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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> | |
4 | .\" | |
93015253 | 5 | .\" %%%LICENSE_START(VERBATIM) |
17d2ffdf MK |
6 | .\" Permission is granted to make and distribute verbatim copies of this |
7 | .\" manual provided the copyright notice and this permission notice are | |
8 | .\" preserved on all copies. | |
9 | .\" | |
10 | .\" Permission is granted to copy and distribute modified versions of this | |
11 | .\" manual under the conditions for verbatim copying, provided that the | |
12 | .\" entire resulting derived work is distributed under the terms of a | |
13 | .\" permission notice identical to this one. | |
14 | .\" | |
15 | .\" Since the Linux kernel and libraries are constantly changing, this | |
16 | .\" manual page may be incorrect or out-of-date. The author(s) assume no | |
17 | .\" responsibility for errors or omissions, or for damages resulting from | |
18 | .\" the use of the information contained herein. The author(s) may not | |
19 | .\" have taken the same level of care in the production of this manual, | |
20 | .\" which is licensed free of charge, as they might when working | |
21 | .\" professionally. | |
22 | .\" | |
23 | .\" Formatted or processed versions of this manual, if unaccompanied by | |
24 | .\" the source, must acknowledge the copyright and authors of this work. | |
4b72fb64 | 25 | .\" %%%LICENSE_END |
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26 | .\" |
27 | .\" References consulted: | |
28 | .\" Linux libc source code | |
29 | .\" Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991) | |
30 | .\" 386BSD man pages | |
31 | .\" Modified Sat Jul 24 19:08:17 1993 by Rik Faith (faith@cs.unc.edu) | |
32 | .\" Modified 2002-08-25, aeb | |
33 | .\" Modified 2004-11-12 as per suggestion by Fabian Kreutz/AEB | |
34 | .\" 2008-07-24, mtk, created this page, based on material from j0.3. | |
35 | .\" | |
4b8c67d9 | 36 | .TH Y0 3 2017-09-15 "" "Linux Programmer's Manual" |
17d2ffdf MK |
37 | .SH NAME |
38 | y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl \- | |
39 | Bessel functions of the second kind | |
40 | .SH SYNOPSIS | |
41 | .nf | |
42 | .B #include <math.h> | |
68e4db0a | 43 | .PP |
17d2ffdf | 44 | .BI "double y0(double " x ); |
17d2ffdf | 45 | .BI "double y1(double " x ); |
17d2ffdf | 46 | .BI "double yn(int " n ", double " x ); |
68e4db0a | 47 | .PP |
17d2ffdf | 48 | .BI "float y0f(float " x ); |
17d2ffdf | 49 | .BI "float y1f(float " x ); |
17d2ffdf | 50 | .BI "float ynf(int " n ", float " x ); |
68e4db0a | 51 | .PP |
17d2ffdf | 52 | .BI "long double y0l(long double " x ); |
17d2ffdf | 53 | .BI "long double y1l(long double " x ); |
17d2ffdf MK |
54 | .BI "long double ynl(int " n ", long double " x ); |
55 | .fi | |
68e4db0a | 56 | .PP |
17d2ffdf | 57 | Link with \fI\-lm\fP. |
68e4db0a | 58 | .PP |
17d2ffdf MK |
59 | .in -4n |
60 | Feature Test Macro Requirements for glibc (see | |
61 | .BR feature_test_macros (7)): | |
62 | .in | |
68e4db0a | 63 | .PP |
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64 | .ad l |
65 | .BR y0 (), | |
66 | .BR y1 (), | |
67 | .BR yn (): | |
d0f830af | 68 | .RS 4 |
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69 | _XOPEN_SOURCE |
70 | || /* Since glibc 2.19: */ _DEFAULT_SOURCE | |
71 | || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE | |
d0f830af | 72 | .RE |
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73 | .br |
74 | .BR y0f (), | |
75 | .BR y0l (), | |
76 | .BR y1f (), | |
77 | .BR y1l (), | |
78 | .BR ynf (), | |
79 | .BR ynl (): | |
d0f830af | 80 | .RS 4 |
636ed4d5 MK |
81 | _XOPEN_SOURCE \ >=\ 600 |
82 | || (_ISOC99_SOURCE && _XOPEN_SOURCE) | |
83 | || /* Since glibc 2.19: */ _DEFAULT_SOURCE | |
84 | || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE | |
d0f830af | 85 | .RE |
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86 | .ad b |
87 | .SH DESCRIPTION | |
88 | .PP | |
89 | The | |
90 | .BR y0 () | |
91 | and | |
92 | .BR y1 () | |
c6fa0841 MK |
93 | functions return Bessel functions of |
94 | .I x | |
17d2ffdf MK |
95 | of the second kind of orders 0 and 1, respectively. |
96 | The | |
97 | .BR yn () | |
98 | function | |
c6fa0841 MK |
99 | returns the Bessel function of |
100 | .I x | |
101 | of the second kind of order | |
102 | .IR n . | |
17d2ffdf | 103 | .PP |
c6fa0841 MK |
104 | The value of |
105 | .I x | |
106 | must be positive. | |
17d2ffdf MK |
107 | .PP |
108 | The | |
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109 | .BR y0f (), |
110 | .BR y1f (), | |
111 | and | |
112 | .BR ynf () | |
113 | functions are versions that take and return | |
17d2ffdf | 114 | .I float |
80017421 MK |
115 | values. |
116 | The | |
117 | .BR y0l (), | |
118 | .BR y1l (), | |
17d2ffdf | 119 | and |
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120 | .BR ynl () |
121 | functions are versions that take and return | |
17d2ffdf | 122 | .I "long double" |
80017421 | 123 | values. |
17d2ffdf MK |
124 | .SH RETURN VALUE |
125 | On success, these functions return the appropriate | |
126 | Bessel value of the second kind for | |
127 | .IR x . | |
847e0d88 | 128 | .PP |
17d2ffdf MK |
129 | If |
130 | .I x | |
131 | is a NaN, a NaN is returned. | |
847e0d88 | 132 | .PP |
17d2ffdf MK |
133 | If |
134 | .I x | |
135 | is negative, | |
efe294cb | 136 | a domain error occurs, |
17d2ffdf MK |
137 | and the functions return |
138 | .RB - HUGE_VAL , | |
139 | .RB - HUGE_VALF , | |
140 | or | |
141 | .RB - HUGE_VALL , | |
142 | respectively. | |
143 | (POSIX.1-2001 also allows a NaN return for this case.) | |
847e0d88 | 144 | .PP |
17d2ffdf MK |
145 | If |
146 | .I x | |
147 | is 0.0, | |
efe294cb | 148 | a pole error occurs, |
17d2ffdf MK |
149 | and the functions return |
150 | .RB - HUGE_VAL , | |
151 | .RB - HUGE_VALF , | |
152 | or | |
153 | .RB - HUGE_VALL , | |
154 | respectively. | |
847e0d88 | 155 | .PP |
17d2ffdf | 156 | If the result underflows, |
efe294cb | 157 | a range error occurs, |
17d2ffdf | 158 | and the functions return 0.0 |
847e0d88 | 159 | .PP |
17d2ffdf | 160 | If the result overflows, |
efe294cb | 161 | a range error occurs, |
17d2ffdf MK |
162 | and the functions return |
163 | .RB - HUGE_VAL , | |
164 | .RB - HUGE_VALF , | |
165 | or | |
166 | .RB - HUGE_VALL , | |
167 | respectively. | |
168 | (POSIX.1-2001 also allows a 0.0 return for this case.) | |
169 | .SH ERRORS | |
170 | See | |
171 | .BR math_error (7) | |
172 | for information on how to determine whether an error has occurred | |
173 | when calling these functions. | |
174 | .PP | |
175 | The following errors can occur: | |
176 | .TP | |
177 | Domain error: \fIx\fP is negative | |
178 | .I errno | |
179 | is set to | |
180 | .BR EDOM . | |
181 | An invalid floating-point exception | |
182 | .RB ( FE_INVALID ) | |
183 | is raised. | |
184 | .TP | |
185 | Pole error: \fIx\fP is 0.0 | |
186 | .\" Before POSIX.1-2001 TC2, this was (inconsistently) specified | |
187 | .\" as a range error. | |
188 | .I errno | |
189 | is set to | |
190 | .\" FIXME . y0(0.0) gives EDOM | |
385cf745 | 191 | .BR ERANGE |
17d2ffdf MK |
192 | (but see BUGS). |
193 | No | |
194 | .B FE_DIVBYZERO | |
195 | exception is returned by | |
196 | .BR fetestexcept (3) | |
197 | for this case. | |
198 | .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808 | |
199 | .TP | |
200 | Range error: result underflow | |
201 | .\" e.g., y0(1e33) on glibc 2.8/x86-32 | |
202 | .I errno | |
203 | is set to | |
204 | .BR ERANGE . | |
205 | .\" An underflow floating-point exception | |
206 | .\" .RB ( FE_UNDERFLOW ) | |
207 | .\" is raised. | |
208 | .\" FIXME . Is it intentional that these functions do not use FE_*? | |
209 | .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6806 | |
210 | No | |
211 | .B FE_UNDERFLOW | |
212 | exception is returned by | |
213 | .BR fetestexcept (3) | |
214 | for this case. | |
215 | .TP | |
216 | Range error: result overflow | |
217 | .\" e.g., yn(10, 1e-40) on glibc 2.8/x86-32 | |
218 | .\" .I errno | |
219 | .\" is set to | |
220 | .\" .BR ERANGE . | |
221 | .I errno | |
222 | is not set for this case. | |
223 | .\" FIXME . Is it intentional that errno is not set? | |
224 | .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808 | |
225 | An overflow floating-point exception | |
226 | .RB ( FE_OVERFLOW ) | |
227 | is raised. | |
2d3e3a67 MS |
228 | .SH ATTRIBUTES |
229 | For an explanation of the terms used in this section, see | |
230 | .BR attributes (7). | |
231 | .TS | |
232 | allbox; | |
233 | lb lb lb | |
234 | l l l. | |
235 | Interface Attribute Value | |
236 | T{ | |
237 | .BR y0 (), | |
238 | .BR y0f (), | |
239 | .BR y0l () | |
240 | T} Thread safety MT-Safe | |
241 | T{ | |
242 | .BR y1 (), | |
243 | .BR y1f (), | |
244 | .BR y1l () | |
245 | T} Thread safety MT-Safe | |
246 | T{ | |
247 | .BR yn (), | |
248 | .BR ynf (), | |
249 | .BR ynl () | |
250 | T} Thread safety MT-Safe | |
251 | .TE | |
47297adb | 252 | .SH CONFORMING TO |
17d2ffdf MK |
253 | The functions returning |
254 | .I double | |
255 | conform to SVr4, 4.3BSD, | |
9a0216ac | 256 | POSIX.1-2001, POSIX.1-2008. |
c8f2dd47 | 257 | The others are nonstandard functions that also exist on the BSDs. |
17d2ffdf | 258 | .SH BUGS |
f7d3c7a8 | 259 | On a pole error, these functions set |
17d2ffdf MK |
260 | .I errno |
261 | to | |
262 | .BR EDOM , | |
263 | instead of | |
264 | .BR ERANGE | |
265 | as POSIX.1-2004 requires. | |
266 | .\" FIXME . | |
267 | .\" Bug raised: http://sourceware.org/bugzilla/show_bug.cgi?id=6807 | |
847e0d88 | 268 | .PP |
b71168c2 MK |
269 | In glibc version 2.3.2 and earlier, |
270 | .\" FIXME . Actually, 2.3.2 is the earliest test result I have; so yet | |
271 | .\" to confirm if this error occurs only in 2.3.2. | |
272 | these functions do not raise an invalid floating-point exception | |
273 | .RB ( FE_INVALID ) | |