Reflect recent patch for float % and divmod() by Tim Peters. Content

updates by Tim Peters, markup by FLD.

1 files changed, 10 insertions, 3 deletions

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 @@ The integer division and modulo operators are connected by the
 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