man3/erf.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 .\" %%%LICENSE_START(VERBATIM)
   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  16 .\" manual page may be incorrect or out-of-date.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.
  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 1993-07-24 by Rik Faith (faith@cs.unc.edu)
  32 .\" Modified 2002-07-27 by Walter Harms
  33 .\"     (walter.harms@informatik.uni-oldenburg.de)
  34 .\"
  35 .TH ERF 3  2017-09-15 "GNU" "Linux Programmer's Manual"
  36 .SH NAME
  37 erf, erff, erfl, \- error function
  38 .SH SYNOPSIS
  39 .nf
  40 .B #include <math.h>
  41 .PP
  42 .BI "double erf(double " x );
  43 .BI "float erff(float " x );
  44 .BI "long double erfl(long double " x );
  45 .PP
  46 .fi
  47 Link with \fI\-lm\fP.
  48 .PP
  49 .in -4n
  50 Feature Test Macro Requirements for glibc (see
  51 .BR feature_test_macros (7)):
  52 .in
  53 .PP
  54 .ad l
  55 .BR erf ():
  56 .RS 4
  57 _ISOC99_SOURCE || _POSIX_C_SOURCE\ >=\ 200112L || _XOPEN_SOURCE
  58     || /* Since glibc 2.19: */ _DEFAULT_SOURCE
  59     || /* Glibc versions <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
  60 .RE
  61 .br
  62 .BR erff (),
  63 .BR erfl ():
  64 .RS 4
  65 _ISOC99_SOURCE || _POSIX_C_SOURCE\ >=\ 200112L
  66     || /* Since glibc 2.19: */ _DEFAULT_SOURCE
  67     || /* Glibc versions <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
  68 .RE
  69 .ad b
  70 .SH DESCRIPTION
  71 These functions return the error function of
  72 .IR x ,
  73 defined as
  74 .TP
  75     erf(x) = 2/sqrt(pi)* integral from 0 to x of exp(\-t*t) dt
  76 .SH RETURN VALUE
  77 On success, these functions return the error function of
  78 .IR x ,
  79 a value in the range [\-1,\ 1].
  80 .PP
  81 If
  82 .I x
  83 is a NaN, a NaN is returned.
  84 .PP
  85 If
  86 .I x
  87 is +0 (\-0), +0 (\-0) is returned.
  88 .PP
  89 If
  90 .I x
  91 is positive infinity (negative infinity),
  92 +1 (\-1) is returned.
  93 .PP
  94 If
  95 .I x
  96 is subnormal,
  97 a range error occurs,
  98 and the return value is 2*x/sqrt(pi).
  99 .SH ERRORS
 100 See
 101 .BR math_error (7)
 102 for information on how to determine whether an error has occurred
 103 when calling these functions.
 104 .PP
 105 The following errors can occur:
 106 .TP
 107 Range error: result underflow (\fIx\fP is subnormal)
 108 .\" .I errno
 109 .\" is set to
 110 .\" .BR ERANGE .
 111 An underflow floating-point exception
 112 .RB ( FE_UNDERFLOW )
 113 is raised.
 114 .PP
 115 These functions do not set
 116 .IR errno .
 117 .\" FIXME . Is it intentional that these functions do not set errno?
 118 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6785
 119 .SH ATTRIBUTES
 120 For an explanation of the terms used in this section, see
 121 .BR attributes (7).
 122 .TS
 123 allbox;
 124 lbw21 lb lb
 125 l l l.
 126 Interface       Attribute       Value
 127 T{
 128 .BR erf (),
 129 .BR erff (),
 130 .BR erfl ()
 131 T}      Thread safety   MT-Safe
 132 .TE
 133 .SH CONFORMING TO
 134 C99, POSIX.1-2001, POSIX.1-2008.
 135 .PP
 136 The variant returning
 137 .I double
 138 also conforms to
 139 SVr4, 4.3BSD.
 140 .SH SEE ALSO
 141 .BR cerf (3),
 142 .BR erfc (3),
 143 .BR exp (3)