[Bug 2931407]: Clarified semantics of division and remainder operators.

2 files changed, 24 insertions, 6 deletions

diff --git a/doc/expr.n b/doc/expr.n
index 7b29f81..6d965fb 100644
--- a/doc/expr.n
+++ b/doc/expr.n
@@ -134,7 +134,20 @@ Multiply, divide, remainder.  None of these operators may be
 applied to string operands, and remainder may be applied only
 to integers.
 The remainder will always have the same sign as the divisor and
-an absolute value smaller than the divisor.
+an absolute value smaller than the absolute value of the divisor.
+.RS
+.PP
+When applied to integers, the division and remainder operators can be
+considered to partition the number line into a sequence of equal-sized
+adjacent non-overlapping pieces where each piece is the size of the divisor;
+the division result identifies which piece the divisor lay within, and the
+remainder result identifies where within that piece the divisor lay. A
+consequence of this is that the result of
+.QW "-57 \fB/\fR 10"
+is always -6, and the result of
+.QW "-57 \fB%\fR 10"
+is always 3.
+.RE
 .TP 20
 \fB+\0\0\-\fR
 .
diff --git a/doc/mathop.n b/doc/mathop.n
index e359276..ac2ebc1 100644
--- a/doc/mathop.n
+++ b/doc/mathop.n
@@ -126,14 +126,19 @@ will be an integer.
 .TP
 \fB%\fR \fInumber number\fR
 .
-Returns the integral modulus of the first argument with respect to the second.
-Each \fInumber\fR must have an integral value. Note that Tcl defines this
-operation exactly even for negative numbers, so that the following equality
-holds true:
+Returns the integral modulus (i.e., remainder) of the first argument
+with respect to the second.
+Each \fInumber\fR must have an integral value.
+Also, the sign of the result will be the same as the sign of the second
+\fInumber\fR, which must not be zero.
 .RS
 .PP
+Note that Tcl defines this operation exactly even for negative numbers, so
+that the following command returns a true value (omitting the namespace for
+clarity):
+.PP
 .CS
-(\fIx \fB/ \fIy\fR) \fB* \fIy \fB== \fIx \fB\-\fR (\fIx \fB% \fIy\fR)
+\fB==\fR [\fB*\fR [\fB/\fI x y\fR] \fIy\fR] [\fB\-\fI x\fR [\fB%\fI x y\fR]]
 .CE
 .RE
 .TP