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<book>
<preface><title>Notes from the 21st century</title>
single-valued function will be called a "function", and a function
with multiple outputs and/or multiple exits will be called a
"procedure". For the purposes of this manual a recursive function is
-one whose definition contains calls for the function being defined --
+one whose definition contains calls for the function being defined ⅆ
or calls for functions which ultimately call the one being defined.
Recursive functions have the same structure as other functions
although, in general, they will include statements of the type
<sect3 id='external_functions'><title>External Function Definitions</title>
+<!--
+In the original, "variables and functions in the main program" was
+typoed as "variables and function in the main program" (incorrect
+singular).
+-->
<para>These statements define functions not yet available in the
language or as standard package programs ("subroutines"). The
designatyion "EXTERNAL" implies that the statements which follow are
DIMENSION and MODE declaration, etc.) The word "EXTERNAL" also
implies that occurrences of variables and functions in the current
function definition program have no relation whatever with occurrences
-of similarly named variables and function [typo] in the main program
+of similarly named variables and functions in the main program
(or other definition programs), and no difficulties will be
encountered because of the use of similar names. The modes of the
arguments (if other than the normal mode), must be declared in the
zero on the main diagonal of the coefficient matrix during the
solution process.</para>
-<para><emphasis>Analysis</emphasis>: We shall use a Jordan Elimation [typo?]
+<!-- The original had a typo, "Elimation" for "Elimination" -->
+<para><emphasis>Analysis</emphasis>: We shall use a Jordan Elimination
Method, in which each diagonal coefficient is used to "clear" all
other coefficients in its column to zero by appropriate
multiplications and subtractions. Since we shall divide the "clearing
<para>Problem: Mortgage Payment. The type of mortgage we consider is
the fixed principle type for which each installment consists of an
interest payment, a fixed amount to be deducted from the outstanding
-principal, and an additional amount to be placed in escrow--to be used
+principal, and an additional amount to be placed in escrowⅆto be used
to make insurance and tax payments.</para>
<!-- The original says "interest rage" and "nortage number" -->
<para>The printed diagnostic comment may very often have an alternative or
ambiguous form. This results from the fact that it is frequently not
-possible to determine what form was intended--merely that the present
-structure is not admissible--and therefore some of the alternative
+possible to determine what form was intendedⅆmerely that the present
+structure is not admissibleⅆand therefore some of the alternative
possibilities are suggested by the comment.</para>
</sect1>
<!-- beiginpage IV.3 -->
<!-- the original had a tyo, "Probram" for "Program" -->
-<para>Subroutines which are written for use by MAD programs--whether
+<para>Subroutines which are written for use by MAD programsⅆwhether
written in MAD as functions or in SAP<footnote><para>SAP is the SHARE
-Assembly Program [typo] which permits the writing of actual machine
-instructions in symbolic form.</para></footnote>--must be relocatable
+Assembly Program which permits the writing of actual machine
+instructions in symbolic form.</para></footnote>ⅆmust be relocatable
and must operate from the calling sequences the translator produces.
-Consider, for example the function call --FN. (A,B,C)--which might
+Consider, for example the function call - FN. (A,B,C) - which might
appear in the body of a statement. Assume that B is an array which has
an associated dimension vector BDIM. Using SAP notation for
illustrative purposes, the calling sequence produced would be</para>
TXH C
</programlisting>
-<para>Input-output routines utilize two types of parameters--the
+<para>Input-output routines utilize two types of parametersⅆthe
regional and single variable types. In addition an error return is
given as well as a format specification location. The parameter
operation code used is TXI and the end of the parameter list is
<!-- beginpage IV.4 -->
<para>It is important to notice that in this example, as well as in the
-first, the parameters--if executed as instructions--would produce no
+first, the parametersⅆif executed as instructionsⅆwould produce no
operation.</para>
<para>It is beyond the scope of this manual to discuss the structure of
relocatble programs (see IBM FORTRAN II Manual). It is suficient to
-say that a relocatable program must contain--in adidtion to the actual
-instructions in the program--information as to which addresses must be
+say that a relocatable program must containⅆin adidtion to the actual
+instructions in the programⅆinformation as to which addresses must be
relocated at the time of loading for execution and which addresses
must not. In addition, the first card (or record) of such programs
must contain information about the size of the program, the number of
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