1ERF(3P)                    POSIX Programmer's Manual                   ERF(3P)
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PROLOG

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

NAME

12       erf, erff, erfl — error functions
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SYNOPSIS

15       #include <math.h>
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17       double erf(double x);
18       float erff(float x);
19       long double erfl(long double x);
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DESCRIPTION

22       The functionality described on this reference page is aligned with  the
23       ISO C  standard.  Any  conflict between the requirements described here
24       and the ISO C standard is unintentional. This  volume  of  POSIX.1‐2017
25       defers to the ISO C standard.
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27       These  functions  shall compute the error function of their argument x,
28       defined as:
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30              √_2π_x0∫e^t^2 dt
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32       An application wishing to check for error situations should  set  errno
33       to  zero  and  call  feclearexcept(FE_ALL_EXCEPT)  before calling these
34       functions. On return, if errno is non-zero or fetestexcept(FE_INVALID |
35       FE_DIVBYZERO  |  FE_OVERFLOW  | FE_UNDERFLOW) is non-zero, an error has
36       occurred.
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RETURN VALUE

39       Upon successful completion, these functions shall return the  value  of
40       the error function.
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42       If x is NaN, a NaN shall be returned.
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44       If x is ±0, ±0 shall be returned.
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46       If x is ±Inf, ±1 shall be returned.
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48       If  the  correct  value would cause underflow, a range error may occur,
49       and erf(), erff(), and erfl() shall  return  an  implementation-defined
50       value  no  greater  in  magnitude  than DBL_MIN, FLT_MIN, and LDBL_MIN,
51       respectively.
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53       If the IEC 60559 Floating-Point option  is  supported,  2  *  x/sqrt(π)
54       should be returned.
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ERRORS

57       These functions may fail if:
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59       Range Error The result underflows.
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61                   If  the  integer expression (math_errhandling & MATH_ERRNO)
62                   is non-zero, then errno shall be set to [ERANGE].   If  the
63                   integer  expression  (math_errhandling & MATH_ERREXCEPT) is
64                   non-zero, then the underflow floating-point exception shall
65                   be raised.
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67       The following sections are informative.
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EXAMPLES

70   Computing the Probability for a Normal Variate
71       This  example  shows how to use erf() to compute the probability that a
72       normal variate assumes a value in the range [x1,x2] with x1≤x2.
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74       This example uses the constant M_SQRT1_2  which  is  part  of  the  XSI
75       option.
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77
78           #include <math.h>
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80           double
81           Phi(const double x1, const double x2)
82           {
83               return ( erf(x2*M_SQRT1_2) - erf(x1*M_SQRT1_2) ) / 2;
84           }
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APPLICATION USAGE

87       Underflow occurs when |x| < DBL_MIN * (sqrt(π)/2).
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89       On   error,   the   expressions  (math_errhandling  &  MATH_ERRNO)  and
90       (math_errhandling & MATH_ERREXCEPT) are independent of each other,  but
91       at least one of them must be non-zero.
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RATIONALE

94       None.
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FUTURE DIRECTIONS

97       None.
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SEE ALSO

100       erfc(), feclearexcept(), fetestexcept(), isnan()
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102       The Base Definitions volume of POSIX.1‐2017, Section 4.20, Treatment of
103       Error Conditions for Mathematical Functions, <math.h>
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106       Portions of this text are reprinted and reproduced in  electronic  form
107       from  IEEE Std 1003.1-2017, Standard for Information Technology -- Por‐
108       table Operating System Interface (POSIX), The Open Group Base  Specifi‐
109       cations  Issue  7, 2018 Edition, Copyright (C) 2018 by the Institute of
110       Electrical and Electronics Engineers, Inc and The Open Group.   In  the
111       event of any discrepancy between this version and the original IEEE and
112       The Open Group Standard, the original IEEE and The Open Group  Standard
113       is  the  referee document. The original Standard can be obtained online
114       at http://www.opengroup.org/unix/online.html .
115
116       Any typographical or formatting errors that appear  in  this  page  are
117       most likely to have been introduced during the conversion of the source
118       files to man page format. To report such errors,  see  https://www.ker
119       nel.org/doc/man-pages/reporting_bugs.html .
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123IEEE/The Open Group                  2017                              ERF(3P)
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