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| author | Paul Zimmermann <Paul.Zimmermann@inria.fr> | 2017-11-15 15:17:15 +0100 |
|---|---|---|
| committer | Paul Zimmermann <Paul.Zimmermann@inria.fr> | 2017-11-15 15:17:15 +0100 |
| commit | 6f2ca79a19f20307ee3b5f619be2f31cab107bd5 (patch) | |
| tree | a94e61407eec4972f47ce96910799502f3b34a54 | |
| parent | dd32b241d83c3b58cd28815f3ee9adfd2ede7dd1 (diff) | |
| download | mpc-git-6f2ca79a19f20307ee3b5f619be2f31cab107bd5.tar.gz | |
small improvement
| -rw-r--r-- | doc/algorithms.tex | 3 |
1 files changed, 2 insertions, 1 deletions
diff --git a/doc/algorithms.tex b/doc/algorithms.tex index a7b5bcc..0dc83bf 100644 --- a/doc/algorithms.tex +++ b/doc/algorithms.tex @@ -1910,7 +1910,8 @@ First, we compute $\pi$ with rounding to nearest and an absolute error of \ulp{0.5}. Using Proposition~\ref {prop:relerror} we obtain a relative error of $\relerror (\appro {\pi}) \leq 2^{-p}$ at precision~$p$, which would be enough for the following analysis. However, we can be a bit more -precise, knowing the first few binary digits of $\pi$: As soon as $p \geq 8$, +precise, knowing the first few binary digits of $\pi$: As soon as $p \geq 7$, +% for p=6, we get 25/8 < 201/2^6, for p=7 we get 101/32 > 201/2^6 we have $201/2^6 \leq \appro {\pi}$, so \[ \relerror (\appro {\pi}) |