<title>About the Math Toolkit</title>
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</h5>
<p>
Utility functions for dealing with floating-point arithmetic, includes functions
- for floating point classification (fpclassify, isnan, isinf etc), sign manipulation,
- rounding, comparison, and computing the distance between floating point numbers.
+ for floating point classification (<code class="computeroutput"><span class="identifier">fpclassify</span></code>,
+ <code class="computeroutput"><span class="identifier">isnan</span></code>, <code class="computeroutput"><span class="identifier">isinf</span></code>
+ etc), sign manipulation, rounding, comparison, and computing the distance between
+ floating point numbers.
</p>
<h5>
<a name="math_toolkit.main_intro.h1"></a>
Width Floating-Point Types</a>
</h5>
<p>
- A set of typedefs similar to those provided by <code class="computeroutput"><span class="special"><</span><span class="identifier">cstdint</span><span class="special">></span></code>
- but for floating-point types.
+ A set of <code class="computeroutput"><span class="keyword">typedef</span></code>s similar to those
+ provided by <code class="computeroutput"><span class="special"><</span><span class="identifier">cstdint</span><span class="special">></span></code> but for floating-point types.
</p>
<h5>
<a name="math_toolkit.main_intro.h2"></a>
Constants</a>
</h5>
<p>
- A wide range of constants ranging from various multiples of π, fractions, through
- to euler's constant etc.
+ A wide range of high-precision constants ranging from various multiples of
+ π, fractions, through to Euler's constant etc.
</p>
<p>
These are of course usable from template code, or as non-templates with a simplified
Special Functions</a>
</h5>
<p>
- Provides a small number of high quality <a class="link" href="../special.html" title="Chapter 7. Special Functions">special functions</a>,
+ Provides a small number of high quality <a class="link" href="../special.html" title="Chapter 8. Special Functions">special functions</a>,
initially these were concentrated on functions used in statistical applications
along with those in the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Technical
Report on C++ Library Extensions</a>.
<span class="phrase"><a name="math_toolkit.main_intro.interpolation"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.interpolation">Interpolation</a>
</h5>
<p>
- Function interpolation via Barycentric or cubic B_spline approximations.
+ Function interpolation via Barycentric or cubic B_spline approximations. Smoothing.
</p>
<h5>
<a name="math_toolkit.main_intro.h8"></a>
- <span class="phrase"><a name="math_toolkit.main_intro.numerical_integration_and_differ"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.numerical_integration_and_differ">Numerical
- Integration and Differentiation</a>
+ <span class="phrase"><a name="math_toolkit.main_intro.numerical_integration_quadrature"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.numerical_integration_quadrature">Numerical
+ Integration (Quadrature) and Differentiation</a>
</h5>
<p>
A reasonably comprehensive set of routines for integration (trapezoidal, Gauss-Legendre,
- Gauss-Kronrod and double-exponential) and differentiation.
+ Gauss-Kronrod and double-exponential) and differentiation. (See also automatic
+ differentiation).
</p>
<p>
The integration routines are all usable for functions returning complex results
and Octonions</a>
</h5>
<p>
- Quaternion and Octonians as class templates similar to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span></code>.
+ Quaternions and Octonians as class templates similar to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span></code>.
+ </p>
+<h5>
+<a name="math_toolkit.main_intro.h10"></a>
+ <span class="phrase"><a name="math_toolkit.main_intro.automatic_differentiation"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.automatic_differentiation">Automatic
+ Differentiation</a>
+ </h5>
+<p>
+ Autodiff is a header-only C++ library that facilitates the automaticdifferentiation
+ (forward mode) of mathematical functions of single and multiple variables.
</p>
</div>
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