confirm if this error occurs only in 2.3.2.
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these functions do not raise an invalid floating-point exception
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.RB ( FE_INVALID )
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2008-09-29 09:00:36 +00:00
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when a domain error occurs.
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2008-08-01 05:36:10 +00:00
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.SH SEE ALSO
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.BR j0 (3)
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