1ERF(3P) POSIX Programmer's Manual ERF(3P)
2
6 This manual page is part of the POSIX Programmer's Manual. The Linux
7 implementation of this interface may differ (consult the corresponding
8 Linux manual page for details of Linux behavior), or the interface may
9 not be implemented on Linux.
10 delim $$
12
14 erf, erff, erfl — error functions
15
17 #include <math.h>
18 double erf(double x);
20 float erff(float x);
21 long double erfl(long double x);
22
24 The functionality described on this reference page is aligned with the
25 ISO C standard. Any conflict between the requirements described here
26 and the ISO C standard is unintentional. This volume of POSIX.1‐2008
27 defers to the ISO C standard.
28 These functions shall compute the error function of their argument x,
30 defined as:
31 ${2 over sqrt pi} int from 0 to x e"^" " "{- t"^" 2" "} dt$
33 An application wishing to check for error situations should set errno
35 to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these
36 functions. On return, if errno is non-zero or fetestexcept(FE_INVALID |
37 FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has
38 occurred.
39
41 Upon successful completion, these functions shall return the value of
42 the error function.
43 If x is NaN, a NaN shall be returned.
45 If x is ±0, ±0 shall be returned.
47 If x is ±Inf, ±1 shall be returned.
49 If the correct value would cause underflow, a range error may occur,
51 and erf(), erff(), and erfl() shall return an implementation-defined
52 value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN,
53 respectively.
54 If the IEC 60559 Floating-Point option is supported, 2 * x/sqrt(π)
56 should be returned.
57
59 These functions may fail if:
60 Range Error The result underflows.
62 If the integer expression (math_errhandling & MATH_ERRNO)
64 is non-zero, then errno shall be set to [ERANGE]. If the
65 integer expression (math_errhandling & MATH_ERREXCEPT) is
66 non-zero, then the underflow floating-point exception shall
67 be raised.
68 The following sections are informative.
70
72 Computing the Probability for a Normal Variate
73 This example shows how to use erf() to compute the probability that a
74 normal variate assumes a value in the range [x1,x2] with x1≤x2.
75 This example uses the constant M_SQRT1_2 which is part of the XSI
77 option.
78 #include <math.h>
80 double
82 Phi(const double x1, const double x2)
83 {
84 return ( erf(x2*M_SQRT1_2) − erf(x1*M_SQRT1_2) ) / 2;
85 }
86
88 Underflow occurs when |x| < DBL_MIN * (sqrt(π)/2).
89 On error, the expressions (math_errhandling & MATH_ERRNO) and
91 (math_errhandling & MATH_ERREXCEPT) are independent of each other, but
92 at least one of them must be non-zero.
93
95 None.
96
98 None.
99
101 erfc(), feclearexcept(), fetestexcept(), isnan()
102 The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment of
104 Error Conditions for Mathematical Functions, <math.h>
105
107 Portions of this text are reprinted and reproduced in electronic form
108 from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology
109 -- Portable Operating System Interface (POSIX), The Open Group Base
110 Specifications Issue 7, Copyright (C) 2013 by the Institute of Electri‐
111 cal and Electronics Engineers, Inc and The Open Group. (This is
112 POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) In the
113 event of any discrepancy between this version and the original IEEE and
114 The Open Group Standard, the original IEEE and The Open Group Standard
115 is the referee document. The original Standard can be obtained online
116 at http://www.unix.org/online.html .
117 Any typographical or formatting errors that appear in this page are
119 most likely to have been introduced during the conversion of the source
120 files to man page format. To report such errors, see https://www.ker‐
121 nel.org/doc/man-pages/reporting_bugs.html .
122IEEE/The Open Group 2013 ERF(3P)