Reflect recent patch for float % and divmod() by Tim Peters. Content
updates by Tim Peters, markup by FLD.
diff --git a/Doc/lib/libfuncs.tex b/Doc/lib/libfuncs.tex
index df384af..d2167fb 100644
--- a/Doc/lib/libfuncs.tex
+++ b/Doc/lib/libfuncs.tex
@@ -178,8 +178,12 @@
operand types, the rules for binary arithmetic operators apply. For
plain and long integers, the result is the same as
\code{(\var{a} / \var{b}, \var{a} \%{} \var{b})}.
- For floating point numbers the result is the same as
- \code{(math.floor(\var{a} / \var{b}), \var{a} \%{} \var{b})}.
+ For floating point numbers the result is \code{(\var{q}, \var{a} \%{}
+ \var{b})}, where \var{q} is usually \code{math.floor(\var{a} /
+ \var{b})} but may be 1 less than that. In any case \code{\var{q} *
+ \var{b} + \var{a} \%{} \var{b}} is very close to \var{a}, if
+ \code{\var{a} \%{} \var{b}} is non-zero it has the same sign as
+ \var{b}, and \code{0 <= abs(\var{a} \%{} \var{b}) < abs(\var{b})}.
\end{funcdesc}
\begin{funcdesc}{eval}{expression\optional{, globals\optional{, locals}}}
diff --git a/Doc/ref/ref5.tex b/Doc/ref/ref5.tex
index 77496fe..72a2053 100644
--- a/Doc/ref/ref5.tex
+++ b/Doc/ref/ref5.tex
@@ -583,9 +583,16 @@
following identity: \code{x == (x/y)*y + (x\%y)}. Integer division and
modulo are also connected with the built-in function \function{divmod()}:
\code{divmod(x, y) == (x/y, x\%y)}. These identities don't hold for
-floating point and complex numbers; there a similar identity holds where
-\code{x/y} is replaced by \code{floor(x/y)}) or
-\code{floor((x/y).real)}, respectively.
+floating point and complex numbers; there similar identities hold
+approximately where \code{x/y} is replaced by \code{floor(x/y)}) or
+\code{floor(x/y) - 1} (for floats),\footnote{
+ If x is very close to an exact integer multiple of y, it's
+ possible for \code{floor(x/y)} to be one larger than
+ \code{(x-x\%y)/y} due to rounding. In such cases, Python returns
+ the latter result, in order to preserve that \code{divmod(x,y)[0]
+ * y + x \%{} y} be very close to \code{x}.
+} or \code{floor((x/y).real)} (for
+complex).
The \code{+} (addition) operator yields the sum of its arguments.
The arguments must either both be numbers or both sequences of the