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copied!<blockquote> <p><code>MethodImplOptions.InternalCall</code></p> </blockquote> <p>That means that the method is actually implemented in the CLR, written in C++. The just-in-time compiler consults a table with internally implemented methods and compiles the call to the C++ function directly.</p> <p>Having a look at the code requires the source code for the CLR. You can get that from the <a href="http://www.microsoft.com/download/en/details.aspx?displaylang=en&id=4917" rel="noreferrer">SSCLI20 distribution</a>. It was written around the .NET 2.0 time frame, I've found the low-level implementations, like <code>Math.Pow()</code> to be still largely accurate for later versions of the CLR.</p> <p>The lookup table is located in clr/src/vm/ecall.cpp. The section that's relevant to <code>Math.Pow()</code> looks like this:</p> <pre><code>FCFuncStart(gMathFuncs) FCIntrinsic("Sin", COMDouble::Sin, CORINFO_INTRINSIC_Sin) FCIntrinsic("Cos", COMDouble::Cos, CORINFO_INTRINSIC_Cos) FCIntrinsic("Sqrt", COMDouble::Sqrt, CORINFO_INTRINSIC_Sqrt) FCIntrinsic("Round", COMDouble::Round, CORINFO_INTRINSIC_Round) FCIntrinsicSig("Abs", &gsig_SM_Flt_RetFlt, COMDouble::AbsFlt, CORINFO_INTRINSIC_Abs) FCIntrinsicSig("Abs", &gsig_SM_Dbl_RetDbl, COMDouble::AbsDbl, CORINFO_INTRINSIC_Abs) FCFuncElement("Exp", COMDouble::Exp) FCFuncElement("Pow", COMDouble::Pow) // etc.. FCFuncEnd() </code></pre> <p>Searching for "COMDouble" takes you to clr/src/classlibnative/float/comfloat.cpp. I'll spare you the code, just have a look for yourself. It basically checks for corner cases, then calls the CRT's version of <code>pow()</code>.</p> <p>The only other implementation detail that's interesting is the FCIntrinsic macro in the table. That's a hint that the jitter may implement the function as an intrinsic. In other words, substitute the function call with a floating point machine code instruction. Which is not the case for <code>Pow()</code>, there is no FPU instruction for it. But certainly for the other simple operations. Notable is that this can make floating point math in C# substantially faster than the same code in C++, check <a href="https://stackoverflow.com/questions/686483/c-sharp-vs-c-big-performance-difference/687741#687741">this answer</a> for the reason why.</p> <p>By the way, the source code for the CRT is also available if you have the full version of Visual Studio vc/crt/src directory. You'll hit the wall on <code>pow()</code> though, Microsoft purchased that code from Intel. Doing a better job than the Intel engineers is unlikely. Although my high-school book's identity was twice as fast when I tried it:</p> <pre><code>public static double FasterPow(double x, double y) { return Math.Exp(y * Math.Log(x)); } </code></pre> <p>But not a true substitute because it accumulates error from 3 floating point operations and doesn't deal with the weirdo domain problems that Pow() has. Like 0^0 and -Infinity raised to any power.</p>

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