unified computation of pow_ui and pow_si in a function pow_usi, thereby

applying binary exponentiation in the case of negative exponent


git-svn-id: svn://scm.gforge.inria.fr/svn/mpc/trunk@788 211d60ee-9f03-0410-a15a-8952a2c7a4e4

1 files changed, 1 insertions, 1 deletions

diff --git a/doc/algorithms.tex b/doc/algorithms.tex
index 4284ef6..6ca7454 100644
--- a/doc/algorithms.tex
+++ b/doc/algorithms.tex
@@ -1647,7 +1647,7 @@ on the real part and of
 on the imaginary part of the result.
 
 If we further assume that $(n-1) 2^{-p} \leq 1$, then
-$(1 + 2^{-p})^{n-1} - 1 \leq (2 n - 2) 2^{-p}$,
+$(1 + 2^{-p})^{n-1} - 1 \leq 2 (n - 1) 2^{-p}$,
 because $(1+\varepsilon)^m-1 = \exp(m \log(1+\varepsilon)) - 1
 \leq \exp(\varepsilon m) - 1 \leq 2 \varepsilon m$ as long as
 $\varepsilon m \leq 1$. This gives the simplified bounds