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.ll 75
:frontm
:titlep
:title.Extended Precision Programs for the TI-59
:author.Robert AH Prins
:address
:aline.52 Lummis Vale\
:aline.Kesgrave\\\\\\\
:aline.Ipswich\\\\\\\\
:aline.Suffolk\\\\\\\\
:aline.IP5 2FJ\\\\\\\\
:aline.England\\\\\\\\
:eaddress
:etitlep
.sp 46
&cop Copyright 1986-2000 Prino Productions
.sp
.fo off
These programs are free software; you can redistribute them and/or
modify them under the terms of the GNU General Public License as
published by the Free Software Foundation; either version 2, or
(at your option) any later version.

These program are distributed in the hope that they will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with these program; if not, write to the Free Software
Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
.fo on
:preface
<p>This document describes several programs for the TI-59 Programmable
Calculator, which allow the user to calculate factorials, "e", &PI.,
natural logarithms and square roots up to 1300 digits.
<p>The programs included are:
:dl tsize=6
:dt.EPF1
:dd.Extended Precision Factorials I
<br>
This program can calculate factorials up to 442!
:dt.EPF2
:dd.Extended Precision Factorials II
<br>
This program can calculate factorials up to 610!
:dt.EPe1
:dd.Extended Precision e I
<br>
This program calculates e to 980 places.
:dt.EPe2
:dd.Extended Precision e II
<br>
This program calculates e to 1300 places.
:dt.EPe3
:dd.Extended Precision e III
<br>
This program calculates e to 870 places.
:dt.EPP1
:dd.Extended Precision Pi I
<br>
This program can calculate &PI to 1188 places.
:dt.EPP2
:dd.Extended Precision Pi II
<br>
This program can calculate &PI
up to 1287 places. Users of this program are warned that this program
may take up to about 13.5 <b>DAYS</b> to finish the calculations.
:dt.EPL
:dd.Extended Precision Ln(x)
<br>
This program can calculate natural logarithms up to 1188 places.
:dt.EPR1
:dd.Extended Precision Roots I
<br>
This program can calculate square roots up to 155 places.
:dt.EPR2
:dd.Extended Precision Roots II
<br>
This program can calculate square roots up to 400 places, but using an
extension it is possible to extend the number of places to 800.
:edl
<p>All of the programs included were written to be used on a TI-59, and
all but four of them require a PC-100 to print the results. There are
however a lot of people who don't have a PC-100 or just a TI-58 or a
TI-66. To make this document also useful for them, most programs come in
several versions. A summary can be found in the table below.
кФФФФФФФФФТФФФФФФФФФФФФФФФФФФФФФФФФФФФФФФФФП
Г         Г             Version            Г
УФФФФФФФФФХФФФФФФФФТФФФФФФФТФФФФФФФТФФФФФФФД
Г Program Г PC-100 Г TI-59 Г TI-58 Г TI-66 Г
УФФФФФФФФФХФФФФФФФФХФФФФФФФХФФФФФФФХФФФФФФФД
Г EPF1    Г   I    Г  I'   Г  I+   Г  I+   Г
УФФФФФФФФФХФФФФФФФФХФФФФФФФХФФФФФФФХФФФФФФФД
Г EPF2    Г   X    Г  I    Г  I'   Г  D/H  Г
УФФФФФФФФФХФФФФФФФФХФФФФФФФХФФФФФФФХФФФФФФФД
Г EPe1    Г   I    Г  I'   Г  I+   Г  I+   Г
УФФФФФФФФФХФФФФФФФФХФФФФФФФХФФФФФФФХФФФФФФФД
Г EPe2    Г   X    Г  I    Г  I'   Г  I    Г
УФФФФФФФФФХФФФФФФФФХФФФФФФФХФФФФФФФХФФФФФФФД
Г EPe3    Г   I    Г  I'   Г  I'   Г  D/H  Г
УФФФФФФФФФХФФФФФФФФХФФФФФФФХФФФФФФФХФФФФФФФД
Г EPP1    Г   I    Г  I'   Г  C    Г  C    Г
УФФФФФФФФФХФФФФФФФФХФФФФФФФХФФФФФФФХФФФФФФФД
Г EPP2    Г   X    Г  I    Г  I'   Г  I    Г
УФФФФФФФФФХФФФФФФФФХФФФФФФФХФФФФФФФХФФФФФФФД
Г EPL     Г   I    Г  I'   Г  C    Г  C    Г
УФФФФФФФФФХФФФФФФФФХФФФФФФФХФФФФФФФХФФФФФФФД
Г EPR1    Г   I    Г  I'   Г  I    Г  D/H  Г
УФФФФФФФФФХФФФФФФФФХФФФФФФФХФФФФФФФХФФФФФФФД
Г EPR2    Г   I    Г  I'   Г  I'   Г  I-   Г
РФФФФФФФФФСФФФФФФФФСФФФФФФФСФФФФФФФСФФФФФФФй
<p>The codes in the above table have the following meaning:
:dl tsize=5
:dt.I
:dd.Listing is included.
:dt.I'
:dd.Listing is not included, as only minor modifications have to be made
to the PC-100 or TI-59 version.
:dt.I+
:dd.To make the best use of the available memory, two separate programs
have been included:
<ul>
<li>A calculate program.</li>
<li>A program to read out the results.</li>
</ul>
:dt.I-
:dd.Only a limited version of the program has been translated.
:dt.D/H
:dd.Due to the extensive use of HIRs and/or DSZs on registers above R09,
no translation was made.
:dt.C
:dd.Due to the fact that this program uses
magnetic cards for intermediate storage, no translation was made.
:dt.X
:dd.A version of this program that prints the result(s) directly does
not exist, but a separate print/read-out program is included.
:edl
<p>Some notes about the organisation of this document:
<ul>
<li>This document is divided into 10 chapters, each of which describes
one program.</li>
<li>Each of the chapters is divided in the following sections:</li>
<ul>
<li>A short description of the program and its origins.</li>
<li>A description of the method that is used in it.</li>
<li>A program part, which is divided into two sub-sections, and which is
repeated for every version of the program. The two sub-sections are:
<ol>
<li>User instructions.</li>
<li>A listing.</li>
</ol>
<li>Some last notes about the program.</li>
</ul>
<li>An appendix with some guidelines to speed up all of the programs
a little bit.</li>
<li>An appendix with some guidelines to decrease the precision
of the <b>EPe</b>-programs, but to increase the speed of them.</li>
<li>An appendix which describes some special features of the TI-66,
such as a way to save steps when you use absolute addresses and a way
to double the speed.
:note.The TI-66 keycodes used in this book are not discussed in this
appendix, because that would add a lot of pages, which would not be of
any interest to most readers.</li>
<li>An appendix containing four TI-57 programs, two for calculating
factorials and two for calculating "e".</li>
<li>An appendix with some results of the various programs. To make the
programs not completely obsolete, the results are limited to 99, 100 or
101 digits!</li>
</ul>
<p>One last note:
The results generated by all programs are "guaranteed" to be correct to
the very last digit, with one exception:
<ul>
<li>The results of the Very Extended Precision Extension of
<b>EPR2</b> are correct to at least 799 digits. Digit 800 may be
correct, but in the testcase, &SQR.3, it was too large by one.</li>
</ul>
.* toc tag generates Table of Contents here!
:toc
.pn ar
:body
.***************************************
.* Extended Precision Factorials I
.im F1
.***************************************
.* Extended Precision Factorials II
.im F2
.***************************************
.* Extended Precision e I
.im E1
.***************************************
.* Extended Precision e II
.im E2
.***************************************
.* Extended Precision e III
.im E3
.***************************************
.* Extended Precision pi I
.im P1
.***************************************
.* Extended Precision pi II
.im P2
.***************************************
.* Extended Precision Ln(X)
.im LN
.***************************************
.* Extended Precision Roots I
.im R1
.***************************************
.* Extended Precision Roots II
.im R2
.***************************************
.* Appendix A
.im AA
.* Appendix B
.im AB
.* Appendix C
.im AC
.* Appendix D
.im AD
.* Appendix E
.im AE
.***************************************
:egdoc