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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16 | .\" manual page may be incorrect or out-of-date.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 | .\" | |
b71168c2 | 36 | .TH Y0 3 2008-08-10 "" "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> | |
43 | .sp | |
44 | .BI "double y0(double " x ); | |
45 | .br | |
46 | .BI "double y1(double " x ); | |
47 | .br | |
48 | .BI "double yn(int " n ", double " x ); | |
49 | .sp | |
50 | .BI "float y0f(float " x ); | |
51 | .br | |
52 | .BI "float y1f(float " x ); | |
53 | .br | |
54 | .BI "float ynf(int " n ", float " x ); | |
55 | .sp | |
56 | .BI "long double y0l(long double " x ); | |
57 | .br | |
58 | .BI "long double y1l(long double " x ); | |
59 | .br | |
60 | .BI "long double ynl(int " n ", long double " x ); | |
61 | .fi | |
62 | .sp | |
63 | Link with \fI\-lm\fP. | |
64 | .sp | |
65 | .in -4n | |
66 | Feature Test Macro Requirements for glibc (see | |
67 | .BR feature_test_macros (7)): | |
68 | .in | |
69 | .sp | |
70 | .ad l | |
71 | .BR y0 (), | |
72 | .BR y1 (), | |
73 | .BR yn (): | |
d0f830af | 74 | .RS 4 |
17d2ffdf | 75 | _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE |
d0f830af | 76 | .RE |
17d2ffdf MK |
77 | .br |
78 | .BR y0f (), | |
79 | .BR y0l (), | |
80 | .BR y1f (), | |
81 | .BR y1l (), | |
82 | .BR ynf (), | |
83 | .BR ynl (): | |
d0f830af | 84 | .RS 4 |
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85 | _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE\ >=\ 600 |
86 | .\" Also seems to work: -std=c99 -D_XOPEN_SOURCE | |
d0f830af | 87 | .RE |
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88 | .ad b |
89 | .SH DESCRIPTION | |
90 | .PP | |
91 | The | |
92 | .BR y0 () | |
93 | and | |
94 | .BR y1 () | |
95 | functions return Bessel functions of \fIx\fP | |
96 | of the second kind of orders 0 and 1, respectively. | |
97 | The | |
98 | .BR yn () | |
99 | function | |
100 | returns the Bessel function of \fIx\fP of the second kind of order \fIn\fP. | |
101 | .PP | |
102 | The value of \fIx\fP must be positive. | |
103 | .PP | |
104 | The | |
105 | .BR y0f () | |
106 | etc. and | |
107 | .BR y0l () | |
108 | etc. functions are versions that take and return | |
109 | .I float | |
110 | and | |
111 | .I "long double" | |
112 | values, respectively. | |
113 | .SH RETURN VALUE | |
114 | On success, these functions return the appropriate | |
115 | Bessel value of the second kind for | |
116 | .IR x . | |
117 | ||
118 | If | |
119 | .I x | |
120 | is a NaN, a NaN is returned. | |
121 | ||
122 | If | |
123 | .I x | |
124 | is negative, | |
efe294cb | 125 | a domain error occurs, |
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126 | and the functions return |
127 | .RB - HUGE_VAL , | |
128 | .RB - HUGE_VALF , | |
129 | or | |
130 | .RB - HUGE_VALL , | |
131 | respectively. | |
132 | (POSIX.1-2001 also allows a NaN return for this case.) | |
133 | ||
134 | If | |
135 | .I x | |
136 | is 0.0, | |
efe294cb | 137 | a pole error occurs, |
17d2ffdf MK |
138 | and the functions return |
139 | .RB - HUGE_VAL , | |
140 | .RB - HUGE_VALF , | |
141 | or | |
142 | .RB - HUGE_VALL , | |
143 | respectively. | |
144 | ||
145 | If the result underflows, | |
efe294cb | 146 | a range error occurs, |
17d2ffdf MK |
147 | and the functions return 0.0 |
148 | ||
149 | If the result overflows, | |
efe294cb | 150 | a range error occurs, |
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151 | and the functions return |
152 | .RB - HUGE_VAL , | |
153 | .RB - HUGE_VALF , | |
154 | or | |
155 | .RB - HUGE_VALL , | |
156 | respectively. | |
157 | (POSIX.1-2001 also allows a 0.0 return for this case.) | |
158 | .SH ERRORS | |
159 | See | |
160 | .BR math_error (7) | |
161 | for information on how to determine whether an error has occurred | |
162 | when calling these functions. | |
163 | .PP | |
164 | The following errors can occur: | |
165 | .TP | |
166 | Domain error: \fIx\fP is negative | |
167 | .I errno | |
168 | is set to | |
169 | .BR EDOM . | |
170 | An invalid floating-point exception | |
171 | .RB ( FE_INVALID ) | |
172 | is raised. | |
173 | .TP | |
174 | Pole error: \fIx\fP is 0.0 | |
175 | .\" Before POSIX.1-2001 TC2, this was (inconsistently) specified | |
176 | .\" as a range error. | |
177 | .I errno | |
178 | is set to | |
179 | .\" FIXME . y0(0.0) gives EDOM | |
385cf745 | 180 | .BR ERANGE |
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181 | (but see BUGS). |
182 | No | |
183 | .B FE_DIVBYZERO | |
184 | exception is returned by | |
185 | .BR fetestexcept (3) | |
186 | for this case. | |
187 | .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808 | |
188 | .TP | |
189 | Range error: result underflow | |
190 | .\" e.g., y0(1e33) on glibc 2.8/x86-32 | |
191 | .I errno | |
192 | is set to | |
193 | .BR ERANGE . | |
194 | .\" An underflow floating-point exception | |
195 | .\" .RB ( FE_UNDERFLOW ) | |
196 | .\" is raised. | |
197 | .\" FIXME . Is it intentional that these functions do not use FE_*? | |
198 | .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6806 | |
199 | No | |
200 | .B FE_UNDERFLOW | |
201 | exception is returned by | |
202 | .BR fetestexcept (3) | |
203 | for this case. | |
204 | .TP | |
205 | Range error: result overflow | |
206 | .\" e.g., yn(10, 1e-40) on glibc 2.8/x86-32 | |
207 | .\" .I errno | |
208 | .\" is set to | |
209 | .\" .BR ERANGE . | |
210 | .I errno | |
211 | is not set for this case. | |
212 | .\" FIXME . Is it intentional that errno is not set? | |
213 | .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808 | |
214 | An overflow floating-point exception | |
215 | .RB ( FE_OVERFLOW ) | |
216 | is raised. | |
47297adb | 217 | .SH CONFORMING TO |
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218 | The functions returning |
219 | .I double | |
220 | conform to SVr4, 4.3BSD, | |
221 | POSIX.1-2001. | |
c8f2dd47 | 222 | The others are nonstandard functions that also exist on the BSDs. |
17d2ffdf | 223 | .SH BUGS |
f7d3c7a8 | 224 | On a pole error, these functions set |
17d2ffdf MK |
225 | .I errno |
226 | to | |
227 | .BR EDOM , | |
228 | instead of | |
229 | .BR ERANGE | |
230 | as POSIX.1-2004 requires. | |
231 | .\" FIXME . | |
232 | .\" Bug raised: http://sourceware.org/bugzilla/show_bug.cgi?id=6807 | |
b71168c2 MK |
233 | |
234 | In glibc version 2.3.2 and earlier, | |
235 | .\" FIXME . Actually, 2.3.2 is the earliest test result I have; so yet | |
236 | .\" to confirm if this error occurs only in 2.3.2. | |
237 | these functions do not raise an invalid floating-point exception | |
238 | .RB ( FE_INVALID ) | |