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<h3 class="section">4.3 Elementary Functions</h3>
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<p>The following routines provide portable implementations of functions
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found in the BSD math library. When native versions are not available
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the functions described here can be used instead. The substitution can
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be made automatically if you use <code>autoconf</code> to compile your
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application (see <a href="Portability-functions.html#Portability-functions">Portability functions</a>).
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— Function: double <b>gsl_log1p</b> (<var>const double x</var>)<var><a name="index-gsl_005flog1p-80"></a></var><br>
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<blockquote><p><a name="index-log1p-81"></a><a name="index-logarithm_002c-computed-accurately-near-1-82"></a>This function computes the value of \log(1+x) in a way that is
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accurate for small <var>x</var>. It provides an alternative to the BSD math
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function <code>log1p(x)</code>.
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</p></blockquote></div>
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— Function: double <b>gsl_expm1</b> (<var>const double x</var>)<var><a name="index-gsl_005fexpm1-83"></a></var><br>
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<blockquote><p><a name="index-expm1-84"></a><a name="index-exponential_002c-difference-from-1-computed-accurately-85"></a>This function computes the value of \exp(x)-1 in a way that is
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accurate for small <var>x</var>. It provides an alternative to the BSD math
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function <code>expm1(x)</code>.
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</p></blockquote></div>
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— Function: double <b>gsl_hypot</b> (<var>const double x, const double y</var>)<var><a name="index-gsl_005fhypot-86"></a></var><br>
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<blockquote><p><a name="index-hypot-87"></a><a name="index-euclidean-distance-function_002c-hypot-88"></a><a name="index-length_002c-computed-accurately-using-hypot-89"></a>This function computes the value of
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<!-- {$\sqrt{x^2 + y^2}$} -->
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\sqrt{x^2 + y^2} in a way that avoids overflow. It provides an
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alternative to the BSD math function <code>hypot(x,y)</code>.
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</p></blockquote></div>
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— Function: double <b>gsl_acosh</b> (<var>const double x</var>)<var><a name="index-gsl_005facosh-90"></a></var><br>
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<blockquote><p><a name="index-acosh-91"></a><a name="index-hyperbolic-cosine_002c-inverse-92"></a><a name="index-inverse-hyperbolic-cosine-93"></a>This function computes the value of \arccosh(x). It provides an
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alternative to the standard math function <code>acosh(x)</code>.
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</p></blockquote></div>
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— Function: double <b>gsl_asinh</b> (<var>const double x</var>)<var><a name="index-gsl_005fasinh-94"></a></var><br>
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<blockquote><p><a name="index-asinh-95"></a><a name="index-hyperbolic-sine_002c-inverse-96"></a><a name="index-inverse-hyperbolic-sine-97"></a>This function computes the value of \arcsinh(x). It provides an
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alternative to the standard math function <code>asinh(x)</code>.
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</p></blockquote></div>
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— Function: double <b>gsl_atanh</b> (<var>const double x</var>)<var><a name="index-gsl_005fatanh-98"></a></var><br>
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<blockquote><p><a name="index-atanh-99"></a><a name="index-hyperbolic-tangent_002c-inverse-100"></a><a name="index-inverse-hyperbolic-tangent-101"></a>This function computes the value of \arctanh(x). It provides an
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alternative to the standard math function <code>atanh(x)</code>.
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</p></blockquote></div>
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— Function: double <b>gsl_ldexp</b> (<var>double x, int e</var>)<var><a name="index-gsl_005fldexp-102"></a></var><br>
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<blockquote><p><a name="index-ldexp-103"></a>This function computes the value of x * 2^e. It provides an
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alternative to the standard math function <code>ldexp(x,e)</code>.
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</p></blockquote></div>
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— Function: double <b>gsl_frexp</b> (<var>double x, int * e</var>)<var><a name="index-gsl_005ffrexp-104"></a></var><br>
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<blockquote><p><a name="index-frexp-105"></a>This function splits the number x into its normalized fraction
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f and exponent e, such that x = f * 2^e and
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<!-- {$0.5 \le f < 1$} -->
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0.5 <= f < 1. The function returns f and stores the
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exponent in e. If x is zero, both f and e
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are set to zero. This function provides an alternative to the standard
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math function <code>frexp(x, e)</code>.
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</p></blockquote></div>
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