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 .\"
   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.
   8 .\"
   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.
  13 .\"
  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  15 .\" manual page may be incorrect or out-of-date.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
  20 .\" professionally.
  21 .\"
  22 .\" Formatted or processed versions of this manual, if unaccompanied by
  23 .\" the source, must acknowledge the copyright and authors of this work.
  24 .\"
  25 .\" References consulted:
  26 .\"     Linux libc source code
  27 .\"     Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)
  28 .\"     386BSD man pages
  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.
  33 .\"
  34 .TH Y0 3  2008-08-05 "" "Linux Programmer's Manual"
  35 .SH NAME
  36 y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl \-
  37 Bessel functions of the second kind
  38 .SH SYNOPSIS
  39 .nf
  40 .B #include <math.h>
  41 .sp
  42 .BI "double y0(double " x );
  43 .br
  44 .BI "double y1(double " x );
  45 .br
  46 .BI "double yn(int " n ", double " x );
  47 .sp
  48 .BI "float y0f(float " x );
  49 .br
  50 .BI "float y1f(float " x );
  51 .br
  52 .BI "float ynf(int " n ", float " x );
  53 .sp
  54 .BI "long double y0l(long double " x );
  55 .br
  56 .BI "long double y1l(long double " x );
  57 .br
  58 .BI "long double ynl(int " n ", long double " x );
  59 .fi
  60 .sp
  61 Link with \fI\-lm\fP.
  62 .sp
  63 .in -4n
  64 Feature Test Macro Requirements for glibc (see
  65 .BR feature_test_macros (7)):
  66 .in
  67 .sp
  68 .ad l
  69 .BR y0 (),
  70 .BR y1 (),
  71 .BR yn ():
  72 _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE
  73 .br
  74 .BR y0f (),
  75 .BR y0l (),
  76 .BR y1f (),
  77 .BR y1l (),
  78 .BR ynf (),
  79 .BR ynl ():
  80 _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE\ >=\ 600
  81 .\" Also seems to work: -std=c99 -D_XOPEN_SOURCE
  82 .ad b
  83 .SH DESCRIPTION
  84 .PP
  85 The
  86 .BR y0 ()
  87 and
  88 .BR y1 ()
  89 functions return Bessel functions of \fIx\fP
  90 of the second kind of orders 0 and 1, respectively.
  91 The
  92 .BR yn ()
  93 function
  94 returns the Bessel function of \fIx\fP of the second kind of order \fIn\fP.
  95 .PP
  96 The value of \fIx\fP must be positive.
  97 .PP
  98 The
  99 .BR y0f ()
 100 etc. and
 101 .BR y0l ()
 102 etc. functions are versions that take and return
 103 .I float
 104 and
 105 .I "long double"
 106 values, respectively.
 107 .SH RETURN VALUE
 108 On success, these functions return the appropriate
 109 Bessel value of the second kind for
 110 .IR x .
 111
 112 If
 113 .I x
 114 is a NaN, a NaN is returned.
 115
 116 If
 117 .I x
 118 is negative,
 119 a "domain error" occurs,
 120 and the functions return
 121 .RB - HUGE_VAL ,
 122 .RB - HUGE_VALF ,
 123 or
 124 .RB - HUGE_VALL ,
 125 respectively.
 126 (POSIX.1-2001 also allows a NaN return for this case.)
 127
 128 If
 129 .I x
 130 is 0.0,
 131 a "pole error" occurs,
 132 and the functions return
 133 .RB - HUGE_VAL ,
 134 .RB - HUGE_VALF ,
 135 or
 136 .RB - HUGE_VALL ,
 137 respectively.
 138
 139 If the result underflows,
 140 a "range error" occurs,
 141 and the functions return 0.0
 142
 143 If the result overflows,
 144 a "range error" occurs,
 145 and the functions return
 146 .RB - HUGE_VAL ,
 147 .RB - HUGE_VALF ,
 148 or
 149 .RB - HUGE_VALL ,
 150 respectively.
 151 (POSIX.1-2001 also allows a 0.0 return for this case.)
 152 .SH ERRORS
 153 See
 154 .BR math_error (7)
 155 for information on how to determine whether an error has occurred
 156 when calling these functions.
 157 .PP
 158 The following errors can occur:
 159 .TP
 160 Domain error: \fIx\fP is negative
 161 .I errno
 162 is set to
 163 .BR EDOM .
 164 An invalid floating-point exception
 165 .RB ( FE_INVALID )
 166 is raised.
 167 .TP
 168 Pole error: \fIx\fP is 0.0
 169 .\" Before POSIX.1-2001 TC2, this was (inconsistently) specified
 170 .\" as a range error.
 171 .I errno
 172 is set to
 173 .\" FIXME . y0(0.0) gives EDOM
 174 .BR ERANGE
 175 (but see BUGS).
 176 No
 177 .B FE_DIVBYZERO
 178 exception is returned by
 179 .BR fetestexcept (3)
 180 for this case.
 181 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808
 182 .TP
 183 Range error: result underflow
 184 .\" e.g., y0(1e33) on glibc 2.8/x86-32
 185 .I errno
 186 is set to
 187 .BR ERANGE .
 188 .\" An underflow floating-point exception
 189 .\" .RB ( FE_UNDERFLOW )
 190 .\" is raised.
 191 .\" FIXME . Is it intentional that these functions do not use FE_*?
 192 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6806
 193 No
 194 .B FE_UNDERFLOW
 195 exception is returned by
 196 .BR fetestexcept (3)
 197 for this case.
 198 .TP
 199 Range error: result overflow
 200 .\" e.g., yn(10, 1e-40) on glibc 2.8/x86-32
 201 .\" .I errno
 202 .\" is set to
 203 .\" .BR ERANGE .
 204 .I errno
 205 is not set for this case.
 206 .\" FIXME . Is it intentional that errno is not set?
 207 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808
 208 An overflow floating-point exception
 209 .RB ( FE_OVERFLOW )
 210 is raised.
 211 .SH "CONFORMING TO"
 212 The functions returning
 213 .I double
 214 conform to SVr4, 4.3BSD,
 215 POSIX.1-2001.
 216 The others are non-standard functions that also exist on the BSDs.
 217 .SH BUGS
 218 On a pole error, these functions set
 219 .I errno
 220 to
 221 .BR EDOM ,
 222 instead of
 223 .BR ERANGE
 224 as POSIX.1-2004 requires.
 225 .\" FIXME .
 226 .\" Bug raised: http://sourceware.org/bugzilla/show_bug.cgi?id=6807
 227 .SH SEE ALSO
 228 .BR j0 (3)