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pleroyeggrobin
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Update documentation/Sin Cos.tex
Co-authored-by: Robin Leroy <egg.robin.leroy@gmail.com>
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documentation/Sin Cos.tex

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@@ -284,7 +284,7 @@ \subsection*{Argument Reduction Using the Two-Term Approximation}
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Therefore, as long as $\gk'_1 > 2$, there exist arguments $x$ for which $\abs{\gd y} > \abs y$.
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} using algorithm 4 of \cite{HidaLiBailey2007}.
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To compute the overall error on argument reduction\footnote{Note that this error analysis is correct even in the face of misrounding. Misrounding can combine with the argument reduction error, though, to cause $\abs{y - {\gd y}}$ to move farther above $\frac{\Pi}{4}$}, first remember that, from equation (\ref{eqnpitwoterms}), we have:
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To compute the overall error on argument reduction\footnote{Note that this error analysis is correct even in the face of misrounding. Misrounding can combine with the argument reduction error, though, to cause $\abs{y - {\gd y}}$ to move farther above $\frac{\Pi}{4}$.}, first remember that, from equation (\ref{eqnpitwoterms}), we have:
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\[
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C_1 + \gd C_1 = \frac{\Pi}{2} + \gz \quad \text{with} \quad \abs{\gz} \leq 2^{\gk'_1 - M - 1} \ULP\of{\frac{\Pi}{2}}
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\]

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