man3/y0.3

   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 .\"
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  10 .\" Permission is granted to copy and distribute modified versions of this
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  15 .\" Since the Linux kernel and libraries are constantly changing, this
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  25 .\" %%%LICENSE_END
  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 .\"
  36 .TH Y0 3  2017-09-15 "" "Linux Programmer's Manual"
  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 .PP
  44 .BI "double y0(double " x );
  45 .BI "double y1(double " x );
  46 .BI "double yn(int " n ", double " x );
  47 .PP
  48 .BI "float y0f(float " x );
  49 .BI "float y1f(float " x );
  50 .BI "float ynf(int " n ", float " x );
  51 .PP
  52 .BI "long double y0l(long double " x );
  53 .BI "long double y1l(long double " x );
  54 .BI "long double ynl(int " n ", long double " x );
  55 .fi
  56 .PP
  57 Link with \fI\-lm\fP.
  58 .PP
  59 .in -4n
  60 Feature Test Macro Requirements for glibc (see
  61 .BR feature_test_macros (7)):
  62 .in
  63 .PP
  64 .ad l
  65 .BR y0 (),
  66 .BR y1 (),
  67 .BR yn ():
  68 .RS 4
  69 _XOPEN_SOURCE
  70     || /* Since glibc 2.19: */ _DEFAULT_SOURCE
  71     || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
  72 .RE
  73 .br
  74 .BR y0f (),
  75 .BR y0l (),
  76 .BR y1f (),
  77 .BR y1l (),
  78 .BR ynf (),
  79 .BR ynl ():
  80 .RS 4
  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
  85 .RE
  86 .ad b
  87 .SH DESCRIPTION
  88 .PP
  89 The
  90 .BR y0 ()
  91 and
  92 .BR y1 ()
  93 functions return Bessel functions of
  94 .I x
  95 of the second kind of orders 0 and 1, respectively.
  96 The
  97 .BR yn ()
  98 function
  99 returns the Bessel function of
 100 .I x
 101 of the second kind of order
 102 .IR n .
 103 .PP
 104 The value of
 105 .I x
 106 must be positive.
 107 .PP
 108 The
 109 .BR y0f (),
 110 .BR y1f (),
 111 and
 112 .BR ynf ()
 113 functions are versions that take and return
 114 .I float
 115 values.
 116 The
 117 .BR y0l (),
 118 .BR y1l (),
 119 and
 120 .BR ynl ()
 121 functions are versions that take and return
 122 .I "long double"
 123 values.
 124 .SH RETURN VALUE
 125 On success, these functions return the appropriate
 126 Bessel value of the second kind for
 127 .IR x .
 128 .PP
 129 If
 130 .I x
 131 is a NaN, a NaN is returned.
 132 .PP
 133 If
 134 .I x
 135 is negative,
 136 a domain error occurs,
 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.)
 144 .PP
 145 If
 146 .I x
 147 is 0.0,
 148 a pole error occurs,
 149 and the functions return
 150 .RB - HUGE_VAL ,
 151 .RB - HUGE_VALF ,
 152 or
 153 .RB - HUGE_VALL ,
 154 respectively.
 155 .PP
 156 If the result underflows,
 157 a range error occurs,
 158 and the functions return 0.0
 159 .PP
 160 If the result overflows,
 161 a range error occurs,
 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
 191 .BR ERANGE
 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.
 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
 252 .SH CONFORMING TO
 253 The functions returning
 254 .I double
 255 conform to SVr4, 4.3BSD,
 256 POSIX.1-2001, POSIX.1-2008.
 257 The others are nonstandard functions that also exist on the BSDs.
 258 .SH BUGS
 259 On a pole error, these functions set
 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
 268 .PP
 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 )
 274 when a domain error occurs.
 275 .SH SEE ALSO
 276 .BR j0 (3)