1 .\" Copyright 1993 David Metcalfe (david@prism.demon.co.uk)
2 .\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
3 .\" <mtk.manpages@gmail.com>
5 .\" Permission is granted to make and distribute verbatim copies of this
6 .\" manual provided the copyright notice and this permission notice are
7 .\" preserved on all copies.
9 .\" Permission is granted to copy and distribute modified versions of this
10 .\" manual under the conditions for verbatim copying, provided that the
11 .\" entire resulting derived work is distributed under the terms of a
12 .\" permission notice identical to this one.
14 .\" Since the Linux kernel and libraries are constantly changing, this
15 .\" manual page may be incorrect or out-of-date. The author(s) assume no
16 .\" responsibility for errors or omissions, or for damages resulting from
17 .\" the use of the information contained herein. The author(s) may not
18 .\" have taken the same level of care in the production of this manual,
19 .\" which is licensed free of charge, as they might when working
22 .\" Formatted or processed versions of this manual, if unaccompanied by
23 .\" the source, must acknowledge the copyright and authors of this work.
25 .\" References consulted:
26 .\" Linux libc source code
27 .\" Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)
29 .\" Modified Sat Jul 24 19:08:17 1993 by Rik Faith (faith@cs.unc.edu)
30 .\" Modified 2002-08-25, aeb
31 .\" Modified 2004-11-12 as per suggestion by Fabian Kreutz/AEB
32 .\" 2008-07-24, mtk, created this page, based on material from j0.3.
34 .\" Japanese Version Copyright (c) 2008 Akihiro MOTOKI
35 .\" all rights reserved.
36 .\" Translated 2008-09-19, Akihiro MOTOKI <amotoki@dd.iij4u.or.jp>, LDP v3.07
38 .TH Y0 3 2008-08-10 "" "Linux Programmer's Manual"
41 .\"O y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl \-
42 .\"O Bessel functions of the second kind
43 y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl \-
50 .BI "double y0(double " x );
52 .BI "double y1(double " x );
54 .BI "double yn(int " n ", double " x );
56 .BI "float y0f(float " x );
58 .BI "float y1f(float " x );
60 .BI "float ynf(int " n ", float " x );
62 .BI "long double y0l(long double " x );
64 .BI "long double y1l(long double " x );
66 .BI "long double ynl(int " n ", long double " x );
69 .\"O Link with \fI\-lm\fP.
73 .\"O Feature Test Macro Requirements for glibc (see
74 .\"O .BR feature_test_macros (7)):
76 .RB ( feature_test_macros (7)
85 _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE
95 _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE\ >=\ 600
96 .\" Also seems to work: -std=c99 -D_XOPEN_SOURCE
106 .\"O functions return Bessel functions of \fIx\fP
107 .\"O of the second kind of orders 0 and 1, respectively.
111 .\"O returns the Bessel function of \fIx\fP of the second kind of order \fIn\fP.
116 はそれぞれ \fIx\fP の 0 次、1 次の
120 は \fIx\fP の \fIn\fP 次の
123 .\"O The value of \fIx\fP must be positive.
124 \fIx\fP は正の値でなければならない。
130 .\"O etc. functions are versions that take and return
133 .\"O .I "long double"
134 .\"O values, respectively.
143 .\"O .SH RETURN VALUE
145 .\"O On success, these functions return the appropriate
146 .\"O Bessel value of the second kind for
154 .\"O is a NaN, a NaN is returned.
161 .\"O a domain error occurs,
162 .\"O and the functions return
163 .\"O .RB - HUGE_VAL ,
164 .\"O .RB - HUGE_VALF ,
166 .\"O .RB - HUGE_VALL ,
168 .\"O (POSIX.1-2001 also allows a NaN return for this case.)
170 が負の場合、領域エラー (domain error) が発生し、
175 を返す (POSIX.1-2001 ではこの場合に NaN を返すことも認めている)。
180 .\"O a pole error occurs,
181 .\"O and the functions return
182 .\"O .RB - HUGE_VAL ,
183 .\"O .RB - HUGE_VALF ,
185 .\"O .RB - HUGE_VALL ,
188 が 0.0 の場合、極エラー (pole error) が発生し、
195 .\"O If the result underflows,
196 .\"O a range error occurs,
197 .\"O and the functions return 0.0
199 範囲エラー (range error) が発生し、
202 .\"O If the result overflows,
203 .\"O a range error occurs,
204 .\"O and the functions return
205 .\"O .RB - HUGE_VAL ,
206 .\"O .RB - HUGE_VALF ,
208 .\"O .RB - HUGE_VALL ,
210 .\"O (POSIX.1-2001 also allows a 0.0 return for this case.)
211 結果がオーバーフローする場合、範囲エラーが発生し、
216 を返す (POSIX.1-2001 ではこの場合に 0.0 を返すことも認めている)。
220 .\"O .BR math_error (7)
221 .\"O for information on how to determine whether an error has occurred
222 .\"O when calling these functions.
223 これらの関数を呼び出した際にエラーが発生したかの判定方法についての情報は
227 .\"O The following errors can occur:
230 .\"O Domain error: \fIx\fP is negative
235 .\"O An invalid floating-point exception
236 .\"O .RB ( FE_INVALID )
246 .\"O Pole error: \fIx\fP is 0.0
248 .\" Before POSIX.1-2001 TC2, this was (inconsistently) specified
249 .\" as a range error.
252 .\" FIXME . y0(0.0) gives EDOM
257 .\"O exception is returned by
258 .\"O .BR fetestexcept (3)
263 が設定される (「バグ」の節を参照のこと)。
269 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808
271 .\"O Range error: result underflow
273 .\" e.g., y0(1e33) on glibc 2.8/x86-32
281 .\" An underflow floating-point exception
282 .\" .RB ( FE_UNDERFLOW )
284 .\" FIXME . Is it intentional that these functions do not use FE_*?
285 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6806
288 .\"O exception is returned by
289 .\"O .BR fetestexcept (3)
297 .\"O Range error: result overflow
299 .\" e.g., yn(10, 1e-40) on glibc 2.8/x86-32
304 .\"O is not set for this case.
308 .\" FIXME . Is it intentional that errno is not set?
309 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808
310 .\"O An overflow floating-point exception
311 .\"O .RB ( FE_OVERFLOW )
316 .\"O .SH "CONFORMING TO"
318 .\"O The functions returning
320 .\"O conform to SVr4, 4.3BSD,
323 型の値を返す関数は、SVr4, 4.3BSD, POSIX.1-2001
325 .\"O The others are nonstandard functions that also exist on the BSDs.
326 それ以外は非標準の関数で、BSD にも存在する。
329 .\"O On a pole error, these functions set
335 .\"O as POSIX.1-2004 requires.
345 .\" Bug raised: http://sourceware.org/bugzilla/show_bug.cgi?id=6807
347 .\"O In glibc version 2.3.2 and earlier,
348 glibc バージョン 2.3.2 以前では、
349 .\" FIXME . Actually, 2.3.2 is the earliest test result I have; so yet
350 .\" to confirm if this error occurs only in 2.3.2.
351 .\"O these functions do not raise an invalid floating-point exception
352 .\"O .RB ( FE_INVALID )
353 .\"O when a domain error occurs.
354 領域エラーが発生した場合に、これらの関数は