statement.</para>
<para>The question still remains: How does one communicate the
-algorithm to the computer? A translator such as MAD is designed
+algorithm to the computer? A translator such as
+MAD<indexterm><primary>Translator</primary></indexterm> is designed
according to the philosophy: Once the algorithm has been stated, as in
a flow diagram, it should be presented to the computer directly in
that form, or as near to it as possible. The "translator" then has
</programlisting>
<orderedlist>
-<listitem><para>The first statement, labelled ST, causes a value for a,x,
-and ε to be read into computer storage. A block of adjacent
+<listitem><para>The first statement, labelled ST, causes a value for
+a,x, and ε to be read into computer storage. A block of adjacent
storage location in the computer (a "vector") named ALPHA is
-designated as containing a description of how the three
-numbers were punched on the card. (This description – which
-is the value of ALPHA – is described in a later statement; see
-(9) below.)</para></listitem>
+designated as containing a description of how the three numbers were
+punched on the card. <indexterm><primary>Vector</primary></indexterm>
+(This description – which is the value of ALPHA – is
+described in a later statement; see (9) below.)</para></listitem>
<listitem><para>The second statement is a simple conditional which causes
the statement labelled PRT to be the next one executed if a <
ε), the next statement in sequence is executed.</para></listitem>
<listitem><para>The PRINT statement<indexterm><primary>PRINT
- Statement</primary></indexterm> causes three numbers - the current
- values of a, x and ε to be printed. The arrangement and form of
- the numbers on the printed page are controlled by the format
- description which is the value of the vector named
-
ALPHA.<indexterm><primary>Format</primary></indexterm></para></listitem>
+Statement</primary></indexterm> causes three numbers - the current
+values of a, x and ε to be printed. The arrangement and form of
+the numbers on the printed page are controlled by the format
+description which is the value of the vector named
+ALPHA.<indexterm><primary>Format</primary></indexterm></para></listitem>
<listitem><para>The TRANSFER statement following causes the statement
-labelled ST to be the next one performed.</para></listitem>
+labelled ST to be the next one performed.
+<indexterm><primary>TRANSFER Statement</primary></indexterm>
+</para></listitem>
<listitem><para>The statement labelled PRT is the one executed immediately
after the first statement whenever a < 1.0. This statement
<listitem><para>The next two statements following the last TRANSFER TO
ST set the initial values of two vectors named ALPHA and BETA.
-Although VECTOR VALUES statements can be used to preset vectors to
+Although VECTOR VALUES statements<indexterm><primary>VECTOR VALUES
+Statements</primary></indexterm> can be used to preset vectors to
specified numeric values, in both instances here the values are
<emphasis>format descriptions</emphasis>. The strings of characters
between the dollar signs (MAD quotation marks!) are to be taken
<!-- beginpage I.14 at the soft hyphen above -->
-<para>The second statement in the program causes the inout information,
-properly labeled., to print out, preceded by the title "SOLUTION OF
-CUBIC EQUATION". The appropriate alphabetic information is contained
-in the format information which is t be found in the vecvtor TITLE, as
-set by a VECTOR VALUES statement later in the program.</para>
+<para>The second statement in the program causes the inout
+information, properly labeled., to print out, preceded by the title
+"SOLUTION OF CUBIC EQUATION". The appropriate alphabetic information
+is contained in the format information which is t be found in the
+vector TITLE, as set by a VECTOR VALUES statement
+<indexterm><primary>VECTOR VALUES
+Statements</primary></indexterm>later in the program.</para>
<!-- in the original, there was a run-on typo, "NO CONVERGENCEis" -->
<para>Two functions are defined in this program, and each is
Alphabetic</primary></indexterm> consists of from one to six
admissible characters<indexterm><primary>Admissible
Characters</primary></indexterm> preceded and followed by the
-character "$". The admiss- ible characters include all letters of the
+character "$".<indexterm><primary>$ Sign</primary></indexterm>
+The admiss- ible characters include all letters of the
alphabet, the digits 0 through 9, the special characters +, -(minus
sign), -(dash), *, /, =, ). (. ., the comma "," and the blank space,
to be represented here occasionally (but not punched on input cards),
<para>There are two Boolean constants – "true", which is written
1B, and "false" which is written 0B.
-<indexterm><primary>Boolean Constants</primary></indexterm></para>
+<indexterm><primary>Boolean Constants</primary></indexterm>
+<indexterm><primary>0B</primary></indexterm>
+<indexterm><primary>1B</primary></indexterm></para>
</sect3>
</sect2>
<sect2><title>Variables</title>
+<indexterm><primary>Variable</primary></indexterm>
+
<para>The name of a variable consists of one to six letters or digits,
the first of which must be a letter. If the variable is defined as an
n-dimensional array variable<indexterm><primary>Array
<sect2 id='statement_labels'><title>Statement Labels</title>
<indexterm><primary>Statement Labels</primary></indexterm>
+<indexterm><primary>Vector, Statent Label</primary></indexterm>
<para>A statement may be labelled or unlabelled. Labels are used to
refer to a statement in other statements. A statement label consists
<indexterm><primary>.AND.</primary></indexterm></para></listitem>
<listitem><para>M.THEN.P has the value 0B if and only if M has the
-value 1B and P has the value 0B.</para></listitem>
+value 1B and P has the value 0B.</para>
+<indexterm><primary>.THEN.</primary></indexterm>
+</listitem>
<!-- beginpage II.5 -->
<sect2><title>Transfer Statement</title>
+<indexterm><primary>TRANSFER Statement</primary></indexterm>
+
<para>This statement has the form: TRANSFER TO &scriptS;</para>
<para>Here &scriptS; may be any statement label or any expression in
<para>Examples:</para>
<para>(i) To evaluate the polynomial
- c<subscript>n</subscript>x<superscript>n</superscript> +
- c<subscript>n-1</subscript>x<superscript>n+1</superscript> + ...+
- c<subscript>1</subscript>x + c<subscript>0</subscript> using the
- formula (...((c<subscript>n</subscript>x +
- c<subscript>n-1</subscript>)x + c<subscript>n-2</subscript>)x + ...+
- c<subscript>1</subscript>)x + c<subscript>0</subscript> (nested
- multiplication), we may write the program:</para>
+c<subscript>n</subscript>x<superscript>n</superscript> +
+c<subscript>n-1</subscript>x<superscript>n+1</superscript> + ...+
+c<subscript>1</subscript>x + c<subscript>0</subscript> using the
+formula (...((c<subscript>n</subscript>x +
+c<subscript>n-1</subscript>)x + c<subscript>n-2</subscript>)x + ...+
+c<subscript>1</subscript>)x + c<subscript>0</subscript> (nested
+multiplication), we may write the program:</para>
<programlisting>
INTEGER J,N
<para>(iii) If the transformation of the iteration variable is to be
performed within the scope of the iteration, one may use a zero
-increment. E.g., if J is an integer variable, and the scope of the
-iteration is to be performed for those multiples of 2 which are not
-multiples of 5 and which are less than the value of the integer K, one
-might write the iteration as follows:</para>
+increment. <indexterm><primary>Zero Increment for
+Iteration</primary></indexterm> E.g., if J is an integer variable, and
+the scope of the iteration is to be performed for those multiples of 2
+which are not multiples of 5 and which are less than the value of the
+integer K, one might write the iteration as follows:</para>
<!-- beginpage II.17 -->
diagrams represent some valid configurations:</para>
<indexterm><primary>Scope</primary></indexterm>
+<indexterm><primary>Valid Iteration Configuration</primary></indexterm>
+
<!-- beginpage II.18 -->
&scope1;
<para>Normally, the value of a function will occur as part of an expression, as in the statement:</para>
+<indexterm><primary>Value of a Function</primary></indexterm>
+
<programlisting>
Z = COS.(X)/SIN.(X + 2.)
</programlisting>
according to format &scriptF;.
<indexterm><primary>READ BCD TAPE</primary></indexterm>
<indexterm><primary>READ BINARY TAPE</primary></indexterm>
+<indexterm><primary>WRITE BCD TAPE</primary></indexterm>
+<indexterm><primary>WRITE BINARY TAPE</primary></indexterm>
</para>
</listitem>
</varlistentry>
<term>WRITE BINARY TAPE &scriptN;, &scriptL;</term>
<!-- beginpage II.24 -->
<listitem>
-<para>Transmits &scriptL; to tape &scriptN; in binary form as one
-record.</para>
+<para>Transmits &scriptL; to tape &scriptN; in binary form as one record.
+<indexterm><primary>WRITE BINARY TAPE</primary></indexterm></para>
</listitem>
</varlistentry>
<varlistentry>
<para>Transmits &scriptL; to or from drum &scriptN; starting with drum
address &scriptA; (where &scriptA; is an integer expression).</para>
<indexterm><primary>READ DRUM</primary></indexterm>
+<indexterm><primary>WRITE DRUM</primary></indexterm>
</listitem>
</varlistentry>
<varlistentry>
<listitem><para>A vector appearing as the dimension vector of some
array<indexterm><primary>Array Variables</primary></indexterm> in a
dimension declaration is assigned integer mode (see <xref
-linkend='dimension_declaration'/>).</para></listitem>
+linkend='dimension_declaration'/>).
+<indexterm><primary>Vector</primary></indexterm>
+</para></listitem>
<listitem><para>A vector which is preset by a vector values
declaration is assigned a mode consistent with the assigned values
(see <xref linkend='VECTOR_VALUES'/>).<indexterm><primary>Dimension
-Vector</primary></indexterm> </para></listitem>
+Vector</primary></indexterm> <indexterm><primary>VECTOR VALUES
+Statements</primary></indexterm></para></listitem>
</orderedlist>
</sect2>
subscript."<indexterm><primary>Linear Subscript</primary></indexterm>
If A is an array then the name A is equivalent to A(0), e.e., the name
A written without a subscript is assumed to have a subscript of
-zero.</para>
+zero.<indexterm><primary>Zero subscript</primary></indexterm></para>
<para>Two dimensional matrices are stored internally by rows, i.e., an
m × n matrix will be stored in the order: a<subscript>11</subscript>,
although these do not all have to be used. The base element of YT,
i.e., YT(1,1, 1) will correspond to the element YT(4) since K(4) = 4.</para>
-<para>If the array is a vector, i.e., one-dimensional, a special convention
-is adopted. Only the first argument is given to the DIMENSION
-declaration. Thus, in the statement</para>
+<para>If the array is a
+ vector,<indexterm><primary>Vector</primary></indexterm> i.e.,
+ one-dimensional, a special convention is adopted. Only the first
+ argument is given to the DIMENSION declaration. Thus, in the
+ statement</para>
<para role='centered'>
DIMENSION V(10)
used.</para>
<para>(b) If part of all of a linear array is set by a VECTOR VALUES
-declaration the array need not appear in a dimension statement unless
-the maximum linear subscript implied by the initial values is not
-sufficiently high.</para>
+declaration<indexterm><primary>VECTOR VALUES
+Statements</primary></indexterm> the array need not appear in a
+dimension statement unless the maximum linear subscript implied by the
+initial values is not sufficiently high.</para>
</sect2>
<sect2><title>Equivalence Declaration</title>
<indexterm><primary>Hollerith (BCD)</primary></indexterm>
<para>(a) VECTOR VALUES &scriptV; = c<subscript>0</subscript>,
-c<subscript>1</subscript>, ... c<subscript>&scriptL;</subscript></para>
+c<subscript>1</subscript>, ... c<subscript>&scriptL;</subscript>
+<indexterm><primary>VECTOR VALUES Statements</primary></indexterm></para>
<para>Here &scriptV; is of the form N(n) or simply N, if n = 0. The
elements N(n), ... N(n + &scriptL;) are preset to the values
<para>(b) VECTOR VALUES &scriptV; = $ k<subscript>1</subscript>
... k<subscript>m$</subscript>,
-$k<subscript>m</subscript>+1... k<subscript>p$</subscript>, ...</para>
+$k<subscript>m</subscript>+1... k<subscript>p$</subscript>, ...
+<indexterm><primary>$ Sign</primary></indexterm></para>
<!-- the m/6 here is $m over 6$ in eqn notation -->
<para>Here the k<subscript>i</subscript> may be any valid characters
<para>The name of a function with the period deleted must not be used
as the name of a variable or as a statement label. A statement label
must not be identical with any variable
-name.<indexterm><primary>Statement Labels</primary></indexterm></para>
+name.<indexterm><primary>Statement Labels</primary></indexterm>
+<indexterm><primary>Variable</primary></indexterm>
+</para>
<para>The translator automatically calls on some subroutines, hence the
following names may not be used as variable names or statement labels
<indexterm><primary>SETEOF Subroutine</primary></indexterm>
<indexterm><primary>SETETT Subroutine</primary></indexterm>
<indexterm><primary>SYSTEM Subroutine</primary></indexterm>
+<indexterm><primary>TAPERD Subroutine</primary></indexterm>
+<indexterm><primary>TAPEWR Subroutine</primary></indexterm>
<indexterm><primary>Subroutines</primary></indexterm>
<!-- beginpage II.49 -->
</sect2>
<sect2><title>Example 2<emphasis role='note'>: Printing the truth table of a Boolean expression</emphasis></title>
+<indexterm><primary>Truth Table</primary></indexterm>
+
<para><emphasis>Problem:</emphasis> A logical (Boolean) expression
such as (P .AND. Q) .OR.(.NOT. P .AND. R .AND. S).OR.(R .OR. P) will
have a value TRUE or FALSE (represnted here by 1B and 0B,
</programlisting>
<!-- beginpage III.54 -->
+<indexterm><primary>Value of a Function</primary></indexterm>
+
<!-- used in the listing above -->
<indexterm><primary>SET LIST TO Statement</primary></indexterm>
</sect2>
<!-- beginpage III.56 -->
<sect2><title><emphasis role='note'>Example 4: Evaluate Tschebychev polynomials</emphasis></title>
+
+<indexterm><primary>Tschebychev Polynomial Example</primary></indexterm>
+
<para><emphasis>Problem:</emphasis> To evaluate Tschebychev polynomials.</para>
<para><emphasis>Analysis:</emphasis> The Tschebychev polynomial T(N,X)
<para>1.3 The statement may start anywhere in cols. 12-72. With the
exception of characters enclosed between "$" spaces are not relevant.
(Spaces may not be relevant even if they are so enclosed (see section
-2.15) on format specifications).</para>
+2.15) on format specifications).<indexterm><primary>$
+Sign</primary></indexterm></para>
<para>1.4 The identification information in cols. 73-80 is not used by
the computer for any purpose but printing during translation and is
<listitem><para>Entry to this routine causes a return to the operating
system. The END OF PROGRAM statement produces a call for this
routine. <indexterm><primary>END OF PROGRAM Statement</primary></indexterm>
+<indexterm><primary>SYSTEM Subroutine</primary></indexterm>
</para></listitem>
</varlistentry>
<!-- beginpage IV.5 -->
variables to be written. The WRITE BCD TAPE ... statement produces
a call for this subroutine.
-<indexterm><primary>Hollerith (BCD)</primary></indexterm></para></listitem>
+<indexterm><primary>Hollerith (BCD)</primary></indexterm>
+<indexterm><primary>TAPEWR Subroutine</primary></indexterm>
+<indexterm><primary>WRITE BCD TAPE</primary></indexterm>
+<indexterm><primary>WRITE BINARY TAPE</primary></indexterm>
+</para></listitem>
</varlistentry>
<varlistentry>
routine.
<indexterm><primary>READ BCD TAPE</primary></indexterm>
<indexterm><primary>READ BINARY TAPE</primary></indexterm>
+<indexterm><primary>TAPERD Subroutine</primary></indexterm>
</para></listitem>
</varlistentry>
Non-Executable</primary><see>Non-Executable Statements</see></indexterm>
<indexterm><primary>Subscript, Linear</primary><see>Linear Subscript</see></indexterm>
<indexterm><primary>Subscript, Negative</primary><see>Negative Subscript</see></indexterm>
+<indexterm><primary>THROUGH Statement</primary><see>Iteration Statement</see></indexterm>
+<indexterm><primary>Transpose of a Matrix</primary><see>Matrix Transpose</see></indexterm>
+<indexterm><primary>Truncation</primary><see>Intrger Division</see></indexterm>
+<indexterm><primary>Variables, Bound</primary><see>Bound Variables</see></indexterm>
+<indexterm><primary>Variables, Dummy</primary><see>Dummy Variables</see></indexterm>
+<indexterm><primary>Vector, Presetting</primary><see>Presetting Vectors</see></indexterm>
<index/>
</appendix>
projects / mad.git / commitdiff