libzahl

commit 8237156ffb390b38c55863d1b14f246af8a1c19c
parent cb82f578cadb97cdfc79b7e8e160a7a598265a73
Author: Mattias Andrée <maandree@kth.se>
Date:   Sat,  5 Mar 2016 16:36:56 +0100

More detailed description of division and modulus

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

Diffstat:
M
man/zdiv.3
 | 
2
+-
M
man/zdivmod.3
 | 
8
++++++--
M
man/zmod.3
 | 
13
++++++++++++-
M
man/zmodmul.3
 | 
4
++++
M
man/zmodpow.3
 | 
4
++++
M
man/zmodpowu.3
 | 
4
++++
M
man/zmodsqr.3
 | 
4
++++

7 files changed, 35 insertions(+), 4 deletions(-)
diff --git a/man/zdiv.3 b/man/zdiv.3
@@ -9,7 +9,7 @@ void zdiv(z_t \fIquotient\fP, z_t \fIdividend\fP, z_t \fIdivisor\fP);
 .fi
 .SH DESCRIPTION
 .B zdiv
-calculates the quotient of a
+calculates the truncated quotient of a
 .I dividend
 and a
 .IR divisor ,
diff --git a/man/zdivmod.3 b/man/zdivmod.3
@@ -9,11 +9,11 @@ void zdivmod(z_t \fIquotient\fP, z_t \fIremainder\fP, z_t \fIdividend\fP, z_t \f
 .fi
 .SH DESCRIPTION
 .B zdivmod
-calculates the quotient and the remainder of a
+calculates the truncated quotient and the remainder of a
 .I dividend
 and a
 .IR divisor ,
-and stores the quotient in
+and stores the truncated quotient in
 .I quotient
 and the remainder in
 .IR remainder .
@@ -38,6 +38,10 @@ except it is
 safe to call
 .B zdivmod with
 .IR "(quotient==remainder)" .
+.P
+See
+.BR zmod (3)
+for details on modulation.
 .SH RATIONALE
 Calculating the remainder requires calculating division to
 be performed, and performing a division gives the remainder
diff --git a/man/zmod.3 b/man/zmod.3
@@ -24,11 +24,22 @@ Mod
 .P
 The result
 .RI ( remainder )
-is always non-negative.
+is always non-negative. To be more precise,
+a Mod b = |a| Mod |b| 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),
diff --git a/man/zmodmul.3 b/man/zmodmul.3
@@ -29,6 +29,10 @@ Mod
 It is safe to call
 .B zmodmul
 with non-unique parameters.
+.P
+See
+.BR zmod (3)
+for details on modulation.
 .SH RATIONALE
 It is possible to calculate the modular product
 with a faster algorithm than calculating the
diff --git a/man/zmodpow.3 b/man/zmodpow.3
@@ -29,6 +29,10 @@ Mod
 It is safe to call
 .B zmodpow
 with non-unique parameters.
+.P
+See
+.BR zmod (3)
+for details on modulation.
 .SH RATIONALE
 It is possible to calculate the modular power
 with a faster algorithm than calculating the
diff --git a/man/zmodpowu.3 b/man/zmodpowu.3
@@ -29,6 +29,10 @@ Mod
 It is safe to call
 .B zmodpowu
 with non-unique parameters.
+.P
+See
+.BR zmod (3)
+for details on modulation.
 .SH RATIONALE
 It is possible to calculate the modular power
 with a faster algorithm than calculating the
diff --git a/man/zmodsqr.3 b/man/zmodsqr.3
@@ -25,6 +25,10 @@ Mod
 It is safe to call
 .B zmodsqr
 with non-unique parameters.
+.P
+See
+.BR zmod (3)
+for details on modulation.
 .SH RATIONALE
 See rationle for
 .BR zmodmul (3),