Changes in doc/user/user.tex [200fcb3:4e84ef7]

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• doc/user/user.tex (modified) (5 diffs)

doc/user/user.tex

@@ -11 +11 @@
 %% Created On       : Wed Apr  6 14:53:29 2016
 %% Last Modified By : Peter A. Buhr
-%% Last Modified On : Tue Dec 11 23:19:26 2018
-%% Update Count     : 3400
+%% Last Modified On : Sun Apr 14 11:02:34 2019
+%% Update Count     : 3443
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
@@ -508 +508 @@
 
 As for \Index{division}, there are exponentiation operators for integral and floating types, including the builtin \Index{complex} types.
-Unsigned integral exponentiation\index{exponentiation!unsigned integral} is performed with repeated multiplication\footnote{The multiplication computation is $O(\log y)$.} (or shifting if the base is 2).
-Signed integral exponentiation\index{exponentiation!signed integral} is performed with repeated multiplication (or shifting if the base is 2), but yields a floating result because $x^{-y}=1/x^y$.
-Hence, it is important to designate exponent integral-constants as unsigned or signed: ©3 \ 3u© return an integral result, while ©3 \ 3© returns a floating result.
-Floating exponentiation\index{exponentiation!floating} is performed using \Index{logarithm}s\index{exponentiation!logarithm}, so the base cannot be negative.
-\begin{cfa}
-sout | 2 ®\® 8u | 4 ®\® 3u | -4 ®\® 3u | 4 ®\® -3 | -4 ®\® -3 | 4.0 ®\® 2.1 | (1.0f+2.0fi) ®\® (3.0f+2.0fi);
-256 64 -64 0.015625 -0.015625 18.3791736799526 0.264715-1.1922i
-\end{cfa}
+Integral exponentiation\index{exponentiation!unsigned integral} is performed with repeated multiplication\footnote{The multiplication computation is $O(\log y)$.} (or shifting if the exponent is 2).
+Overflow from large exponents or negative exponents return zero.
+Floating exponentiation\index{exponentiation!floating} is performed using \Index{logarithm}s\index{exponentiation!logarithm}, so the exponent cannot be negative.
+\begin{cfa}
+sout | 1 ®\® 0 | 1 ®\® 1 | 2 ®\® 8 | -4 ®\® 3 | 5 ®\® 3 | 5 ®\® 32 | 5L ®\® 32 | 5L ®\® 64 | -4 ®\® -3 | -4.0 ®\® -3 | 4.0 ®\® 2.1
+           | (1.0f+2.0fi) ®\® (3.0f+2.0fi);
+1 1 256 -64 125 ®0® 3273344365508751233 ®0® ®0® -0.015625 18.3791736799526 0.264715-1.1922i
+\end{cfa}
+Note, ©5 ®\® 32© and ©5L ®\® 64© overflow, and ©-4 ®\® -3© is a fraction but stored in an integer so all three computations generate an integral zero.
 Parenthesis are necessary for complex constants or the expression is parsed as ©1.0f+®(®2.0fi \ 3.0f®)®+2.0fi©.
-The exponentiation operator is available for all the basic types, but for user-defined types, only the integral-computation versions are available.
-For returning an integral value, the user type ©T© must define multiplication, ©*©, and one, ©1©;
-for returning a floating value, an additional divide of type ©T© into a ©double© returning a ©double© (©double ?/?( double, T )©) is necessary for negative exponents.
+The exponentiation operator is available for all the basic types, but for user-defined types, only the integral-computation version is available.
+\begin{cfa}
+forall( otype OT | { void ?{}( OT & this, one_t ); OT ?*?( OT, OT ); } )
+OT ?®\®?( OT ep, unsigned int y );
+forall( otype OT | { void ?{}( OT & this, one_t ); OT ?*?( OT, OT ); } )
+OT ?®\®?( OT ep, unsigned long int y );
+\end{cfa}
+The user type ©T© must define multiplication, one, ©1©, and, ©*©.
 
 
@@ -549 +555 @@
 \subsection{Loop Control}
 
-The ©for©/©while©/©do-while© loop-control allows empty or simplified ranges.
+The ©for©/©while©/©do-while© loop-control allows empty or simplified ranges (see Figure~\ref{f:LoopControlExamples}).
+\begin{itemize}
+\item
 An empty conditional implies ©1©.
-The up-to range ©~©\index{~@©~©} means exclusive range [M,N);
-the up-to range ©~=©\index{~=@©~=©} means inclusive range [M,N].
-The down-to range ©-~©\index{-~@©-~©} means exclusive range [N,M);
-the down-to range ©-~=©\index{-~=@©-~=©} means inclusive range [N,M].
+\item
+The up-to range ©~©\index{~@©~©} means exclusive range [M,N).
+\item
+The up-to range ©~=©\index{~=@©~=©} means inclusive range [M,N].
+\item
+The down-to range ©-~©\index{-~@©-~©} means exclusive range [N,M).
+\item
+The down-to range ©-~=©\index{-~=@©-~=©} means inclusive range [N,M].
+\item
+©@© means put nothing in this field.
+\item
 ©0© is the implicit start value;
+\item
 ©1© is the implicit increment value.
+\item
 The up-to range uses ©+=© for increment;
-the down-to range uses ©-=© for decrement.
+\item
+The down-to range uses ©-=© for decrement.
+\item
 The loop index is polymorphic in the type of the start value or comparison value when start is implicitly ©0©.
+\end{itemize}
+
+\begin{figure}
 \begin{cquote}
-\begin{tabular}{@{}ll|l@{}}
-\multicolumn{2}{c|}{loop control} & \multicolumn{1}{c}{output} \\
+\begin{tabular}{@{}l|l@{}}
+\multicolumn{1}{c|}{loop control} & \multicolumn{1}{c}{output} \\
 \hline
 \begin{cfa}
-while ®()® { sout | "empty"; break; }
-do { sout | "empty"; break; } while ®()®;
-for ®()® { sout | "empty"; break; }
-for ( ®0® ) { sout | "A"; }
-for ( ®1® ) { sout | "A"; }
-for ( ®10® ) { sout | "A"; }
-for ( ®1 ~= 10 ~ 2® ) { sout | "B"; }
-for ( ®10 -~= 1 ~ 2® ) { sout | "C"; }
-for ( ®0.5 ~ 5.5® ) { sout | "D"; }
-for ( ®5.5 -~ 0.5® ) { sout | "E"; }
-for ( ®i; 10® ) { sout | i; }
-for ( ®i; 1 ~= 10 ~ 2® ) { sout | i; }
-for ( ®i; 10 -~= 1 ~ 2® ) { sout | i; }
-for ( ®i; 0.5 ~ 5.5® ) { sout | i; }
-for ( ®i; 5.5 -~ 0.5® ) { sout | i; }
-for ( ®ui; 2u ~= 10u ~ 2u® ) { sout | ui; }
-for ( ®ui; 10u -~= 2u ~ 2u® ) { sout | ui; }
+sout | nlOff;
+while ®()® { sout | "empty"; break; } sout | nl;
+do { sout | "empty"; break; } while ®()®; sout | nl;
+for ®()® { sout | "empty"; break; } sout | nl;
+for ( ®0® ) { sout | "A"; } sout | "zero" | nl;
+for ( ®1® ) { sout | "A"; } sout | nl;
+for ( ®10® ) { sout | "A"; } sout | nl;
+for ( ®1 ~= 10 ~ 2® ) { sout | "B"; } sout | nl;
+for ( ®10 -~= 1 ~ 2® ) { sout | "C"; } sout | nl;
+for ( ®0.5 ~ 5.5® ) { sout | "D"; } sout | nl;
+for ( ®5.5 -~ 0.5® ) { sout | "E"; } sout | nl;
+for ( ®i; 10® ) { sout | i; } sout | nl;
+for ( ®i; 1 ~= 10 ~ 2® ) { sout | i; } sout | nl;
+for ( ®i; 10 -~= 1 ~ 2® ) { sout | i; } sout | nl;
+for ( ®i; 0.5 ~ 5.5® ) { sout | i; } sout | nl;
+for ( ®i; 5.5 -~ 0.5® ) { sout | i; } sout | nl;
+for ( ®ui; 2u ~= 10u ~ 2u® ) { sout | ui; } sout | nl;
+for ( ®ui; 10u -~= 2u ~ 2u® ) { sout | ui; } sout | nl;
 enum { N = 10 };
-for ( ®N® ) { sout | "N"; }
-for ( ®i; N® ) { sout | i; }
-for ( ®i; N -~ 0® ) { sout | i; }
+for ( ®N® ) { sout | "N"; } sout | nl;
+for ( ®i; N® ) { sout | i; } sout | nl;
+for ( ®i; N -~ 0® ) { sout | i; } sout | nl;
 const int start = 3, comp = 10, inc = 2;
-for ( ®i; start ~ comp ~ inc + 1® ) { sout | i; }
+for ( ®i; start ~ comp ~ inc + 1® ) { sout | i; } sout | nl;
+for ( ®i; 1 ~ @® ) { if ( i > 10 ) break;
+        sout | i; } sout | nl;
+for ( ®i; 10 -~ @® ) { if ( i < 0 ) break;
+        sout | i; } sout | nl;
+for ( ®i; 2 ~ @ ~ 2® ) { if ( i > 10 ) break;
+        sout | i; } sout | nl;
+for ( ®i; 2.1 ~ @ ~ @® ) { if ( i > 10.5 ) break;
+        sout | i; i += 1.7; } sout | nl;
+for ( ®i; 10 -~ @ ~ 2® ) { if ( i < 0 ) break;
+        sout | i; } sout | nl;
+for ( ®i; 12.1 ~ @ ~ @® ) { if ( i < 2.5 ) break;
+        sout | i; i -= 1.7; } sout | nl;
+for ( ®i; 5 : j; -5 ~ @® ) { sout | i | j; } sout | nl;
+for ( ®i; 5 : j; -5 -~ @® ) { sout | i | j; } sout | nl;
+for ( ®i; 5 : j; -5 ~ @ ~ 2® ) { sout | i | j; } sout | nl;
+for ( ®i; 5 : j; -5 -~ @ ~ 2® ) { sout | i | j; } sout | nl;
+for ( ®j; -5 ~ @ : i; 5® ) { sout | i | j; } sout | nl;
+for ( ®j; -5 -~ @ : i; 5® ) { sout | i | j; } sout | nl;
+for ( ®j; -5 ~ @ ~ 2 : i; 5® ) { sout | i | j; } sout | nl;
+for ( ®j; -5 -~ @ ~ 2 : i; 5® ) { sout | i | j; } sout | nl;
+for ( ®j; -5 -~ @ ~ 2 : i; 5 : k; 1.5 ~ @® ) {
+        sout | i | j | k; } sout | nl;
+for ( ®j; -5 -~ @ ~ 2 : k; 1.5 ~ @ : i; 5® ) {
+        sout | i | j | k; } sout | nl;
+for ( ®k; 1.5 ~ @ : j; -5 -~ @ ~ 2 : i; 5® ) {
+        sout | i | j | k; } sout | nl;
 \end{cfa}
 &
 \begin{cfa}
-sout | nl;
-sout | nl;
-sout | nl;
-sout | "zero" | nl;
-sout | nl;
-sout | nl;
-sout | nl;
-sout | nl;
-sout | nl;
-sout | nl;
-sout | nl;
-sout | nl;
-sout | nl;
-sout | nl;
-sout | nl;
-sout | nl;
-sout | nl | nl;
-
-sout | nl;
-sout | nl;
-sout | nl | nl;
-
-sout | nl;
-\end{cfa}
-&
-\begin{cfa}
+
 empty
 empty
@@ -640 +664 @@
 
 3 6 9
+
+1 2 3 4 5 6 7 8 9 10
+
+10 9 8 7 6 5 4 3 2 1 0
+
+2 4 6 8 10
+
+2.1 3.8 5.5 7.2 8.9
+
+10 8 6 4 2 0
+
+12.1 10.4 8.7 7 5.3 3.6
+0 -5 1 -4 2 -3 3 -2 4 -1
+0 -5 1 -6 2 -7 3 -8 4 -9
+0 -5 1 -3 2 -1 3 1 4 3
+0 -5 1 -7 2 -9 3 -11 4 -13
+0 -5 1 -4 2 -3 3 -2 4 -1
+0 -5 1 -6 2 -7 3 -8 4 -9
+0 -5 1 -3 2 -1 3 1 4 3
+0 -5 1 -7 2 -9 3 -11 4 -13
+
+0 -5 1.5 1 -7 2.5 2 -9 3.5 3 -11 4.5 4 -13 5.5
+
+0 -5 1.5 1 -7 2.5 2 -9 3.5 3 -11 4.5 4 -13 5.5
+
+0 -5 1.5 1 -7 2.5 2 -9 3.5 3 -11 4.5 4 -13 5.5
 \end{cfa}
 \end{tabular}
 \end{cquote}
+\caption{Loop Control Examples}
+\label{f:LoopControlExamples}
+\end{figure}
 
 
@@ -1320 +1373 @@
 \end{cfa}
 Essentially, the return type is wrapped around the routine name in successive layers (like an \Index{onion}).
-While attempting to make the two contexts consistent is a laudable goal, it has not worked out in practice.
+While attempting to make the two contexts consistent is a laudable goal, it has not worked out in practice, even though Dennis Richie believed otherwise:
+\begin{quote}
+In spite of its difficulties, I believe that the C's approach to declarations remains plausible, and am comfortable with it; it is a useful unifying principle.~\cite[p.~12]{Ritchie93}
+\end{quote}
 
 \CFA provides its own type, variable and routine declarations, using a different syntax.