Always satisfy n=qd+r to avoid confusion

Signed-off-by: Mattias Andrée <maandree@kth.se>

2 files changed, 4 insertions, 39 deletions

diff --git a/man/zdivmod.3 b/man/zdivmod.3
index d63405a..f0cd9e4 100644
--- a/man/zdivmod.3
+++ b/man/zdivmod.3
@@ -30,34 +30,6 @@ gets
 Mod
 .IR divisor .
 .P
-Be aware,
-.I remainder
-gets
-.RI | dividend |
-Mod
-.RI | divisor |,
-this means that it is only guaranteed to be true that
-.I dividend
-=
-.I quotient
-⋅
-.I divisor
-+
-.IR remainder
-if
-.I dividend
-and
-.I divisor
-are both non-negative.
-It is up to the user, to make the necessary adjustment to
-.I remainder
-to make this true or to satisfy any desired property. This
-exceptional behaviour has been choosen because it is the
-simplies, works just fine if you are working with natural
-numbers only, and there are two many ways to define
-modulus; this one is advantages when you want to make
-adjustments, it is straight-forward.
-.P
 It is safe to call
 .B zdivmod
 with non-unique parameters,
diff --git a/man/zmod.3 b/man/zmod.3
index a6cd21d..b2588d1 100644
--- a/man/zmod.3
+++ b/man/zmod.3
@@ -24,22 +24,15 @@ Mod
 .P
 The result
 .RI ( remainder )
-is always non-negative. To be more precise,
-a Mod b = |a| Mod |b| for all integers a
+is negative if and only if the
+.I dividend
+is negative. To be more precise,
+a Mod b = (|a| Mod |b|) sgn a for all integers a
 and b.
 .P
 It is safe to call
 .B zmod
 with non-unique parameters.
-.SH RATIONALE
-There are many ways to define modulus with
-negative integers. You have to select how the
-signness is selected, and when to invert
-(in respect to modulated addition) the remainder.
-The simplest way to implement modulus is to
-ignore the sign of the operands. This solution
-also makes it very easy for those that which
-to write a wrapper that changes the definition.
 .SH SEE ALSO
 .BR zdivmod (3),
 .BR zstr (3),