man3/erf.3

   1 '\" t
   2 .\" Copyright 1993 David Metcalfe (david@prism.demon.co.uk)
   3 .\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
   4 .\"     <mtk.manpages@gmail.com>
   5 .\"
   6 .\" SPDX-License-Identifier: Linux-man-pages-copyleft
   7 .\"
   8 .\" References consulted:
   9 .\"     Linux libc source code
  10 .\"     Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)
  11 .\"     386BSD man pages
  12 .\" Modified 1993-07-24 by Rik Faith (faith@cs.unc.edu)
  13 .\" Modified 2002-07-27 by Walter Harms
  14 .\"     (walter.harms@informatik.uni-oldenburg.de)
  15 .\"
  16 .TH erf 3 (date) "Linux man-pages (unreleased)"
  17 .SH NAME
  18 erf, erff, erfl \- error function
  19 .SH LIBRARY
  20 Math library
  21 .RI ( libm ", " \-lm )
  22 .SH SYNOPSIS
  23 .nf
  24 .B #include <math.h>
  25 .PP
  26 .BI "double erf(double " x );
  27 .BI "float erff(float " x );
  28 .BI "long double erfl(long double " x );
  29 .PP
  30 .fi
  31 .RS -4
  32 Feature Test Macro Requirements for glibc (see
  33 .BR feature_test_macros (7)):
  34 .RE
  35 .PP
  36 .BR erf ():
  37 .nf
  38     _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE
  39         || /* Since glibc 2.19: */ _DEFAULT_SOURCE
  40         || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
  41 .fi
  42 .PP
  43 .BR erff (),
  44 .BR erfl ():
  45 .nf
  46     _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
  47         || /* Since glibc 2.19: */ _DEFAULT_SOURCE
  48         || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
  49 .fi
  50 .SH DESCRIPTION
  51 These functions return the error function of
  52 .IR x ,
  53 defined as
  54 .PP
  55 .in +4n
  56 .EX
  57 erf(x) = 2/sqrt(pi) * integral from 0 to x of exp(\-t*t) dt
  58 .EE
  59 .in
  60 .SH RETURN VALUE
  61 On success, these functions return the value of the error function of
  62 .IR x ,
  63 a value in the range [\-1,\ 1].
  64 .PP
  65 If
  66 .I x
  67 is a NaN, a NaN is returned.
  68 .PP
  69 If
  70 .I x
  71 is +0 (\-0), +0 (\-0) is returned.
  72 .PP
  73 If
  74 .I x
  75 is positive infinity (negative infinity),
  76 +1 (\-1) is returned.
  77 .PP
  78 If
  79 .I x
  80 is subnormal,
  81 a range error occurs,
  82 and the return value is 2*x/sqrt(pi).
  83 .SH ERRORS
  84 See
  85 .BR math_error (7)
  86 for information on how to determine whether an error has occurred
  87 when calling these functions.
  88 .PP
  89 The following errors can occur:
  90 .TP
  91 Range error: result underflow (\fIx\fP is subnormal)
  92 .\" .I errno
  93 .\" is set to
  94 .\" .BR ERANGE .
  95 An underflow floating-point exception
  96 .RB ( FE_UNDERFLOW )
  97 is raised.
  98 .PP
  99 These functions do not set
 100 .IR errno .
 101 .\" It is intentional that these functions do not set errno for this case
 102 .\" see https://www.sourceware.org/bugzilla/show_bug.cgi?id=6785
 103 .SH ATTRIBUTES
 104 For an explanation of the terms used in this section, see
 105 .BR attributes (7).
 106 .TS
 107 allbox;
 108 lbx lb lb
 109 l l l.
 110 Interface       Attribute       Value
 111 T{
 112 .na
 113 .nh
 114 .BR erf (),
 115 .BR erff (),
 116 .BR erfl ()
 117 T}      Thread safety   MT-Safe
 118 .TE
 119 .sp 1
 120 .SH STANDARDS
 121 C11, POSIX.1-2008.
 122 .SH HISTORY
 123 C99, POSIX.1-2001.
 124 .PP
 125 The variant returning
 126 .I double
 127 also conforms to
 128 SVr4, 4.3BSD.
 129 .SH SEE ALSO
 130 .BR cerf (3),
 131 .BR erfc (3),
 132 .BR exp (3)