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    <p>The binary splitting method lends itself nicely to a template metaprogram which produces a type which represents a rational corresponding to an approximation of e. 13 iterations seems to be the maximum - any higher will produce a "integral constant overflow" error.</p> <pre><code>#include &lt;iostream&gt; #include &lt;iomanip&gt; template&lt;int NUMER = 0, int DENOM = 1&gt; struct Rational { enum {NUMERATOR = NUMER}; enum {DENOMINATOR = DENOM}; static double value; }; template&lt;int NUMER, int DENOM&gt; double Rational&lt;NUMER, DENOM&gt;::value = static_cast&lt;double&gt; (NUMER) / DENOM; template&lt;int ITERS, class APPROX = Rational&lt;2, 1&gt;, int I = 2&gt; struct CalcE { typedef Rational&lt;APPROX::NUMERATOR * I + 1, APPROX::DENOMINATOR * I&gt; NewApprox; typedef typename CalcE&lt;ITERS, NewApprox, I + 1&gt;::Result Result; }; template&lt;int ITERS, class APPROX&gt; struct CalcE&lt;ITERS, APPROX, ITERS&gt; { typedef APPROX Result; }; int test (int argc, char* argv[]) { std::cout &lt;&lt; std::setprecision (9); // ExpType is the type containing our approximation to e. typedef CalcE&lt;13&gt;::Result ExpType; // Call result() to produce the double value. std::cout &lt;&lt; "e ~ " &lt;&lt; ExpType::value &lt;&lt; std::endl; return 0; } </code></pre> <p>Another (non-metaprogram) templated variation will, at compile-time, calculate a double approximating e. This one doesn't have the limit on the number of iterations.</p> <pre><code>#include &lt;iostream&gt; #include &lt;iomanip&gt; template&lt;int ITERS, long long NUMERATOR = 2, long long DENOMINATOR = 1, int I = 2&gt; struct CalcE { static double result () { return CalcE&lt;ITERS, NUMERATOR * I + 1, DENOMINATOR * I, I + 1&gt;::result (); } }; template&lt;int ITERS, long long NUMERATOR, long long DENOMINATOR&gt; struct CalcE&lt;ITERS, NUMERATOR, DENOMINATOR, ITERS&gt; { static double result () { return (double)NUMERATOR / DENOMINATOR; } }; int main (int argc, char* argv[]) { std::cout &lt;&lt; std::setprecision (16); std::cout &lt;&lt; "e ~ " &lt;&lt; CalcE&lt;16&gt;::result () &lt;&lt; std::endl; return 0; } </code></pre> <p>In an optimised build the expression <code>CalcE&lt;16&gt;::result ()</code> will be replaced by the actual double value.</p> <p>Both are arguably quite efficient since they calculate e at compile time :-)</p>
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    1. POAn efficient way to compute mathematical constant e
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    1. COOVERKILL...Don't need to be this complex
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    2. COIt's just for fun...
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