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<title>GNU Scientific Library &ndash; Reference Manual: Elementary Functions</title>

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<a name="Elementary-Functions"></a>
<div class="header">
<p>
Next: <a href="Small-integer-powers.html#Small-integer-powers" accesskey="n" rel="next">Small integer powers</a>, Previous: <a href="Infinities-and-Not_002da_002dnumber.html#Infinities-and-Not_002da_002dnumber" accesskey="p" rel="previous">Infinities and Not-a-number</a>, Up: <a href="Mathematical-Functions.html#Mathematical-Functions" accesskey="u" rel="up">Mathematical Functions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Elementary-Functions-1"></a>
<h3 class="section">4.3 Elementary Functions</h3>

<p>The following routines provide portable implementations of functions
found in the BSD math library.  When native versions are not available
the functions described here can be used instead.  The substitution can
be made automatically if you use <code>autoconf</code> to compile your
application (see <a href="Portability-functions.html#Portability-functions">Portability functions</a>).
</p>
<dl>
<dt><a name="index-gsl_005flog1p"></a>Function: <em>double</em> <strong>gsl_log1p</strong> <em>(const double <var>x</var>)</em></dt>
<dd><a name="index-log1p"></a>
<a name="index-logarithm_002c-computed-accurately-near-1"></a>
<p>This function computes the value of <em>\log(1+x)</em> in a way that is
accurate for small <var>x</var>. It provides an alternative to the BSD math
function <code>log1p(x)</code>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fexpm1"></a>Function: <em>double</em> <strong>gsl_expm1</strong> <em>(const double <var>x</var>)</em></dt>
<dd><a name="index-expm1"></a>
<a name="index-exponential_002c-difference-from-1-computed-accurately"></a>
<p>This function computes the value of <em>\exp(x)-1</em> in a way that is
accurate for small <var>x</var>. It provides an alternative to the BSD math
function <code>expm1(x)</code>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fhypot"></a>Function: <em>double</em> <strong>gsl_hypot</strong> <em>(const double <var>x</var>, const double <var>y</var>)</em></dt>
<dd><a name="index-hypot"></a>
<a name="index-euclidean-distance-function_002c-hypot"></a>
<a name="index-length_002c-computed-accurately-using-hypot"></a>
<p>This function computes the value of
<em>\sqrt{x^2 + y^2}</em> in a way that avoids overflow. It provides an
alternative to the BSD math function <code>hypot(x,y)</code>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fhypot3"></a>Function: <em>double</em> <strong>gsl_hypot3</strong> <em>(const double <var>x</var>, const double <var>y</var>, const double <var>z</var>)</em></dt>
<dd><a name="index-euclidean-distance-function_002c-hypot-1"></a>
<a name="index-length_002c-computed-accurately-using-hypot-1"></a>
<p>This function computes the value of
<em>\sqrt{x^2 + y^2 + z^2}</em> in a way that avoids overflow.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005facosh"></a>Function: <em>double</em> <strong>gsl_acosh</strong> <em>(const double <var>x</var>)</em></dt>
<dd><a name="index-acosh"></a>
<a name="index-hyperbolic-cosine_002c-inverse"></a>
<a name="index-inverse-hyperbolic-cosine"></a>
<p>This function computes the value of <em>\arccosh(x)</em>. It provides an
alternative to the standard math function <code>acosh(x)</code>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fasinh"></a>Function: <em>double</em> <strong>gsl_asinh</strong> <em>(const double <var>x</var>)</em></dt>
<dd><a name="index-asinh"></a>
<a name="index-hyperbolic-sine_002c-inverse"></a>
<a name="index-inverse-hyperbolic-sine"></a>
<p>This function computes the value of <em>\arcsinh(x)</em>. It provides an
alternative to the standard math function <code>asinh(x)</code>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fatanh"></a>Function: <em>double</em> <strong>gsl_atanh</strong> <em>(const double <var>x</var>)</em></dt>
<dd><a name="index-atanh"></a>
<a name="index-hyperbolic-tangent_002c-inverse"></a>
<a name="index-inverse-hyperbolic-tangent"></a>
<p>This function computes the value of <em>\arctanh(x)</em>. It provides an
alternative to the standard math function <code>atanh(x)</code>.
</p></dd></dl>


<dl>
<dt><a name="index-gsl_005fldexp"></a>Function: <em>double</em> <strong>gsl_ldexp</strong> <em>(double <var>x</var>, int <var>e</var>)</em></dt>
<dd><a name="index-ldexp"></a>
<p>This function computes the value of <em>x * 2^e</em>. It provides an
alternative to the standard math function <code>ldexp(x,e)</code>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005ffrexp"></a>Function: <em>double</em> <strong>gsl_frexp</strong> <em>(double <var>x</var>, int * <var>e</var>)</em></dt>
<dd><a name="index-frexp"></a>
<p>This function splits the number <em>x</em> into its normalized fraction
<em>f</em> and exponent <em>e</em>, such that <em>x = f * 2^e</em> and
<em>0.5 &lt;= f &lt; 1</em>. The function returns <em>f</em> and stores the
exponent in <em>e</em>. If <em>x</em> is zero, both <em>f</em> and <em>e</em>
are set to zero. This function provides an alternative to the standard
math function <code>frexp(x, e)</code>.
</p></dd></dl>

<hr>
<div class="header">
<p>
Next: <a href="Small-integer-powers.html#Small-integer-powers" accesskey="n" rel="next">Small integer powers</a>, Previous: <a href="Infinities-and-Not_002da_002dnumber.html#Infinities-and-Not_002da_002dnumber" accesskey="p" rel="previous">Infinities and Not-a-number</a>, Up: <a href="Mathematical-Functions.html#Mathematical-Functions" accesskey="u" rel="up">Mathematical Functions</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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