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         Volume 2 Number 12       48/39              December 1977

                     Newsletter of the SR-52 Users Club
                                published at
                           9459 Taylorsville Road
                              Dayton, OH 45424
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     Double Precision (56,57,58,59):  Norman Herzberg (688) suggests
that putting together a library of optimized fully double precision
arithmetic routines would be a worthy endeavor for the membership.
He leads off with the following integer multiplication routine which
runs fast and appears to give correct results to 20 places.  Printing
the product on a 20-digit line might be a useful enhancement.  To use
Norman's routine:  Key 10-digit multiplicand, press A; key 10-digit
multiplier, press B, 10 MSDs of the product displayed; press x:t, see
10 LSDs of product.  Multiplicand remains intact for use with a new
multiplier.  LE' ÷ x:t 1 EE 5 = Int x:t - x:t X x:t 1 EE 5 = rtn LB
E' S4 x:t INV SUM4 X R1 S7 = S5 x:t X R2 INV SUM7 = S6 E' Exc6 + x:t
+ R7 X R4 + R5 = E' X 1 EE 5 = SUM6 x:t SUM5 CLR R6 x:t R5 rtn LA S1 E'
S2 x:t Exc1 rtn.  Members are invited to try to improve upon Norman's
routine and/or address other double precision functions.
     The Mathematical Integer Function (56,57,58,59):  Joel Pitcairn
(514) notes that the built-in Int function does not handle negative
reals properly, since for mathematicians the integer part of x is
defined as being the greatest integer ≤ x.  Joel suggests using the
following routine (slightly revised) to get the integer part of all
reals:  ...CP + INV Int Op 10 x≥t 1' + L1' 0 = Int... .  I invite
56/57 versions (which will have to do without the Op 10 signum function).
     More Conditionals (56,57,58,59):  Although data can usually be
arranged so that the conditionals x=t, x≥t, and their inverses will
handle all required comparisons, there are times when it would be
handy to have x≤t and its inverse as well. Jared Weinberger (221)
suggests:  ...x:t x≥t... for an effective x≤t, and ...x:t INV x≥t...
for an effective x>t. Ofcourse, the user needs to take into account
the x-t reversal in subsequent processing.
     Automatic Number Printer (58,59) Revisited (V2N10p2):  It has
been brought to my attention that R G Snow's routine might have a
flaw, since an input 88888 returns 1111111109 instead of 1111111111.
Well, it turns out that RG's routine translates 7s or 8s at either
the MSD or LSD position into 8s or 9s, respectively, instead of 11s
or 12s.  But this is all right since print code 8 prints a 7, and a 9
prints an 8 (see V2N10p4).

Membership Address Changes
     203:  9423 Bickford Rd Kernersville, NC 27284;  533:  Mink Creek
Rd  Star Rte Box 431 Pocatello, Idaho 83201.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  The SR-52 Users Club is a non-profit loosely organised group of TI PPC owners/users
  who wish to get more out of their machines by exchanging ideas.  Activity centers
  on a monthly newsletter, 52-NOTES edited and published by Richard C Vanderburgh
  in Dayton, Ohio.  The SR-52 Users Club is neither sponsored nor officially sanctioned
  by Texas Instruments, Inc.  Membership is open to any interested person:  $6.00
  includes six future issues of 52-NOTES; back issues start June 1976 @ $1.00 each.
Tips and Miscellany
     TI-58 Users Assistance:  Roy Chardon (515) has a TI-59, and has
kindly volunteered to broaden my offer to 58 users (V2N7p5):  On a
"to an extent determined by the circumstances" basis, Roy will 1)
attempt to "complete" problems which won't fit on a 58, and 2) will
serve as a PPX-59 channel... both "on a best effort basis, with no
money (or mag cards) exchanged."  Note that Roy's address changed
recently (V2N10p5).
     A p31 Application (52,58,59):  Roy notes that p31 can be put to
good use in programs requiring the user to write special applications
code.  For example, replace the R/S at step 373 of the V2N8p5 program
with p31, and delete the first LRN in step 1 of the user instructions.
     References to the 58/59 Owners Manual:  I plan to continue refer-
ing to the original (dash one) version.  When 52-NOTES references
identify errors or omissions corrected by later versions, there is no
harm done, but in cases where apparent contradiction or confusion
results, I ask that cognizant members so inform me.
     CROM Vs User Code Execution Speed (58,59):  Tom Ferguson (421)
found that CROM code executed within the module runs faster than the
same code downloaded into user memory and then run.  For example, the
routine C part of getting 69! with ML-16 takes almost twice as long
to execute in user memory as it does in the CROM.  Members are invited
to explore this further, and see if there are certain functions or
sequences that show more marked CROM/user-execution speed differences
than others.
     LRN Mode Lockout (58,59):  Fred Fish (606) notes that manual
partitioning that leaves the program pointer out of bounds disables
the LRN key.  An RST restores LRN mode access, although a 0.59 TI-58
partition absolutely disables the LRN key as long as that partition is
in effect.
     More on Dsz (58,59):  Jack Thompson (531) notes an exception to
all-register Dsz-ing (V2N8p2):  Dsz "40" is interpreted as Dsz Ind.
So don't try to Dsz Reg 40 directly.
     Ideas for a "Support Software" CROM (58,59):  Several members
have suggested that a CROM composed of widely used program building
blocks would be especially useful.  Send me your candidate routines
or ideas, and I'll consolidate them and see if we can interest TI.
     More on Printer Head Cleaning:  John Allen (104) reports that
printer head cleaning with the heavy paper really works (V2N10p5).
His PC-100A failed to print certain columns when he first bought it,
but performing the cleaning instructions fixed it right up.
     Protected Editing (58,59):  If you don't want to disturb unre-
locatable code near the bottom of program memory while editing code
near the top, temporarily repartition to make into data the code to
be protected.
     INV Viability (58,59):  The lack of INV viability noted in
V2N6p3 does not apply to INV instructions placed before labels. For
example:  LA INV LB Sin rtn executes as sin when called by B; as INV
sin when called by A.  Also, the normally merged rtn (INVSBR) can be
broken up as:  LA INV LB SBR 1' R/S L1' ... which if called by A
returns without doing anything; calls SBR 1' with a call to B.
     Mag Card Printing (52,59):  Horizons Technology Inc is marketing
ways to letter mag cards.  For details, write Tom Schroeder (663).

                              52-NOTES V2N12p2

     SR-51/51A/PC-100A:  Several members have called attention to the
Byte (Sept 77 p 176) letter describing SR-51/PC-100A compatibility.
Michael DeTraglia (544) found that his SR-51A doesn't have to be
"jammed" on to work.  For best results, select SR-52 switch position,
and trace mode.  Printout of non-SR-52 mnemonics suggests that the
extra SR-51 functions might at one time have been considered as part
of the SR-52 design.  Leon Ablon (619) notes that the PC-100 also
works in this SR-51/51A application, and that for dollar totals the
51s are better than the 52 since all addends are printed to 2 decimal
places with a fix 2 format (the 52 drops trailing zeros, as do the
55, 58 and 59).
     SR-52 Extended Memory:  Robin Wooding (350) has for several
months been using an SR-52 modified with extra memory such that 160
of the normal 224 program steps can be manually switched out and
replaced with 160 new steps, or vice versa.  Write him for details of
some of his applications.
     HLT-R/S, rset-RST, and rtn-INVSBR 52-58/59 Differences:  While
the 52's HLT hardens a soft display, the 58/59's R/S does not.  Bob
Myers (566) notes that a programmed 52 HLT with one or more pending
subroutine returns followed by a manually keyed A-E' that ends in
rtn causes control to move back through the original calling path.
For the 58/59, following a program-executed R/S and the manual A-E'
the next INVSBR encountered executes as an R/S, and effectively
clears the subroutine return address register.  Upon encountering an
rset, the 52 clears a soft display, while the 58/59 RST does not
affect the display.
     Fractured Display (58/59):  Rusty Wright (581) found that in
LRN mode at the last step of the current partition, keying a multi-
step instruction causes the display to be reformatted in strange
ways.  For example, with a 59 at turn-on, key 1234 GTO 479 LRG GTO
SBR, and see ".00000 1234".  The number of digits in the preset
display appears to determine the number of zeros appearing to the
right of the decimal point.  Other rules prevail with a floating
point (scientific) display, and Dsz a b or Dsz*cd e at step 479 do
even stranger things (the contents of reg cd shows up in the display).
     Corrections:  Gerald Donnelly (203) and Roy Chardon (515) note
that I got the "mental" and "spiritual" categories interchanged in
translating from Heinrich's German (V2N9p3).  Interchanging the reg-
ister pairs 19-20 with 21-22 should set things straight.  And, as
printed, Bob Myers' printer sensing routine (V2N10p4) sets flag 7
when the printer is not connected.
     Decapower Zero Suppression (52):  Douglass Darrow (687) notes
that the SSTd return from a called subroutine suppresses decapower
zeros just as the unmet conditional test does (V2N7p4).
     More on INV' and Dummy operations (56,58,59):  Rusty Wright (581)
notes that for the 56, INV' supplies a missing operand, but requires
2 successive = or ) strokes for completion of the pending arithmetic.
The Owners Manual specifies only CE as a shortcut to supplying missing
operands, but Rusty finds that RST also works.  The 58 and 59 act like
the 56, except that STO, RCL, and SUM also produce missing operands
when keyed manually, but as Jared Weinberger (221) found, when execu-
ted under program control treat the intended operation as a register

                              52-NOTES V2N12p3

     Program/Routine Listings for TI-56,57,58,59 Use:  52-NOTES
articles whose titles are followed by: (56,57,58,59) or some subset
thereof are likely to contain listings written for TI-59 use.  Generally
no changes are necessary for the 58, although in some cases, register
addresses and partitioning need to be scaled down.  For the 56, labels
and their associated relative addressing must be replaced with abso-
lute addressing, and for the 57, available labels should be substitu-
ted for specified A-E' ones.  For both the 56 and 57, register assign-
ments should be carefully assessed vis-a-vis existence and special use
(such as by statistics functions).  By and large, if a PPC's identi-
fier doesn't appear in the title, application of associated routines
may require non-trivial translation effort (see V2N8p6).
     SR-52A Zero Divide:  Paul Blair (526) notes that the special
zero divide error state (V2N11p3) does not occur with his SR-52A
     Flashing Display Variations:  Mark Stevans (216) notes that there
are 2 types of flashing display for the SR-52:  1) Display is com-
pletely blank between flashed positive numbers > 1, and 2) The 2
minus signs appear dimly between flashed numbers.  Mark refers to the
first as a hard flash, and the second as a soft flash.  Dividing by
zero or taking the INV sin of a number > 1 produces a hard flash;
keying an undefined label produces a soft one.  An SR-56 error condi-
tion caused by a manual or SSTd STO INV' (discovered by Rusty Wright)
is soft.  I haven't yet found a way to produce a soft flash on the
58 or 59.
     More on Execution of Unintended CROM Code (58,59):  Rusty Wright
found a code 81 at step 139 of Pgm 3 of the Statistics CROM, and
reports that it executes as RST:  control returns to step 000 of user
memory (see V2N8p6).  Rusty also found a couple of code 31s (steps
074 and 077) in the same CROM program, and found that they are ignored
... like p31 in protected code (V2N9p4).
     Another SR-52 Analytic Model (V2N10p5):  Ron has another program,
titled:  Computer Queuing Analysis on a Handheld Calculator (COMPUTER
DESIGN Nov 77 pp85-94).  Write Ron for details.
     Quaternion Arithmetic (59):  Joel Rice (3) has written programs
to perform quaternion (spinor) arithmetic for both real and complex
inputs, and is prepared to share his listings with members who send
him a SASE with 2 stamps.

Friendly Competition
     At least one HP-25 user has conceded that 100 unmerged SR-56
steps amount to more effective memory than 49 merged HP-25 steps
(comment by Jim Davidson 65-Notes V4N8p21)... and Jim has done a lot
of HP-25 programming.  Both machines are still powerful PPCs for the
money, but the SR-56 has always cost less, and so far, no HP-25 pro-
gram has come to my attention that couldn't be duplicated or bettered
on the SR-56.
     A year ago in a 65-Notes article on Taylor Series Summations on
Programmable Calculators (V3N9p17), Jim challenged users of AOS machines
with:  can you "...do as well as RPN for Taylor's series?  Or even
come close?" citing some HP-25 routines he had written.  Well, Rein-
hold Patzer (689) has risen to the challenge with some SR-56 routines,
all of which take less effective memory than the corresponding HP-25
routines, and produce results more accurate by a factor of 100.  As
a specific SR-56 response to Jim's benchmark program for ex (65-Notes

                              52-NOTES V2N12p4
V3N9p42 - Program 3), Reinhold offers:  00:  S0 1 S1 X x:t R0 ÷ R1 X
(CE + x:t X x:t 1 SUM 1) INV x=t 06 = x:t R/S, which in 30 steps takes
less effective program memory than Jim's HP-25 routine:  01:  S0 0 S1
1 S2 R2 R1 1 + S1 ÷ R0 X S2 + x≠y GTO 06 GTO 00, where 18 HP-25 steps
use 36.7% of memory compared with Reinhold's 30% (29% if one omits
the last x:t, which appears to be unnecessary).  On a test case of e25
I find that Jim's routine gets 6-place accuracy in 64 iterations, tak-
ing 46.1 seconds.  Reinhold's gets 9 places in 71 iterations, taking
67.3 seconds.  Thus it would appear that Jim's runs significantly
faster, at 1.39 iterations/second vs Reinhold's as 1.05, but it would
take Reinhold's only 50.4 seconds to get 6-place accuracy.  In his
article, Jim points out the HP RPN features that facilitate his
approach, but it is worth noting that one of the key features:  datum
replication from T to Z when the stack is dropped is nicely matched in
this exercise by the SR-56 T register feature that its contents is not
altered by AOS stack movement, or arithmetic operations.  It should
also be noted that AOS machines without the T register (notably the
SR-52) would be at a significant disadvantage in this competition.
Another point:  When HP-25/SR-56 routines are being compared, if their
application is enhanced by being subroutine-callable, as might well be
the case in this exercise, the HP-25 loses.  However, if Reinhold's
routine is called by a main program, there is a pending arithmetic
operation that must be cleared following disposition of the results if
further use of the arithmetic stack is to be made.
     Challenges aside, I recommend Jim's article to PPC users who
need help in formulating problems and synthesizing algorithms.  Jim
takes the reader from brute force, inefficient, but easy-to-understand
approaches to trickier more efficient ones, which as Reinhold shows
can apply to AOS as well as to RPN machines.  Reinhold acknowledges
that Jim gets the credit for tricky exiting, and efficient xi and x!
     Hal Brown has succeeded in getting a new version (65-Notes V4N8p10)
of his 5 X 5 matrix program (52-NOTES V2N8p3 and V2N10p2) to solve
more special-case problems without manual intervention, and appears to
have eliminated the error-without-warning cases.  Interested members
may send a SASE to Richard Nelson (2) for copies of this latest version,
but are advised to insert 2 missing steps:  50: GTO 0 and 150: x≠0.  I
invite comments.  The only other HP-67/97 5 X 5 program to come to my
attention is in the "High Level Math" volume of HP's recently published
Users Library Solutions.  This is a 1-card program by John L Gustafson
Ruddock House Caltech Pasadena, CA 91126 that calculates the determin-
ant and inverse by a method similar to Barbara Osofsky's (V2N5p5),
requiring no manual permutation of rows or columns, but which is less
compact, slower (takes about half an hour to run), and does not handle
ill-conditioned matrices as well as either Barbara's or Hal's.  For
the ill-conditioned matrix A whose elements are aij=1/(i+j-1), John's
program doesn't quite get one-place accuracy, Barbara's gets 4, but
Hal's wins with 5 (TI-58/59 ML-02 gets 8).  Here is a situation where
for a particular approach the greater arithmetic precision of the TI
machines is significant.  If Barbara's program were to be run with 10-
digit precision, results would probably be similar to John's.  Hal's
and ML-02 both employ pivoting, and I would expect ML-02 results to be
similar to Hal's if produced with 10-digit precision.

                              52-NOTES V2N12p5
Keying Printer Character Code (58/59)
     While the Rausch Overlay method (V1N3p2) works well to number-code
the alphabet for non-alphanumeric machines, it does not handle all 64
of the 58/59 print characters, and requires code-translation-machine-
execution time.  Lou Cargile (625) has tried a different approach,
which in one form or another looks promising:  He has typed/written
out the 64 characters on strips of paper which he fastens conveniently
on the printer.  Characters are grouped according to the first digit
of their print codes, and are annotated with the second digit.  For
example, associated with the numeral       2     key are the
                            characters  FGHIJKL  which have as their
              respective second digits  1234567  .  Some might find it
easier just to string out all 64 characters with the corresponding
2-digit print codes beneath each; or perhaps Lou's method could be
sufficiently miniaturized to make feasible a direct keyboard overlay.
Whatever the approach, the goal is to optimize the speed and accuracy
with which the user converts the characters to 2-digit keystrokes,
until such time as he has memorized them.  Other ideas are invited from
the membership.

Editorial:  52-NOTES Style/Club Philosophy Revisited
     A majority of members who comment on 52-NOTES style and content
continue to like things as they are.  Complaints haven't changed much
since we began, and generally reduce to:  1) material is too technical
and/or terse, 2) important items are buried in long paragraphs, 3)
abbreviations/mnemonics are not defined often enough, and 4) membership
expiration notices should be issued.  The nature of these complaints
suggests that the few dissatisfied members regard their membership as
a one-way magazine subscription, and I recommend that they reexamine
the Club's purpose (V1N1p1), and my approach to writing 52-NOTES
(V1N5p1, V2N7p1).  People teaching technical disciplines often find it
helpful to point out to their students that they should not consider
such courses to be spectator sports.  Learning to use modern computing
machinery is no exception, and I reemphasize the importance of
actually working examples on your PPC, and carefully and thoroughly
covering all references.  Don't skip over something you don't under-
stand at first glance; dig into it, and write for help if need be.
One advantage of a 6-page newsletter is that it is not impractical to
re-read many back issues from time to time... a good way to put lost
or overlooked tools within reach, and to refocus your attention on
topics whose value to you has waxed since first acquaintance.
     I'm pleased that the ranks of the productive minority are growing,
but suspect that there are still many in the silent majority who are
hiding their lamps under the proverbial bushel.  Members who partici-
pate the most seem to have the least difficulty getting all the infor-
mation they want from each issue of 52-NOTES, and they rarely miss an
issue due to forgetting membership expiration dates!  I think it benefits
all concerned to keep 52-Notes' technical level reasonably high,
otherwise the top contributors will lose interest.
     As the end of 1977 approaches, I take this opportunity to wish
you and yours a happy holiday season, and another challenging year

                              52-NOTES V2N12p6 (end)