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 .\" SPDX-License-Identifier: Linux-man-pages-copyleft
   6 .\"
   7 .\" References consulted:
   8 .\"     Linux libc source code
   9 .\"     Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)
  10 .\"     386BSD man pages
  11 .\" Modified 1993-07-24 by Rik Faith (faith@cs.unc.edu)
  12 .\" Modified 2002-07-27 by Walter Harms
  13 .\"     (walter.harms@informatik.uni-oldenburg.de)
  14 .\"
  15 .TH ERF 3  2021-03-22 "Linux man-pages (unreleased)"
  16 .SH NAME
  17 erf, erff, erfl \- error function
  18 .SH LIBRARY
  19 Math library
  20 .RI ( libm ", " \-lm )
  21 .SH SYNOPSIS
  22 .nf
  23 .B #include <math.h>
  24 .PP
  25 .BI "double erf(double " x );
  26 .BI "float erff(float " x );
  27 .BI "long double erfl(long double " x );
  28 .PP
  29 .fi
  30 .RS -4
  31 Feature Test Macro Requirements for glibc (see
  32 .BR feature_test_macros (7)):
  33 .RE
  34 .PP
  35 .BR erf ():
  36 .nf
  37     _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE
  38         || /* Since glibc 2.19: */ _DEFAULT_SOURCE
  39         || /* Glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
  40 .fi
  41 .PP
  42 .BR erff (),
  43 .BR erfl ():
  44 .nf
  45     _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
  46         || /* Since glibc 2.19: */ _DEFAULT_SOURCE
  47         || /* Glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
  48 .fi
  49 .SH DESCRIPTION
  50 These functions return the error function of
  51 .IR x ,
  52 defined as
  53 .PP
  54 .in +4n
  55 .EX
  56 erf(x) = 2/sqrt(pi) * integral from 0 to x of exp(\-t*t) dt
  57 .EE
  58 .in
  59 .SH RETURN VALUE
  60 On success, these functions return the value of the error function of
  61 .IR x ,
  62 a value in the range [\-1,\ 1].
  63 .PP
  64 If
  65 .I x
  66 is a NaN, a NaN is returned.
  67 .PP
  68 If
  69 .I x
  70 is +0 (\-0), +0 (\-0) is returned.
  71 .PP
  72 If
  73 .I x
  74 is positive infinity (negative infinity),
  75 +1 (\-1) is returned.
  76 .PP
  77 If
  78 .I x
  79 is subnormal,
  80 a range error occurs,
  81 and the return value is 2*x/sqrt(pi).
  82 .SH ERRORS
  83 See
  84 .BR math_error (7)
  85 for information on how to determine whether an error has occurred
  86 when calling these functions.
  87 .PP
  88 The following errors can occur:
  89 .TP
  90 Range error: result underflow (\fIx\fP is subnormal)
  91 .\" .I errno
  92 .\" is set to
  93 .\" .BR ERANGE .
  94 An underflow floating-point exception
  95 .RB ( FE_UNDERFLOW )
  96 is raised.
  97 .PP
  98 These functions do not set
  99 .IR errno .
 100 .\" It is intentional that these functions do not set errno for this case
 101 .\" see http://sources.redhat.com/bugzilla/show_bug.cgi?id=6785
 102 .SH ATTRIBUTES
 103 For an explanation of the terms used in this section, see
 104 .BR attributes (7).
 105 .ad l
 106 .nh
 107 .TS
 108 allbox;
 109 lbx lb lb
 110 l l l.
 111 Interface       Attribute       Value
 112 T{
 113 .BR erf (),
 114 .BR erff (),
 115 .BR erfl ()
 116 T}      Thread safety   MT-Safe
 117 .TE
 118 .hy
 119 .ad
 120 .sp 1
 121 .SH STANDARDS
 122 C99, POSIX.1-2001, POSIX.1-2008.
 123 .PP
 124 The variant returning
 125 .I double
 126 also conforms to
 127 SVr4, 4.3BSD.
 128 .SH SEE ALSO
 129 .BR cerf (3),
 130 .BR erfc (3),
 131 .BR exp (3)