man3/erfc.3

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  26 .TH ERFC 3  2017-09-15 "GNU" "Linux Programmer's Manual"
  27 .SH NAME
  28 erfc, erfcf, erfcl \- complementary error function
  29 .SH SYNOPSIS
  30 .nf
  31 .B #include <math.h>
  32 .PP
  33 .BI "double erfc(double " x );
  34 .BI "float erfcf(float " x );
  35 .BI "long double erfcl(long double " x );
  36 .fi
  37 .PP
  38 Link with \fI\-lm\fP.
  39 .PP
  40 .in -4n
  41 Feature Test Macro Requirements for glibc (see
  42 .BR feature_test_macros (7)):
  43 .in
  44 .PP
  45 .ad l
  46 .BR erfc ():
  47 .RS 4
  48 _ISOC99_SOURCE || _POSIX_C_SOURCE\ >=\ 200112L || _XOPEN_SOURCE
  49     || /* Since glibc 2.19: */ _DEFAULT_SOURCE
  50     || /* Glibc versions <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
  51 .RE
  52 .br
  53 .BR erfcf (),
  54 .BR erfcl ():
  55 .RS 4
  56 _ISOC99_SOURCE || _POSIX_C_SOURCE\ >=\ 200112L
  57     || /* Since glibc 2.19: */ _DEFAULT_SOURCE
  58     || /* Glibc versions <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
  59 .RE
  60 .ad b
  61 .SH DESCRIPTION
  62 These functions return the complementary error function of
  63 .IR x ,
  64 that is, 1.0 \- erf(x).
  65 .SH RETURN VALUE
  66 On success, these functions return the complementary error function of
  67 .IR x ,
  68 a value in the range [0,2].
  69 .PP
  70 If
  71 .I x
  72 is a NaN, a NaN is returned.
  73 .PP
  74 If
  75 .I x
  76 is +0 or \-0, 1 is returned.
  77 .PP
  78 If
  79 .I x
  80 is positive infinity,
  81 +0 is returned.
  82 .PP
  83 If
  84 .I x
  85 is negative infinity,
  86 +2 is returned.
  87 .PP
  88 If the function result underflows and produces an unrepresentable value,
  89 the return value is 0.0.
  90 .PP
  91 If the function result underflows but produces a representable
  92 (i.e., subnormal) value,
  93 .\" e.g., erfc(27) on x86-32
  94 that value is returned, and
  95 a range error occurs.
  96 .SH ERRORS
  97 See
  98 .BR math_error (7)
  99 for information on how to determine whether an error has occurred
 100 when calling these functions.
 101 .PP
 102 The following errors can occur:
 103 .TP
 104 Range error: result underflow (result is subnormal)
 105 .\" .I errno
 106 .\" is set to
 107 .\" .BR ERANGE .
 108 An underflow floating-point exception
 109 .RB ( FE_UNDERFLOW )
 110 is raised.
 111 .PP
 112 These functions do not set
 113 .IR errno .
 114 .\" It is intentional that these functions do not set errno for this case
 115 .\" see http://sources.redhat.com/bugzilla/show_bug.cgi?id=6785
 116 .SH ATTRIBUTES
 117 For an explanation of the terms used in this section, see
 118 .BR attributes (7).
 119 .TS
 120 allbox;
 121 lbw24 lb lb
 122 l l l.
 123 Interface       Attribute       Value
 124 T{
 125 .BR erfc (),
 126 .BR erfcf (),
 127 .BR erfcl ()
 128 T}      Thread safety   MT-Safe
 129 .TE
 130 .SH CONFORMING TO
 131 C99, POSIX.1-2001, POSIX.1-2008.
 132 .PP
 133 The variant returning
 134 .I double
 135 also conforms to
 136 SVr4, 4.3BSD.
 137 .SH NOTES
 138 The
 139 .BR erfc (),
 140 .BR erfcf (),
 141 and
 142 .BR erfcl ()
 143 functions are provided to avoid the loss accuracy that
 144 would occur for the calculation 1-erf(x) for large values of
 145 .IR x
 146 (for which the value of erf(x) approaches 1).
 147 .SH SEE ALSO
 148 .BR cerf (3),
 149 .BR erf (3),
 150 .BR exp (3)