X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/8017495b1a3ba7f0edbe3ca2edb004aefbc2c9b6..674cd11ec63b56561980249cb19a0db54bacfa86:/manual/mp-mpx.tex

diff --git a/manual/mp-mpx.tex b/manual/mp-mpx.tex
index f775f6b..28c1424 100644
--- a/manual/mp-mpx.tex
+++ b/manual/mp-mpx.tex
@@ -54,7 +54,7 @@ frequently used abbreviation for |(mpw)(|$x$| & MPW_MAX)|.
 
 \fsec{Returns}
 
-The number of bytes occupied by an array of $n$ \code{mpw}s (i.e., $n \cdot
+The number of bytes occupied by an array of $n$~\code{mpw}s (i.e., $n \cdot
 |sizeof(mpw)|$).
 
 \subsubsection{The \code{MPW_RQ} macro}
@@ -70,7 +70,7 @@ The number of bytes occupied by an array of $n$ \code{mpw}s (i.e., $n \cdot
 \fsec{Returns}
 
 The number of \code{mpw}s required to represent a multiprecision integer
-occupying $\sz$ octets in an external representation.
+occupying $\sz$~octets in an external representation.
 
 
 \subsection{Low-level multiprecision integer representation}
@@ -85,7 +85,7 @@ pointers to the array's \emph{base} (i.e., its first element) and
 \emph{limit} (i.e., the location immediately following its last element).
 
 Let $v$ be the base and $\vl$ the limit of a multiprecision integer array.
-The array itself is notated as $v .. \vl$.  The array's size in words may be
+The array itself is notated as~$v .. \vl$.  The array's size in words may be
 computed as $\vl - v$ in the normal C fashion.  The integer represented by
 the array, denoted $\mp(v .. \vl)$, is defined to be
 \[
@@ -100,8 +100,8 @@ the arithmetic algorithms don't need to consider high-order words which make
 no difference to the final result anyway.
 
 Whenever a result is too large to be represented in the memory allocated for
-it, high-order bits are discarded.  Thus, a result written to an array of $k$
-words is reduced modulo $2^{\code{MPW_BITS} \cdot k}$.
+it, high-order bits are discarded.  Thus, a result written to an array of
+$k$~words is reduced modulo $2^{\code{MPW_BITS} \cdot k}$.
 
 
 \subsection{Low-level macros}
@@ -122,9 +122,8 @@ manipulating multiprecision integers at the MPX level.
 
 \fsec{Description}
 
-The \code{MPX_SHRINK} macro reduces the limit $\vl$ of a multiprecision
-integer array so that either $v = \vl$ or $\vl[-1] \ne 0$.  The $\vl$
-argument must be an lvalue, since the macro writes the result back when it
+The \code{MPX_SHRINK} macro reduces the limit~$\vl$ of a multiprecision
+integer array so that either $v = \vl$ or~$\vl[-1] \ne 0$.  The argument~$\vl$ must be an lvalue, since the macro writes the result back when it
 finishes.
 
 \subsubsection{The \code{MPX_BITS} macro}
@@ -140,7 +139,7 @@ finishes.
 \fsec{Description}
 
 Determines the smallest number of bits which could represent the number
-$\mp(v .. \vl)$, and writes the answer to $b$, which must therefore be an
+$\mp(v .. \vl)$, and writes the answer to~$b$, which must therefore be an
 lvalue.  The result is zero if the number is zero; otherwise $b$ is the
 largest integer such that
 \[ \mp(v .. \vl) \ge 2^{(b - 1) \bmod \code{MPW_BITS}}.\]
@@ -159,11 +158,11 @@ largest integer such that
 \fsec{Description}
 
 Determines the smallest number of octets which could represent the number
-$\mp(v .. \vl)$, and writes the answer to $o$, which must therefore be an
+$\mp(v .. \vl)$, and writes the answer to~$o$, which must therefore be an
 lvalue.  This is useful for determining appropriate buffer sizes for the
 results of \code{mpx_storel} and \code{mpx_storeb}.
 
-The result $o$ can be calculated from the number of bits $b$ reported by
+The result $o$ can be calculated from the number of bits~$b$ reported by
 \code{MPX_BITS} as $o = \lceil b / 8 \rceil$; the algorithm used by
 \code{MPX_OCTETS} is more efficient than this, however.
 
@@ -240,8 +239,8 @@ in an octet array of a particular size.
 
 \fsec{Description}
 
-Stores the number held in the array $v .. \vl$ to the array of $\sz$ octets
-starting at address $p$ in little-endian byte order (i.e., least significant
+Stores the number held in the array $v .. \vl$ to the array of $\sz$~octets
+starting at address~$p$ in little-endian byte order (i.e., least significant
 byte first).
 
 \subsubsection{The \code{mpx_loadl} function}
@@ -257,8 +256,8 @@ byte first).
 
 \fsec{Description}
 
-Loads into the array $v .. \vl$ the number represented in the array of $\sz$
-octets starting at address $p$ in little-endian byte order (i.e., least
+Loads into the array $v .. \vl$ the number represented in the array of
+$\sz$~octets starting at address~$p$ in little-endian byte order (i.e., least
 significant byte first).
 
 \subsubsection{The \code{mpx_storeb} function}
@@ -274,8 +273,8 @@ significant byte first).
 
 \fsec{Description}
 
-Stores the number held in the array $v .. \vl$ to the array of $\sz$ octets
-starting at address $p$ in big-endian byte order (i.e., least significant
+Stores the number held in the array $v .. \vl$ to the array of $\sz$~octets
+starting at address~$p$ in big-endian byte order (i.e., least significant
 byte last).
 
 \subsubsection{The \code{mpx_loadb} function}
@@ -291,8 +290,8 @@ byte last).
 
 \fsec{Description}
 
-Loads into the array $v .. \vl$ the number represented in the array of $\sz$
-octets starting at address $p$ in big-endian byte order (i.e., least
+Loads into the array $v .. \vl$ the number represented in the array of
+$\sz$~octets starting at address $p$ in big-endian byte order (i.e., least
 significant byte last).
 
 
@@ -326,8 +325,8 @@ integer.
 
 \fsec{Description}
 
-Stores in $\dv .. \dvl$ the result of shifting $\mp(\av .. \avl)$ left by $n$
-bits (i.e., multiplying it by $2^n$).
+Stores in $\dv .. \dvl$ the result of shifting $\mp(\av .. \avl)$ left by
+$n$~bits (i.e., multiplying it by~$2^n$).
 
 \subsubsection{The \code{mpx_lsr} function}
 \label{fn:mpx-lsr}
@@ -345,10 +344,10 @@ bits (i.e., multiplying it by $2^n$).
 \fsec{Description}
 
 Stores in $\dv .. \dvl$ the result of shifting $\mp(\av .. \avl)$ right by
-$n$ bits (i.e., dividing it by $2^n$, rounding towards zero).
+$n$~bits (i.e., dividing it by~$2^n$, rounding towards zero).
 
 
-\subsection{Low level arithmetic}
+\subsection{Low-level arithmetic}
 
 The remaining functions perform standard arithmetic operations on large
 integers.  The form for the arguments is fairly well-standardized:
@@ -395,7 +394,7 @@ $\dv .. \dvl$.  The two arrays $v .. \vl$ and $\dv .. \dvl$ may be the same.
 \fsec{Description}
 
 The function \code{mpx_ucmp} performs an unsigned comparison of two unsigned
-multiprecision integers $a$ and $b$, passed in the arrays $\av .. \avl$ and
+multiprecision integers $a$ and~$b$, passed in the arrays $\av .. \avl$ and
 $\bv .. \bvl$ respectively.
 
 The macro \code{MPX_UCMP} provides a slightly more readable interface for
@@ -407,7 +406,7 @@ $a \mathrel{\synt{rel-op}} b$.
 
 The function \code{mpx_ucmp} returns a value less then, equal to, or
 greater than zero depending on whether $a$ is less than, equal to or greater
-than $b$.
+than~$b$.
 
 The macro \code{MPX_UCMP} returns a nonzero result if $a
 \mathrel{\synt{rel-op}} b$ is true, and zero if false.
@@ -447,7 +446,7 @@ destination array may be equal to either or both source arrays.\footnote{%
 
 \fsec{Description}
 
-The function \code{mpx_uaddn} adds a small integer $n$ (expressed as a single
+The function \code{mpx_uaddn} adds a small integer~$n$ (expressed as a single
 \code{mpw}) to the multiprecision integer held in $\dv .. \dvl$.
 
 The macro \code{MPX_UADDN} performs exactly the same operation, but uses
@@ -494,7 +493,7 @@ obtained.
 
 \fsec{Description}
 
-The function \code{mpx_usubn} subtracts a small integer $n$ (expressed as a
+The function \code{mpx_usubn} subtracts a small integer~$n$ (expressed as a
 single \code{mpw}) from the multiprecision integer held in $\dv .. \dvl$.
 
 The macro \code{MPX_USUBN} performs exactly the same operation, but uses
@@ -538,7 +537,7 @@ destination array may not be equal to either source array.
 \fsec{Description}
 
 The function \code{mpx_umuln} multiplies the multiprecision integer passed in
-$\av .. \avl$ by a small integer $n$ (expressed as a single \code{mpw}),
+$\av .. \avl$ by a small integer~$n$ (expressed as a single \code{mpw}),
 writing the product $n \cdot \mp(\av .. \avl)$ to the destination array $\dv
 .. \dvl$.  The destination array may be equal to the source array $\av
 .. \avl$.
@@ -564,7 +563,7 @@ inline code rather than calling a function.
 \fsec{Description}
 
 The function \code{mpx_umlan} multiplies the multiprecision integer passed in
-$\av .. \avl$ by a small integer $n$ (expressed as a single \code{mpw}), and
+$\av .. \avl$ by a small integer~$n$ (expressed as a single \code{mpw}), and
 adds it to the value already stored in the destination array $\dv .. \dvl$.
 The destination array may be equal to the source array $\av .. \avl$,
 although this isn't very useful.