As the other reply said, the function contract and an explanation of the implementation are different beasts. The Intel manual said that fsin is accurate across a huge range of values. Elsewhere the Manual hinted at Intel's range reduction algorithm such that a numerical analyst could suspect that there was a problem. So, to a numerical analyst the documentation was contradictory. To anybody else it was clear -- guaranteed one ulps precision. The documentation was therefore at best misleading, but for most people it was just wrong. Linus Torvalds was fooled, for example.

> If you let x = pi, then people would ordinarily expect that sin (x) = 0.

Many people would expect that, although the article (my article) most certainly did not expect that.

The calculation being done in the article takes into account the fact that double(pi) is not the same as the mathematical constant pi and it uses that and the properties of sine to measure the error in double(pi). This is an unusual but perfectly reasonable calculation to make. It failed because of the limitations of fsin. Those limitations are contradictory to the documentation. Hence the article.

> A more precise approximation according to Wikipedia would have been...

You don't need to go to Wikipedia, you just have to RTA. It lists a 192-bit hexadecimal approximation of pi.

> The reality is that the correct result would have been zero

No. Zero is the correct answer if doing symbolic or infinite precision math, but I did not make that assumption because I was doing double-precision math.