196 lines
7.3 KiB
HTML
196 lines
7.3 KiB
HTML
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<title>expm1</title>
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<basefont size="3"> <a name="expm1"></a> <a name="tag_03_134"></a><!-- expm1 -->
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<!--header start-->
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<center><font size="2">The Open Group Base Specifications Issue 6<br>
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IEEE Std 1003.1-2001<br>
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Copyright © 2001 The IEEE and The Open Group, All Rights reserved.</font></center>
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<!--header end-->
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<hr size="2" noshade>
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<h4><a name="tag_03_134_01"></a>NAME</h4>
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<blockquote>expm1, expm1f, expm1l - compute exponential functions</blockquote>
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<h4><a name="tag_03_134_02"></a>SYNOPSIS</h4>
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<blockquote class="synopsis">
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<p><code><tt>#include <<a href="../basedefs/math.h.html">math.h</a>><br>
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<br>
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double expm1(double</tt> <i>x</i><tt>);<br>
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float expm1f(float</tt> <i>x</i><tt>);<br>
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long double expm1l(long double</tt> <i>x</i><tt>);<br>
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</tt></code></p>
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</blockquote>
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<h4><a name="tag_03_134_03"></a>DESCRIPTION</h4>
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<blockquote>
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<div class="box"><sup>[<a href="javascript:open_code('CX')">CX</a>]</sup> <img src="../images/opt-start.gif" alt="[Option Start]"
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border="0"> The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the
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requirements described here and the ISO C standard is unintentional. This volume of IEEE Std 1003.1-2001 defers to
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the ISO C standard. <img src="../images/opt-end.gif" alt="[Option End]" border="0"></div>
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<p>These functions shall compute <i>e<sup><small>x</small></sup></i>-1.0.</p>
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<p>An application wishing to check for error situations should set <i>errno</i> to zero and call
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<i>feclearexcept</i>(FE_ALL_EXCEPT) before calling these functions. On return, if <i>errno</i> is non-zero or
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<i>fetestexcept</i>(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.</p>
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</blockquote>
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<h4><a name="tag_03_134_04"></a>RETURN VALUE</h4>
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<blockquote>
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<p>Upon successful completion, these functions return <i>e<small><sup>x</sup></small></i>-1.0.</p>
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<p>If the correct value would cause overflow, a range error shall occur and <i>expm1</i>(), <i>expm1f</i>(), and <i>expm1l</i>()
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shall return the value of the macro HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively.</p>
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<p><sup>[<a href="javascript:open_code('MX')">MX</a>]</sup> <img src="../images/opt-start.gif" alt="[Option Start]" border="0"> If
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<i>x</i> is NaN, a NaN shall be returned.</p>
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<p>If <i>x</i> is ±0, ±0 shall be returned.</p>
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<p>If <i>x</i> is -Inf, -1 shall be returned.</p>
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<p>If <i>x</i> is +Inf, <i>x</i> shall be returned.</p>
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<p>If <i>x</i> is subnormal, a range error may occur and <i>x</i> should be returned. <img src="../images/opt-end.gif" alt=
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"[Option End]" border="0"></p>
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</blockquote>
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<h4><a name="tag_03_134_05"></a>ERRORS</h4>
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<blockquote>
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<p>These functions shall fail if:</p>
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<dl compact>
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<dt>Range Error</dt>
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<dd>The result overflows.
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<p>If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then <i>errno</i> shall be set to [ERANGE]. If the
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integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be
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raised.</p>
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</dd>
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</dl>
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<p>These functions may fail if:</p>
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<dl compact>
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<dt>Range Error</dt>
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<dd><sup>[<a href="javascript:open_code('MX')">MX</a>]</sup> <img src="../images/opt-start.gif" alt="[Option Start]" border="0">
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The value of <i>x</i> is subnormal.
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<p>If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then <i>errno</i> shall be set to [ERANGE]. If the
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integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be
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raised. <img src="../images/opt-end.gif" alt="[Option End]" border="0"></p>
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</dd>
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</dl>
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</blockquote>
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<hr>
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<div class="box"><em>The following sections are informative.</em></div>
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<h4><a name="tag_03_134_06"></a>EXAMPLES</h4>
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<blockquote>
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<p>None.</p>
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</blockquote>
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<h4><a name="tag_03_134_07"></a>APPLICATION USAGE</h4>
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<blockquote>
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<p>The value of <i>expm1</i>(<i>x</i>) may be more accurate than <i>exp</i>(<i>x</i>)-1.0 for small values of <i>x</i>.</p>
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<p>The <i>expm1</i>() and <a href="../functions/log1p.html"><i>log1p</i>()</a> functions are useful for financial calculations of
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((1+<i>x</i>)<sup><small><i>n</i></small></sup>-1)/<i>x</i>, namely:</p>
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<pre>
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<tt>expm1(</tt><i>n</i> <tt>* log1p(</tt><i>x</i><tt>))/</tt><i>x</i>
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</pre>
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<p>when <i>x</i> is very small (for example, when calculating small daily interest rates). These functions also simplify writing
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accurate inverse hyperbolic functions.</p>
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<p>For IEEE Std 754-1985 <b>double</b>, 709.8 < <i>x</i> implies <i>expm1</i>( <i>x</i>) has overflowed.</p>
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<p>On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of
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each other, but at least one of them must be non-zero.</p>
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</blockquote>
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<h4><a name="tag_03_134_08"></a>RATIONALE</h4>
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<blockquote>
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<p>None.</p>
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</blockquote>
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<h4><a name="tag_03_134_09"></a>FUTURE DIRECTIONS</h4>
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<blockquote>
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<p>None.</p>
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</blockquote>
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<h4><a name="tag_03_134_10"></a>SEE ALSO</h4>
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<blockquote>
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<p><a href="exp.html"><i>exp</i>()</a> , <a href="feclearexcept.html"><i>feclearexcept</i>()</a> , <a href=
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"fetestexcept.html"><i>fetestexcept</i>()</a> , <a href="ilogb.html"><i>ilogb</i>()</a> , <a href="log1p.html"><i>log1p</i>()</a> ,
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the Base Definitions volume of IEEE Std 1003.1-2001, <a href="../basedefs/xbd_chap04.html#tag_04_18">Section 4.18,
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Treatment of Error Conditions for Mathematical Functions</a>, <a href="../basedefs/math.h.html"><i><math.h></i></a></p>
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</blockquote>
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<h4><a name="tag_03_134_11"></a>CHANGE HISTORY</h4>
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<blockquote>
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<p>First released in Issue 4, Version 2.</p>
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</blockquote>
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<h4><a name="tag_03_134_12"></a>Issue 5</h4>
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<blockquote>
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<p>Moved from X/OPEN UNIX extension to BASE.</p>
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</blockquote>
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<h4><a name="tag_03_134_13"></a>Issue 6</h4>
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<blockquote>
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<p>The <i>expm1f</i>() and <i>expm1l</i>() functions are added for alignment with the ISO/IEC 9899:1999 standard.</p>
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<p>The <i>expm1</i>() function is no longer marked as an extension.</p>
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<p>The DESCRIPTION, RETURN VALUE, ERRORS, and APPLICATION USAGE sections are revised to align with the ISO/IEC 9899:1999
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standard.</p>
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<p>IEC 60559:1989 standard floating-point extensions over the ISO/IEC 9899:1999 standard are marked.</p>
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</blockquote>
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<div class="box"><em>End of informative text.</em></div>
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<hr>
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UNIX ® is a registered Trademark of The Open Group.<br>
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POSIX ® is a registered Trademark of The IEEE.<br>
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[ <a href="../mindex.html">Main Index</a> | <a href="../basedefs/contents.html">XBD</a> | <a href=
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"../utilities/contents.html">XCU</a> | <a href="../functions/contents.html">XSH</a> | <a href="../xrat/contents.html">XRAT</a>
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