man3/erfc.3

   1 .\" Copyright 2008, Linux Foundation, written by Michael Kerrisk
   2 .\"     <mtk.manpages@gmail.com>
   3 .\"
   4 .\" SPDX-License-Identifier: Linux-man-pages-copyleft
   5 .\"
   6 .TH erfc 3 (date) "Linux man-pages (unreleased)"
   7 .SH NAME
   8 erfc, erfcf, erfcl \- complementary error function
   9 .SH LIBRARY
  10 Math library
  11 .RI ( libm ", " \-lm )
  12 .SH SYNOPSIS
  13 .nf
  14 .B #include <math.h>
  15 .PP
  16 .BI "double erfc(double " x );
  17 .BI "float erfcf(float " x );
  18 .BI "long double erfcl(long double " x );
  19 .fi
  20 .PP
  21 .RS -4
  22 Feature Test Macro Requirements for glibc (see
  23 .BR feature_test_macros (7)):
  24 .RE
  25 .PP
  26 .BR erfc ():
  27 .nf
  28     _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE
  29         || /* Since glibc 2.19: */ _DEFAULT_SOURCE
  30         || /* Glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
  31 .fi
  32 .PP
  33 .BR erfcf (),
  34 .BR erfcl ():
  35 .nf
  36     _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
  37         || /* Since glibc 2.19: */ _DEFAULT_SOURCE
  38         || /* Glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
  39 .fi
  40 .SH DESCRIPTION
  41 These functions return the complementary error function of
  42 .IR x ,
  43 that is, 1.0 \- erf(x).
  44 .SH RETURN VALUE
  45 On success, these functions return the complementary error function of
  46 .IR x ,
  47 a value in the range [0,2].
  48 .PP
  49 If
  50 .I x
  51 is a NaN, a NaN is returned.
  52 .PP
  53 If
  54 .I x
  55 is +0 or \-0, 1 is returned.
  56 .PP
  57 If
  58 .I x
  59 is positive infinity,
  60 +0 is returned.
  61 .PP
  62 If
  63 .I x
  64 is negative infinity,
  65 +2 is returned.
  66 .PP
  67 If the function result underflows and produces an unrepresentable value,
  68 the return value is 0.0.
  69 .PP
  70 If the function result underflows but produces a representable
  71 (i.e., subnormal) value,
  72 .\" e.g., erfc(27) on x86-32
  73 that value is returned, and
  74 a range error occurs.
  75 .SH ERRORS
  76 See
  77 .BR math_error (7)
  78 for information on how to determine whether an error has occurred
  79 when calling these functions.
  80 .PP
  81 The following errors can occur:
  82 .TP
  83 Range error: result underflow (result is subnormal)
  84 .\" .I errno
  85 .\" is set to
  86 .\" .BR ERANGE .
  87 An underflow floating-point exception
  88 .RB ( FE_UNDERFLOW )
  89 is raised.
  90 .PP
  91 These functions do not set
  92 .IR errno .
  93 .\" It is intentional that these functions do not set errno for this case
  94 .\" see http://sources.redhat.com/bugzilla/show_bug.cgi?id=6785
  95 .SH ATTRIBUTES
  96 For an explanation of the terms used in this section, see
  97 .BR attributes (7).
  98 .ad l
  99 .nh
 100 .TS
 101 allbox;
 102 lbx lb lb
 103 l l l.
 104 Interface       Attribute       Value
 105 T{
 106 .BR erfc (),
 107 .BR erfcf (),
 108 .BR erfcl ()
 109 T}      Thread safety   MT-Safe
 110 .TE
 111 .hy
 112 .ad
 113 .sp 1
 114 .SH STANDARDS
 115 C99, POSIX.1-2001, POSIX.1-2008.
 116 .PP
 117 The variant returning
 118 .I double
 119 also conforms to
 120 SVr4, 4.3BSD.
 121 .SH NOTES
 122 The
 123 .BR erfc (),
 124 .BR erfcf (),
 125 and
 126 .BR erfcl ()
 127 functions are provided to avoid the loss accuracy that
 128 would occur for the calculation 1-erf(x) for large values of
 129 .I x
 130 (for which the value of erf(x) approaches 1).
 131 .SH SEE ALSO
 132 .BR cerf (3),
 133 .BR erf (3),
 134 .BR exp (3)