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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"><html><head><meta name="generator" content="HTML Tidy, see www.w3.org"><meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"><link type="text/css" rel="stylesheet" href="style.css"><!-- Generated by The Open Group's rhtm tool v1.2.1 --><!-- Copyright (c) 2001-2004 IEEE and The Open Group, All Rights Reserved --><title>erf</title></head><body bgcolor="white"><script type="text/javascript" language="JavaScript" src="../jscript/codes.js"></script><basefont size="3"> <a name="erf"></a> <a name="tag_03_126"></a><!-- erf --> <!--header start--><center><font size="2">The Open Group Base Specifications Issue 6<br>IEEE Std 1003.1, 2004 Edition<br>Copyright © 2001-2004 The IEEE and The Open Group, All Rights reserved.</font></center><!--header end--><hr size="2" noshade><h4><a name="tag_03_126_01"></a>NAME</h4><blockquote>erf, erff, erfl - error functions</blockquote><h4><a name="tag_03_126_02"></a>SYNOPSIS</h4><blockquote class="synopsis"><p><code><tt>#include <<a href="../basedefs/math.h.html">math.h</a>><br><br> double erf(double</tt> <i>x</i><tt>);<br> float erff(float</tt> <i>x</i><tt>);<br> long double erfl(long double</tt> <i>x</i><tt>);<br></tt></code></p></blockquote><h4><a name="tag_03_126_03"></a>DESCRIPTION</h4><blockquote><div class="box"><sup>[<a href="javascript:open_code('CX')">CX</a>]</sup> <img src="../images/opt-start.gif" alt="[Option Start]"border="0"> The functionality described on this reference page is aligned with the ISO C standard. Any conflict between therequirements described here and the ISO C standard is unintentional. This volume of IEEE Std 1003.1-2001 defers tothe ISO C standard. <img src="../images/opt-end.gif" alt="[Option End]" border="0"></div><p>These functions shall compute the error function of their argument <i>x</i>, defined as:</p><blockquote><img src="../images/erf.gif"></blockquote><p>An application wishing to check for error situations should set <i>errno</i> to zero and call<i>feclearexcept</i>(FE_ALL_EXCEPT) before calling these functions. On return, if <i>errno</i> is non-zero or<i>fetestexcept</i>(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.</p></blockquote><h4><a name="tag_03_126_04"></a>RETURN VALUE</h4><blockquote><p>Upon successful completion, these functions shall return the value of the error function.</p><p><sup>[<a href="javascript:open_code('MX')">MX</a>]</sup> <img src="../images/opt-start.gif" alt="[Option Start]" border="0"> If<i>x</i> is NaN, a NaN shall be returned.</p><p>If <i>x</i> is ±0, ±0 shall be returned.</p><p>If <i>x</i> is ±Inf, ±1 shall be returned.</p><p>If <i>x</i> is subnormal, a range error may occur, and 2 * <i>x</i>/ <i>sqrt</i>(<img src="../images/pi.gif" border="0">) shouldbe returned. <img src="../images/opt-end.gif" alt="[Option End]" border="0"></p></blockquote><h4><a name="tag_03_126_05"></a>ERRORS</h4><blockquote><p>These functions may fail if:</p><dl compact><dt>Range Error</dt><dd><sup>[<a href="javascript:open_code('MX')">MX</a>]</sup> <img src="../images/opt-start.gif" alt="[Option Start]" border="0">The result underflows. <p>If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then <i>errno</i> shall be set to [ERANGE]. If theinteger expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall beraised. <img src="../images/opt-end.gif" alt="[Option End]" border="0"></p></dd></dl></blockquote><hr><div class="box"><em>The following sections are informative.</em></div><h4><a name="tag_03_126_06"></a>EXAMPLES</h4><blockquote><h5><a name="tag_03_126_06_01"></a>Computing the Probability for a Normal Variate</h5><p>This example shows how to use <i>erf</i>() to compute the probability that a normal variate assumes a value in the range[<i>x</i>1,<i>x</i>2] with <i>x</i>1<=<i>x</i>2. This example uses the constant M_SQRT1_2 which is an XSI extension.</p><pre><tt>#include <math.h><br>doublePhi(const double x1, const double x2){ return ( erf(x2*M_SQRT1_2) - erf(x1*M_SQRT1_2) ) / 2;}</tt></pre></blockquote><h4><a name="tag_03_126_07"></a>APPLICATION USAGE</h4><blockquote><p>Underflow occurs when |<i>x</i>| < DBL_MIN * ( <i>sqrt</i>(<img src="../images/pi.gif" border="0">)/2).</p><p>On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent ofeach other, but at least one of them must be non-zero.</p></blockquote><h4><a name="tag_03_126_08"></a>RATIONALE</h4><blockquote><p>None.</p></blockquote><h4><a name="tag_03_126_09"></a>FUTURE DIRECTIONS</h4><blockquote><p>None.</p></blockquote><h4><a name="tag_03_126_10"></a>SEE ALSO</h4><blockquote><p><a href="erfc.html"><i>erfc</i>()</a>, <a href="feclearexcept.html"><i>feclearexcept</i>()</a>, <a href="fetestexcept.html"><i>fetestexcept</i>()</a>, <a href="isnan.html"><i>isnan</i>()</a>, the Base Definitions volume ofIEEE Std 1003.1-2001, <a href="../basedefs/xbd_chap04.html#tag_04_18">Section 4.18, Treatment of Error Conditions forMathematical Functions</a>, <a href="../basedefs/math.h.html"><i><math.h></i></a></p></blockquote><h4><a name="tag_03_126_11"></a>CHANGE HISTORY</h4><blockquote><p>First released in Issue 1. Derived from Issue 1 of the SVID.</p></blockquote><h4><a name="tag_03_126_12"></a>Issue 5</h4><blockquote><p>The DESCRIPTION is updated to indicate how an application should check for an error. This text was previously published in theAPPLICATION USAGE section.</p></blockquote><h4><a name="tag_03_126_13"></a>Issue 6</h4><blockquote><p>The <i>erf</i>() function is no longer marked as an extension.</p><p>The <a href="../functions/erfc.html"><i>erfc</i>()</a> function is split out onto its own reference page.</p><p>The <i>erff</i>() and <i>erfl</i>() functions are added for alignment with the ISO/IEC 9899:1999 standard.</p><p>The DESCRIPTION, RETURN VALUE, ERRORS, and APPLICATION USAGE sections are revised to align with the ISO/IEC 9899:1999standard.</p><p>IEC 60559:1989 standard floating-point extensions over the ISO/IEC 9899:1999 standard are marked.</p><p>IEEE Std 1003.1-2001/Cor 2-2004, item XSH/TC2/D6/22 is applied, adding the example to the EXAMPLES section.<br></p></blockquote><div class="box"><em>End of informative text.</em></div><hr size="2" noshade><center><font size="2"><!--footer start-->UNIX ® is a registered Trademark of The Open Group.<br>POSIX ® is a registered Trademark of The IEEE.<br>[ <a href="../mindex.html">Main Index</a> | <a href="../basedefs/contents.html">XBD</a> | <a href="../utilities/contents.html">XCU</a> | <a href="../functions/contents.html">XSH</a> | <a href="../xrat/contents.html">XRAT</a>]</font></center><!--footer end--><hr size="2" noshade></body></html>⌨️ 快捷键说明
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