From 34b5f7d3099adbc3e294b64fedad6e09ea5a7364 Mon Sep 17 00:00:00 2001 From: Taylor R Campbell Date: Sat, 10 Aug 2019 15:18:41 +0000 Subject: [PATCH] Clarify error amplification. --- doc/ref-manual/numbers.texi | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/doc/ref-manual/numbers.texi b/doc/ref-manual/numbers.texi index 060106f88..750582c0d 100644 --- a/doc/ref-manual/numbers.texi +++ b/doc/ref-manual/numbers.texi @@ -863,8 +863,11 @@ via log rather than via log1p.) Similarly, although the condition number of exp near @math{0} is near @math{0}, its @emph{value} near @math{0} is near @math{1}, and the condition number of @math{y - 1} is unbounded for @math{y} near -@math{1}; in contrast, the condition number of expm1 near @math{0} is -near @math{1}: +@math{1}, so the intermediate error introduced by @code{(exp @var{z})} +may be amplified arbitrarily by then computing @code{(- (exp @var{z}) +1)}. +In contrast, the condition number of expm1 itself near @math{0} is +near @math{1}, so it does not inherently amplify errors: @iftex @tex -- 2.25.1