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copied!<p>In GNU libm, the implementation of <code>sin</code> is system-dependent. Therefore you can find the implementation, for each platform, somewhere in the appropriate subdirectory of <a href="http://sourceware.org/git/?p=glibc.git;a=tree;f=sysdeps;hb=HEAD" rel="noreferrer">sysdeps</a>.</p> <p>One directory includes an implementation in C, contributed by IBM. Since October 2011, this is the code that actually runs when you call <code>sin()</code> on a typical x86-64 Linux system. It is apparently faster than the <code>fsin</code> assembly instruction. Source code: <a href="https://sourceware.org/git/?p=glibc.git;a=blob;f=sysdeps/ieee754/dbl-64/s_sin.c;hb=HEAD#l281" rel="noreferrer">sysdeps/ieee754/dbl-64/s_sin.c</a>, look for <code>__sin (double x)</code>.</p> <p>This code is very complex. No one software algorithm is as fast as possible and also accurate over the whole range of <em>x</em> values, so the library implements many different algorithms and its first job is to look at <em>x</em> and decide which algorithm to use. In some regions it uses what looks like the familiar Taylor series. Several of the algorithms first compute a quick result, then if that's not accurate enough, discard it and fall back on a slower algorithm.</p> <p>Older 32-bit versions of GCC/glibc used the <code>fsin</code> instruction, which is surprisingly inaccurate for some inputs. There's a <a href="http://randomascii.wordpress.com/2014/10/09/intel-underestimates-error-bounds-by-1-3-quintillion/" rel="noreferrer">fascinating blog post illustrating this with just 2 lines of code</a>.</p> <p>fdlibm's implementation of <code>sin</code> in pure C is much simpler than glibc's and is nicely commented. Source code: <a href="http://www.netlib.org/fdlibm/s_sin.c" rel="noreferrer">fdlibm/s_sin.c</a> and <a href="http://www.netlib.org/fdlibm/k_sin.c" rel="noreferrer">fdlibm/k_sin.c</a></p>

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