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<h1 id="firstHeading" class="firstHeading">expm1, expm1f, expm1l</h1> <table class="t-dcl-begin"> <tr class="t-dsc-header"> <th> Defined in header <code><math.h></code> </th> <th> </th> <th> </th> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">float expm1f( float arg );</pre>
</td> <td> (1) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">double expm1( double arg );</pre>
</td> <td> (2) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">long double expm1l( long double arg );</pre>
</td> <td> (3) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> <tr class="t-dsc-header"> <th> Defined in header <code><tgmath.h></code> </th> <th> </th> <th> </th> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">#define expm1( arg )</pre>
</td> <td> (4) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> </table> <div class="t-li1">
<span class="t-li">1-3)</span> Computes the <i>e</i> (Euler's number, <code>2.7182818</code>) raised to the given power <code>arg</code>, minus <code>1.0</code>. This function is more accurate than the expression <code><a href="http://en.cppreference.com/w/c/numeric/math/exp"><span class="kw657">exp</span></a><span class="br0">(</span>arg<span class="br0">)</span><span class="sy2">-</span><span class="nu16">1.0</span></code> if <code>arg</code> is close to zero.</div> <div class="t-li1">
<span class="t-li">4)</span> Type-generic macro: If <code>arg</code> has type <code>long double</code>, <code>expm1l</code> is called. Otherwise, if <code>arg</code> has integer type or the type <code>double</code>, <code>expm1</code> is called. Otherwise, <code>expm1f</code> is called.</div> <h3 id="Parameters"> Parameters</h3> <table class="t-par-begin"> <tr class="t-par"> <td> arg </td> <td> - </td> <td> floating point value </td>
</tr>
</table> <h3 id="Return_value"> Return value</h3> <p>If no errors occur e<sup class="t-su">arg</sup>-1 is returned.</p>
<p>If a range error due to overflow occurs, <code><a href="huge_val" title="c/numeric/math/HUGE VAL">+HUGE_VAL</a></code>, <code>+HUGE_VALF</code>, or <code>+HUGE_VALL</code> is returned.</p>
<p>If a range error occurs due to underflow, the correct result (after rounding) is returned.</p>
<h3 id="Error_handling"> Error handling</h3> <p>Errors are reported as specified in <code>math_errhandling</code>.</p>
<p>If the implementation supports IEEE floating-point arithmetic (IEC 60559),</p>
<ul>
<li> If the argument is ±0, it is returned, unmodified </li>
<li> If the argument is -∞, -1 is returned </li>
<li> If the argument is +∞, +∞ is returned </li>
<li> If the argument is NaN, NaN is returned </li>
</ul> <h3 id="Notes"> Notes</h3> <p>The functions <code>expm1</code> and <code><a href="log1p" title="c/numeric/math/log1p">log1p</a></code> are useful for financial calculations, for example, when calculating small daily interest rates: (1+x)<sup class="t-su">n</sup>-1 can be expressed as <code>expm1<span class="br0">(</span>n <span class="sy2">*</span> <a href="http://en.cppreference.com/w/c/numeric/math/log1p"><span class="kw661">log1p</span></a><span class="br0">(</span>x<span class="br0">)</span><span class="br0">)</span></code>. These functions also simplify writing accurate inverse hyperbolic functions.</p>
<p>For IEEE-compatible type <code>double</code>, overflow is guaranteed if 709.8 < arg.</p>
<h3 id="Example"> Example</h3> <div class="t-example"> <div class="c source-c"><pre data-language="c">#include <stdio.h>
#include <math.h>
#include <float.h>
#include <errno.h>
#include <fenv.h>
// #pragma STDC FENV_ACCESS ON
int main(void)
{
printf("expm1(1) = %f\n", expm1(1));
printf("Interest earned in 2 days on $100, compounded daily at 1%%\n"
" on a 30/360 calendar = %f\n",
100*expm1(2*log1p(0.01/360)));
printf("exp(1e-16)-1 = %g, but expm1(1e-16) = %g\n",
exp(1e-16)-1, expm1(1e-16));
// special values
printf("expm1(-0) = %f\n", expm1(-0.0));
printf("expm1(-Inf) = %f\n", expm1(-INFINITY));
//error handling
errno = 0; feclearexcept(FE_ALL_EXCEPT);
printf("expm1(710) = %f\n", expm1(710));
if(errno == ERANGE) perror(" errno == ERANGE");
if(fetestexcept(FE_OVERFLOW)) puts(" FE_OVERFLOW raised");
}</pre></div> <p>Possible output:</p>
<div class="text source-text"><pre data-language="c">expm1(1) = 1.718282
Interest earned in 2 days on $100, compounded daily at 1%
on a 30/360 calendar = 0.005556
exp(1e-16)-1 = 0, but expm1(1e-16) = 1e-16
expm1(-0) = -0.000000
expm1(-Inf) = -1.000000
expm1(710) = inf
errno == ERANGE: Result too large
FE_OVERFLOW raised</pre></div> </div> <h3 id="References"> References</h3> <ul>
<li> C17 standard (ISO/IEC 9899:2018): </li>
<ul>
<li> 7.12.6.3 The expm1 functions (p: 177) </li>
<li> 7.25 Type-generic math <tgmath.h> (p: 272-273) </li>
<li> F.10.3.3 The expm1 functions (p: 379) </li>
</ul>
<li> C11 standard (ISO/IEC 9899:2011): </li>
<ul>
<li> 7.12.6.3 The expm1 functions (p: 243) </li>
<li> 7.25 Type-generic math <tgmath.h> (p: 373-375) </li>
<li> F.10.3.3 The expm1 functions (p: 521) </li>
</ul>
<li> C99 standard (ISO/IEC 9899:1999): </li>
<ul>
<li> 7.12.6.3 The expm1 functions (p: 223-224) </li>
<li> 7.22 Type-generic math <tgmath.h> (p: 335-337) </li>
<li> F.9.3.3 The expm1 functions (p: 458) </li>
</ul>
</ul> <h3 id="See_also"> See also</h3> <table class="t-dsc-begin"> <tr class="t-dsc"> <td> <div><a href="exp" title="c/numeric/math/exp"> <span class="t-lines"><span>exp</span><span>expf</span><span>expl</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes <i>e</i> raised to the given power (\({\small e^x}\)e<sup>x</sup>) <br> <span class="t-mark">(function)</span> </td>
</tr> <tr class="t-dsc"> <td> <div><a href="exp2" title="c/numeric/math/exp2"> <span class="t-lines"><span>exp2</span><span>exp2f</span><span>exp2l</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes <i>2</i> raised to the given power (\({\small 2^x}\)2<sup>x</sup>) <br> <span class="t-mark">(function)</span> </td>
</tr> <tr class="t-dsc"> <td> <div><a href="log1p" title="c/numeric/math/log1p"> <span class="t-lines"><span>log1p</span><span>log1pf</span><span>log1pl</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes natural (base-<i>e</i>) logarithm of 1 plus the given number (\({\small \ln{(1+x)} }\)ln(1+x)) <br> <span class="t-mark">(function)</span> </td>
</tr> <tr class="t-dsc"> <td colspan="2"> <span><a href="https://en.cppreference.com/w/cpp/numeric/math/expm1" title="cpp/numeric/math/expm1">C++ documentation</a></span> for <code>expm1</code> </td>
</tr> </table> <div class="_attribution">
<p class="_attribution-p">
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<a href="https://en.cppreference.com/w/c/numeric/math/expm1" class="_attribution-link">https://en.cppreference.com/w/c/numeric/math/expm1</a>
</p>
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