commit 781e9d05388539d989e3578ebc7f8a7cd038aeb0
parent 183bfa766f29b3eb46b01c7b6e82d71d822b02d5
Author: Mattias Andrée <maandree@kth.se>
Date: Tue, 29 Nov 2016 23:55:29 +0100
Fix errors in the manual (most of them found by Ivan Zuboff)
Signed-off-by: Mattias Andrée <maandree@kth.se>
Diffstat:
8 files changed, 68 insertions(+), 52 deletions(-)
diff --git a/doc/arithmetic.tex b/doc/arithmetic.tex
@@ -69,7 +69,7 @@ instruction specifically for performing
addition with ripple-carry over multiple words,
adds twos numbers plus the carry from the
last addition. libzahl uses assembly to
-implement this efficiently. If however, an
+implement this efficiently. If, however, an
assembly implementation is not available for
the on which machine it is running, libzahl
implements ripple-carry less efficiently
@@ -80,8 +80,8 @@ the compiler is known to support this
extension, it is implemented using inefficient
pure C code. This last resort manually
predicts whether an addition will overflow;
-this could be made more efficent, but never
-using the highest bit, in each character,
+this could be made more efficient, by never
+using the highest bit in each character,
except to detect overflow. This optimisation
is however not implemented because it is
not deemed important enough and would
@@ -100,9 +100,9 @@ in-place operation:
\noindent
Use this whenever possible, it will improve
your performance, as it will involve less
-CPU instructions for each character-addition
+CPU instructions for each character addition
and it may be possible to eliminate some
-character-additions.
+character additions.
\newpage
@@ -138,7 +138,7 @@ These function \emph{do not} allow {\tt NULL}
for the output parameters: {\tt quotient} and
{\tt remainder}. The quotient and remainder are
calculated simultaneously and indivisibly, hence
-{\tt zdivmod} is provided to calculated both, if
+{\tt zdivmod} is provided to calculated both; if
you are only interested in the quotient or only
interested in the remainder, use {\tt zdiv} or
{\tt zmod}, respectively.
@@ -146,14 +146,14 @@ interested in the remainder, use {\tt zdiv} or
These functions calculate a truncated quotient.
That is, the result is rounded towards zero. This
means for example that if the quotient is in
-$(-1,~1)$, {\tt quotient} gets 0. That that, this
+$(-1,~1)$, {\tt quotient} gets 0. That is, this % TODO try to clarify
would not be the case for one of the sides of zero.
For example, if the quotient would have been
floored, negative quotients would have been rounded
away from zero. libzahl only provides truncated
-division,
+division.
-The remain is defined such that $n = qd + r$ after
+The remainder is defined such that $n = qd + r$ after
calling {\tt zdivmod(q, r, n, d)}. There is no
difference in the remainer between {\tt zdivmod}
and {\tt zmod}. The sign of {\tt d} has no affect
@@ -188,7 +188,7 @@ lend you a hand.
% Floored division
\begin{alltt}
- void \textcolor{c}{/* \textrm{All arguments most be unique.} */}
+ void \textcolor{c}{/* \textrm{All arguments must be unique.} */}
divmod_floor(z_t q, z_t r, z_t n, z_t d)
\{
zdivmod(q, r, n, d);
@@ -199,7 +199,7 @@ lend you a hand.
% Ceiled division
\begin{alltt}
- void \textcolor{c}{/* \textrm{All arguments most be unique.} */}
+ void \textcolor{c}{/* \textrm{All arguments must be unique.} */}
divmod_ceiling(z_t q, z_t r, z_t n, z_t d)
\{
zdivmod(q, r, n, d);
@@ -214,7 +214,7 @@ lend you a hand.
% commercial rounding
\begin{alltt}
/* \textrm{This is how we normally round numbers.} */
- void \textcolor{c}{/* \textrm{All arguments most be unique.} */}
+ void \textcolor{c}{/* \textrm{All arguments must be unique.} */}
divmod_half_from_zero(z_t q, z_t r, z_t n, z_t d)
\{
zdivmod(q, r, n, d);
@@ -237,7 +237,7 @@ not award you a face-slap. % Had positive punishment
% This rounding method is also called:
% round half away from infinity
\begin{alltt}
- void \textcolor{c}{/* \textrm{All arguments most be unique.} */}
+ void \textcolor{c}{/* \textrm{All arguments must be unique.} */}
divmod_half_to_zero(z_t q, z_t r, z_t n, z_t d)
\{
zdivmod(q, r, n, d);
@@ -254,7 +254,7 @@ not award you a face-slap. % Had positive punishment
% This rounding method is also called:
% round half towards positive infinity
\begin{alltt}
- void \textcolor{c}{/* \textrm{All arguments most be unique.} */}
+ void \textcolor{c}{/* \textrm{All arguments must be unique.} */}
divmod_half_up(z_t q, z_t r, z_t n, z_t d)
\{
int cmp;
@@ -272,7 +272,7 @@ not award you a face-slap. % Had positive punishment
% This rounding method is also called:
% round half towards negative infinity
\begin{alltt}
- void \textcolor{c}{/* \textrm{All arguments most be unique.} */}
+ void \textcolor{c}{/* \textrm{All arguments must be unique.} */}
divmod_half_down(z_t q, z_t r, z_t n, z_t d)
\{
int cmp;
@@ -297,7 +297,7 @@ not award you a face-slap. % Had positive punishment
% bankers' rounding
% It is the default rounding method used in IEEE 754.
\begin{alltt}
- void \textcolor{c}{/* \textrm{All arguments most be unique.} */}
+ void \textcolor{c}{/* \textrm{All arguments must be unique.} */}
divmod_half_to_even(z_t q, z_t r, z_t n, z_t d)
\{
int cmp;
@@ -316,7 +316,7 @@ not award you a face-slap. % Had positive punishment
% Division with round half to odd
\newpage
\begin{alltt}
- void \textcolor{c}{/* \textrm{All arguments most be unique.} */}
+ void \textcolor{c}{/* \textrm{All arguments must be unique.} */}
divmod_half_to_odd(z_t q, z_t r, z_t n, z_t d)
\{
int cmp;
@@ -342,7 +342,7 @@ not award you a face-slap. % Had positive punishment
Currently, libzahl uses an almost trivial division
algorithm. It operates on positive numbers. It begins
-by left-shifting the divisor as must as possible with
+by left-shifting the divisor as much as possible with
letting it exceed the dividend. Then, it subtracts
the shifted divisor from the dividend and add 1,
left-shifted as much as the divisor, to the quotient.
@@ -350,7 +350,7 @@ The quotient begins at 0. It then right-shifts
the shifted divisor as little as possible until
it no longer exceeds the diminished dividend and
marks the shift in the quotient. This process is
-repeated on till the unshifted divisor is greater
+repeated until the unshifted divisor is greater
than the diminished dividend. The final diminished
dividend is the remainder.
@@ -376,7 +376,7 @@ exponentiation are
\noindent
They are identical, except {\tt zpowu} expects
-and intrinsic type as the exponent. Both functions
+an intrinsic type as the exponent. Both functions
calculate
\vspace{1em}
@@ -410,7 +410,7 @@ exponentiation by squaring. {\tt zmodpow} and
{\tt zmodpowu} are optimised, they modulate
results for multiplication and squaring at
every multiplication and squaring, rather than
-modulating every at the end. Exponentiation
+modulating the result at the end. Exponentiation
by modulation is a very simple algorithm which
can be expressed as a simple formula
diff --git a/doc/bit-operations.tex b/doc/bit-operations.tex
@@ -160,7 +160,7 @@ calculate division by a power of two and
modulus a power of two efficiently using
bit-shift and bit-truncation operations. libzahl
also has a bit-split operation that can be used
-to efficently calculate both division and
+to efficiently calculate both division and
modulus a power of two efficiently in the same
operation, or equivalently, storing low bits
in one integer and high bits in another integer.
diff --git a/doc/get-started.tex b/doc/get-started.tex
@@ -58,7 +58,7 @@ are done using it, for example before the program exits.
\}}
\end{alltt}
-{\tt zunsetup} all memory that has been reclaimed to
+{\tt zunsetup} frees all memory that has been reclaimed to
the memory pool, and all memory allocated by {\tt zsetup}.
Note that this does not free integers that are still
in use. It is possible to simply call {\tt zunsetup}
diff --git a/doc/libzahl.tex b/doc/libzahl.tex
@@ -78,7 +78,7 @@ copyright notice and this permission notice appear in all copies.}
% It should look just like a sentience except it may not end with a
% period unless that is part of an ellipsis or an abbreviation.
% I would also like to use straight apostrophes, like in French, (and
-% reserve the curved ones for quotes,) but that is just too painful in
+% reserve the curved ones for quotes), but that is just too painful in
% LaTeX, so I will only be do so for French words. Most style guides
% for English will be followed. They will only be broken if they are
% stupid or inferior. For example, I will never write ‘CPU's’ for
diff --git a/doc/libzahls-design.tex b/doc/libzahls-design.tex
@@ -155,7 +155,7 @@ allows you do so if you so choose.
The {\tt .sign} member, is either $-1$, 0, or 1,
when the integer is negative, zero, or positive,
-respectively. Whenever, {\tt .sign} is 0, the value
+respectively. Whenever {\tt .sign} is 0, the value
of {\tt .used} and {\tt .chars} are undefined.
{\tt .used} holds to the number of elements used in
@@ -192,7 +192,7 @@ they are not considered input integers. The order
of the input parameters are that of the order you
would write them using mathematical notation, this
also holds true if you include the output parameter
-(as long as there is exactly one output,) for example
+(as long as there is exactly one output), for example
\vspace{1em}
$a \gets b^c \mod d$
@@ -256,7 +256,7 @@ This assumption is not made for non-commutative
functions.
When writting your own functions, be aware,
-input-parameters are generally not declared {\tt const}
+input parameters are generally not declared {\tt const}
in libzahl. Currently, some functions actually make
modifications (that do not affect the value) to
-input-parameters.
+input parameters.
diff --git a/doc/miscellaneous.tex b/doc/miscellaneous.tex
@@ -65,7 +65,7 @@ a proper UCS minus sign is not supported.
Using what we have learned so far, and {\tt zstr}
which we will learn about in \secref{sec:String output},
we can construct a simple program that calculates the
-sum of a set of number.
+sum of a set of numbers.
\begin{alltt}
\textcolor{c}{#include <stdio.h>
@@ -153,10 +153,10 @@ there are cases where it is needed. In some case
\noindent
however its implementation is optimised to be
around three times as fast. It just swaps the members
-of the parameters, and thereby the values, There
+of the parameters, and thereby the values. There
is no rewriting of {\tt .chars} involved; thus
it runs in constant time. It also does not
-require that any argument has be initialised.
+require that any argument has been initialised.
After the call, {\tt a} will be initialised
if and only if {\tt b} was initialised, and
vice versa.
@@ -301,11 +301,11 @@ The return for {\tt zcmpmag} value is defined
\vspace{1em}
\noindent
-It is discouraged, stylistically, to compare
-against, $-1$ and $+1$, rather, you should
-always compare against $0$. Think of it as
-returning $a - b$, or $\lvert a \rvert - \lvert b \rvert$
-in the case of {\tt zcmpmag}.
+It is discouraged, stylistically, to compare against
+$-1$ and $+1$, rather, you should always compare
+against $0$. Think of it as returning $a - b$, or
+$\lvert a \rvert - \lvert b \rvert$ in the case of
+{\tt zcmpmag}.
\newpage
@@ -320,7 +320,7 @@ run the same version of libzahl, and run on compatible
microarchitectures, that is, the processors must have
endianness, and the intrinsic integer types in C must
have the same widths on all processors. When this is not
-the case, string conversion (see \secref{sec:Assignment}
+the case, string conversion can be used (see \secref{sec:Assignment}
and \secref{sec:String output}), but when it is the case
{\tt zsave} and {\tt zload} can be used. {\tt zsave} and
{\tt zload} are declared as
@@ -331,11 +331,11 @@ and \secref{sec:String output}), but when it is the case
\end{alltt}
\noindent
-{\tt zsave} stores a version- and microarchitecture-depend
+{\tt zsave} stores a version- and microarchitecture-dependent
binary representation of {\tt a} in {\tt buf}, and returns
the number of bytes written to {\tt buf}. If {\tt buf} is
-{\tt NULL}, the numbers that will be written is returned.
-{\tt zload} unmarshals an integers from {\tt buf}, created
-with {\tt zsave}, into {\tt a}, and returns the number of
-read bytes. {\tt zload} and will return the value returned
-by {\tt zsave}.
+{\tt NULL}, the numbers bytes that would have be written is
+returned. {\tt zload} unmarshals an integers from {\tt buf},
+created with {\tt zsave}, into {\tt a}, and returns the number
+of read bytes. {\tt zload} returns the value returned by
+{\tt zsave}.
diff --git a/doc/not-implemented.tex b/doc/not-implemented.tex
@@ -84,9 +84,12 @@ more about this, I refer you to Wikipeida.
\( \displaystyle{
\mbox{lcm}(a, b) = \frac{\lvert a \cdot b \rvert}{\mbox{gcd}(a, b)}
}\)
+\vspace{1em}
-Be aware, {\tt zgcd} can return zero.
-
+$\mbox{lcm}(a, b)$ is undefined when $a$ or
+$b$ is zero, because division by zero is
+undefined. Note however that $\mbox{gcd}(a, b)$
+is only zero when both $a$ and $b$ is zero.
\newpage
\section{Modular multiplicative inverse}
@@ -309,7 +312,7 @@ TODO % Square: Cipolla's algorithm, Pocklington's algorithm, Tonelli–Shanks al
}\)
\vspace{1em}
-This can be implemented much more efficently
+This can be implemented much more efficiently
than using the naïve method, and is a very
important function for many combinatorial
applications, therefore it may be implemented
diff --git a/doc/what-is-libzahl.tex b/doc/what-is-libzahl.tex
@@ -57,8 +57,8 @@ it can still be improved. Furthermore, GNU MP cannot be
used for robust applications.
\item
-LibTomMath is very slow, infact performance is not its
-priority, rather its simplicit is the priority. Despite
+LibTomMath is very slow, in fact performance is not its
+priority, rather its simplicity is the priority. Despite
this, it is not really that simple.
\item
@@ -73,8 +73,8 @@ philosophy.\footnote{\href{http://suckless.org/philosophy}
{http://suckless.org/philosophy}} libzahl is simple,
very fast, simple to use, and can be used in robust
applications. Currently however, it does not support
-multithreading, but it has better support multiprocessing
-and distributed computing than its competitor.
+multithreading, but it has better support for multiprocessing
+and distributed computing than its competitors.
Lesser ``competitors'' (less known) to libzahl include
Hebimath and bsdnt.
@@ -142,10 +142,10 @@ caught using {\tt setjmp}. This ensure that it can be
used in robust applications, catching errors does not
become a mess, and it minimises the overhead of
catching errors. Errors are only checked when they can
-occur, not also after each function-return.
+occur, not also after each function return.
Additionally, libzahl tries to keep the functions'
-names simple and natural rather than techniqual or
+names simple and natural rather than technical or
mathematical. The names resemble those of the standard
integer operators. For example, the left-shift, right-shift
and truncation bit-operations in libzahl are called
@@ -214,6 +214,19 @@ strictly necessary for it to be an CPU-intrinsic,
but that would be favourable for performance.)
\end{itemize}
+Because of the prevalence of theses properties
+in contemporary machines, and the utilisation of
+these properties in software, especially software
+for POSIX and popular platforms with similar
+properties, any new general-purpose machine most
+have these properties lest, it but useless with
+today's software. Therefore, libzahl can make
+the assumption that the machine has these
+properties. If the machine does not have these
+properties, the compiler must compensate for
+these machines deficiencies, making it generally
+slower.
+
These limitations may be removed later. And there
is some code that does not make these assumptions
but acknowledge that it may be a case. On the other
