From: Taylor R Campbell <campbell@mumble.net>
Date: Sat, 10 Aug 2019 15:18:41 +0000 (+0000)
Subject: Clarify error amplification.
X-Git-Tag: mit-scheme-pucked-10.1.20~11^2~90
X-Git-Url: https://birchwood-abbey.net/git?a=commitdiff_plain;h=34b5f7d3099adbc3e294b64fedad6e09ea5a7364;p=mit-scheme.git

Clarify error amplification.
---

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