diff options
Diffstat (limited to 'man/man3/y0.3')
| -rw-r--r-- | man/man3/y0.3 | 276 |
1 files changed, 276 insertions, 0 deletions
diff --git a/man/man3/y0.3 b/man/man3/y0.3 new file mode 100644 index 0000000..af9628f --- /dev/null +++ b/man/man3/y0.3 @@ -0,0 +1,276 @@ +'\" t +.\" Copyright 1993 David Metcalfe (david@prism.demon.co.uk) +.\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk +.\" <mtk.manpages@gmail.com> +.\" +.\" SPDX-License-Identifier: Linux-man-pages-copyleft +.\" +.\" 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 2024-05-02 "Linux man-pages (unreleased)" +.SH NAME +y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl \- +Bessel functions of the second kind +.SH LIBRARY +Math library +.RI ( libm ", " \-lm ) +.SH SYNOPSIS +.nf +.B #include <math.h> +.P +.BI "double y0(double " x ); +.BI "double y1(double " x ); +.BI "double yn(int " n ", double " x ); +.P +.BI "float y0f(float " x ); +.BI "float y1f(float " x ); +.BI "float ynf(int " n ", float " x ); +.P +.BI "long double y0l(long double " x ); +.BI "long double y1l(long double " x ); +.BI "long double ynl(int " n ", long double " x ); +.fi +.P +.RS -4 +Feature Test Macro Requirements for glibc (see +.BR feature_test_macros (7)): +.RE +.P +.BR y0 (), +.BR y1 (), +.BR yn (): +.nf + _XOPEN_SOURCE + || /* Since glibc 2.19: */ _DEFAULT_SOURCE + || /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE +.fi +.P +.BR y0f (), +.BR y0l (), +.BR y1f (), +.BR y1l (), +.BR ynf (), +.BR ynl (): +.nf + _XOPEN_SOURCE >= 600 + || (_ISOC99_SOURCE && _XOPEN_SOURCE) + || /* Since glibc 2.19: */ _DEFAULT_SOURCE + || /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE +.fi +.SH DESCRIPTION +The +.BR y0 () +and +.BR y1 () +functions return Bessel functions of +.I x +of the second kind of orders 0 and 1, respectively. +The +.BR yn () +function +returns the Bessel function of +.I x +of the second kind of order +.IR n . +.P +The value of +.I x +must be positive. +.P +The +.BR y0f (), +.BR y1f (), +and +.BR ynf () +functions are versions that take and return +.I float +values. +The +.BR y0l (), +.BR y1l (), +and +.BR ynl () +functions are versions that take and return +.I "long double" +values. +.SH RETURN VALUE +On success, these functions return the appropriate +Bessel value of the second kind for +.IR x . +.P +If +.I x +is a NaN, a NaN is returned. +.P +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.) +.P +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. +.P +If the result underflows, +a range error occurs, +and the functions return 0.0 +.P +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. +.P +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 +.B ERANGE +and an +.B FE_DIVBYZERO +exception is raised +(but see BUGS). +.TP +Range error: result underflow +.\" e.g., y0(1e33) on glibc 2.8/x86-32 +.I errno +is set to +.BR ERANGE . +No +.B FE_UNDERFLOW +exception is returned by +.\" This is intended behavior +.\" See https://www.sourceware.org/bugzilla/show_bug.cgi?id=6806 +.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 +.B ERANGE +(but see BUGS). +An overflow floating-point exception +.RB ( FE_OVERFLOW ) +is raised. +.SH ATTRIBUTES +For an explanation of the terms used in this section, see +.BR attributes (7). +.TS +allbox; +lbx lb lb +l l l. +Interface Attribute Value +T{ +.na +.nh +.BR y0 (), +.BR y0f (), +.BR y0l () +T} Thread safety MT-Safe +T{ +.na +.nh +.BR y1 (), +.BR y1f (), +.BR y1l () +T} Thread safety MT-Safe +T{ +.na +.nh +.BR yn (), +.BR ynf (), +.BR ynl () +T} Thread safety MT-Safe +.TE +.SH STANDARDS +.TP +.BR y0 () +.TQ +.BR y1 () +.TQ +.BR yn () +POSIX.1-2008. +.TP +Others: +BSD. +.SH HISTORY +.TP +.BR y0 () +.TQ +.BR y1 () +.TQ +.BR yn () +SVr4, 4.3BSD, +POSIX.1-2001. +.TP +Others: +BSD. +.SH BUGS +Before glibc 2.19, +.\" http://sourceware.org/bugzilla/show_bug.cgi?id=6807 +these functions misdiagnosed pole errors: +.I errno +was set to +.BR EDOM , +instead of +.B ERANGE +and no +.B FE_DIVBYZERO +exception was raised. +.P +Before glibc 2.17, +.\" https://www.sourceware.org/bugzilla/show_bug.cgi?id=6808 +did not set +.I errno +for "range error: result underflow". +.P +In glibc 2.3.2 and earlier, +.\" Actually, 2.3.2 is the earliest test result I have; so yet +.\" to confirm if this error occurs only in glibc 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) |