On sign manipulation - libzahl - big integer library
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DIR Log
DIR Files
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DIR LICENSE
---
DIR commit a70f79dfb22e8ea00231f5739f89ecc8d552643f
DIR parent 3a3ea3e654fa7131c0812977f92dc923d4daf9ce
HTML Author: Mattias Andrée <maandree@kth.se>
Date: Wed, 11 May 2016 22:26:27 +0200
On sign manipulation
Signed-off-by: Mattias Andrée <maandree@kth.se>
Diffstat:
M doc/arithmetic.tex | 65 ++++++++++++++++++++++++++++---
1 file changed, 60 insertions(+), 5 deletions(-)
---
DIR diff --git a/doc/arithmetic.tex b/doc/arithmetic.tex
@@ -91,10 +91,10 @@ be detrimental to libzahl's simplicity.
in-place operation:
\begin{alltt}
- zadd(a, a, b);
- zadd(b, a, b); \textcolor{c}{/* \textrm{should be avoided} */}
- zadd_unsigned(a, a, b);
- zadd_unsigned(b, a, b); \textcolor{c}{/* \textrm{should be avoided} */}
+ zadd(a, a, b);
+ zadd(b, a, b); \textcolor{c}{/* \textrm{should be avoided} */}
+ zadd_unsigned(a, a, b);
+ zadd_unsigned(b, a, b); \textcolor{c}{/* \textrm{should be avoided} */}
\end{alltt}
\noindent
@@ -137,4 +137,59 @@ TODO % zpow zpowu zmodpow zmodpowu
\section{Sign manipulation}
\label{sec:Sign manipulation}
-TODO % zabs zneg
+libzahl provides two functions for manipulating
+the sign of integers:
+
+\begin{alltt}
+ void zabs(z_t r, z_t a);
+ void zneg(z_t r, z_t a);
+\end{alltt}
+
+{\tt zabs} stores the absolute value of {\tt a}
+in {\tt r}, that is, it creates a copy of
+{\tt a} to {\tt r}, unless {\tt a} and {\tt r}
+are the same reference, and then removes its sign;
+if the value is negative, it becomes positive.
+
+\vspace{1em}
+\(
+ r \gets \lvert a \rvert =
+ \left \lbrace \begin{array}{rl}
+ -a & \quad \textrm{if}~a \le 0 \\
+ +a & \quad \textrm{if}~a \ge 0 \\
+ \end{array} \right .
+\)
+\vspace{1em}
+
+{\tt zneg} stores the negated of {\tt a}
+in {\tt r}, that is, it creates a copy of
+{\tt a} to {\tt r}, unless {\tt a} and {\tt r}
+are the same reference, and then flips sign;
+if the value is negative, it becomes positive,
+if the value is positive, it becomes negative.
+
+\vspace{1em}
+\(
+ r \gets -a
+\)
+\vspace{1em}
+
+Note that there is no function for
+
+\vspace{1em}
+\(
+ r \gets -\lvert a \rvert =
+ \left \lbrace \begin{array}{rl}
+ a & \quad \textrm{if}~a \le 0 \\
+ -a & \quad \textrm{if}~a \ge 0 \\
+ \end{array} \right .
+\)
+\vspace{1em}
+
+\noindent
+calling {\tt zabs} followed by {\tt zneg}
+should be sufficient for most users:
+
+\begin{alltt}
+ #define my_negabs(r, a) (zabs(r, a), zneg(r, r))
+\end{alltt}