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         Volume 2 Number 2        48/39              February 1977

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

Tips
     Clever Uses of INV P/R:  Dix Fulton (83) suggests the following
sequences to handle raising a negative number (in Reg 01) to an integer
power (in Reg 02):  for the SR-52:  RCL 01 STO 00 0 INV *P/R X RCL 02
= cos X RCL 00 yx RCL 02 =; for SR-56:  RCL 1 x:t 0 *f(n) R-P X RCL 2
= cos X x:t yx RCL 2 =.  Jared Weinberger (221) notes that: 0 INV *P/R
for the SR-52 or 0 *f(n) R-P for the SR-56 replaces the contents of
Reg 00 (t) with its absolute value.  For a practical application of
these facets of INV *P/R see "Short, fast quadratic solutions" in the
Routines column below.
     More on Charger Connection:  Larry Mayhew (145) reports that
John Allen's charger connection method (V1N7p4) appears to cause
execution speed to slow slightly (he had to change the constants in
his timer program (V1N7p6) to around 9600... a change of 1-2%).  This
condition appears to hold until the machine is turned off.  Subsequent
"normal" turn-ons apparently produce normal execution rates.  Anyone
care to venture a guess as to what's going on?
     A Decrement-Only dsz (52):  Larry has found the sequence ... *dsz
0 op ... (where op is any non-numeral instruction) to work whenever
Reg 00 is to be decremented without a zero-test for transfer.
     1/0=0:  Larry further notes that in cases where reciprocals of
sequenced numbers are calculated and it is desired to have 1/0=0, the
sequence: n yx 1 +/- = will work, where n ≥ 0.  However, results are
not always exact, and rounding may be necessary if integer results
are required.
     Trig Function Anomalies:  In the course of trying to get a
practical program to work, Larry found that there are normal trig
sequences which can hang up and produce an error condition.  There
appear to be critical numbers close to 90° (pi/2 in radian mode)
which when operated upon by INV sin produce numbers slightly larger
than one, and other critical numbers close to zero which when operated
upon by INV cos also produce such numbers (SR-56 too).  Unfortunately,
some of these critical numbers can be created by the sin and cos
functions themselves.  The sequence (in degree mode):  0 INV cos sin
INV sin produces an error condition, since 0 INV cos sin produces
89.99999999987 and the machine sine of that is 1.000000000001.  The
worst case I have found so far is to take the Sine of 89.99999999540
which produces 1.000000000004.  So the moral of the story is: if in
doubt, round!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  The SR-52 Users Club is a non-profit loosely organized group of SR-52/56 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, Incorporated.  Membership is open to any interested person:
  $6.00 includes six future issues of 52-NOTES; back issues start June 1976 @ $1.00 ea.

Tips (con)
     More on + STO 6O (52):  Chuck Sanford (214) and Dallas Egbert (384)
note that the sequence:  + STO 60 = leaves a pending INV, and Chuck
points out that + STO 60 = EE is a short manual method of displaying
the 4th through 13th digits (of numbers greater than one).  The EE
executes as INV EE.
     The Printed "?" as an Identifier (PC-100):  Sandy Greenfarb (200)
has found that purposely creating an error condition prior to a *prt
is a handy way to mark selected outputs, since the printed "?" is
easy to spot as well as to create.
     Step 223 (99) *list:  executes as a normal HLT (R/S) when run with
the printer; otherwise a run-past-last-step error condition is created.
     Optimized Hardware Interrupts:  Jared Weinberger (221) points out
that the approach suggested in V1N2p4 (top) requires more execution
time than necessary, since advantage can be taken of the fact that the
machine executes the sine function quicker if the result is zero than
otherwise.  If the sequence is rearranged as follows: ... *pi sin
*ifzro *pi HLT *LBL *pi ... then uninterrupted loop execution occurs in
radian mode.  SR-56 mechanization needs to take into account the fact
that the choice of angle modes during program execution is between
degrees and grads.  The sequence starting at step 00:  90 cos *x=t 07
R/S ... RST executes uninterrupted when in degree mode and halts at the
H/S when in grad mode.  (The t register must be zeroed prior to execution)
     Re-softening a Hardened Display:  Dallas Egbert (384) notes that
the sequence EE INV EE softens a hardened display to the extent that
successive keyed numerals are positioned at the LSD of the mantissa.
For example, key: 1.23 = EE INV EE 45 and you get 1.2345.  Dallas also
notes that any hardened number followed by EE INV EE CE can be fully
restored via Ed Haas' routine (V1N6p3).  However, the EE rounds the
mantissa to ten places.

Routines
     Short Fibonacci Sequence (56):  Paralleling the SR-52 routine
(V1N1p3), Sandy Greenfarb (200) has devised a short SR-56 Fibonacci
sequencer which, slightly modified, lists starting at step 00 as:
+ *pause x:t RST;  (x:t means x exchange t).  In run mode key: CLR x:t
1 RST R/S, and see each successive Fibonacci number pause-displayed.
(Replace the *pause with a *Prt for printed output via the PC-100).
     Short, Fast Quadratic Solutions:  A couple of years ago, John
Herro (HP-65 Users Club member #47) found a clever use of the rectangu-
lar to and from polar conversion functions (see Tips above) in develop-
ing an efficient algorithm for calculating both real and complex roots
of quadratic equations with real coefficients.  The following routines
are my mechanizations of John's algorithm:  for the SR-52:  *LBL A
STO 01 *1/x X HLT div 2 = STO 02 *x2 - HLT div RCL 01 = STO 00 0 INV
*P/R div 2 = *EXC 00 *rtx *EXC 00 *P/R HLT RCL 00 - RCL 02 = HLT RCL 02
+/- - RCL 00 = *rtn; for the SR-56:  starting at step 00:  STO 1 *1/x
X R/S div 2 = STO 2 x2 - R/S div RCL 1 = x:t 0 *f(n) R-P div 2 = x:t
*rtx x:t *f(n) P-R R/S x:t + (CE - RCL 2) R/S RCL 2 = +/- R/S.  To run
them (SR-56 instructions in parentheses):  Key a, press A (RST, R/S);
key b, RUN (R/S); key c, RUN (R/S); see imaginary part of root displayed;
key RUN (R/S) and see real part of root one; key RUN (R/S) and see real
part of root two.  a, b, c are the coefficients of a quadratic in the
form ax2 + bx + c = 0.

                         - - - - - - - - - - -

                              52-NOTES V2N2p2

Analysis of a Super Program
     Barbara Osofsky (420) has indeed produced a one-card program that
not only calculates the determinant and inverse of a 5 X 5 matrix, but
also does a 4 X 4 determinant and solves a system of four simultaneous
equations.  While many of you may be wearying of matrix programs, I
think you will find the time taken to see how this one is structured
to be well spent, since many constructs are applicable to other how-to-
get-it-all-to-fit situations, and the analysis that follows is concerned
with programming techniques, not applied matrix theory.  As it lists
below, Barbara's program was modified to reduce the amount of manual
keying required, and a few labels and registers were rearranged for
I/O ease.
     Let's begin by looking at the input routine, beginning at step
138.  At first glance it looks straight forward enough, except for the
error test and the extra summing.  But note that routines D', D and A'
all run right through it!  Thus routine A is used each time D', D or A'
is called (which is quite a few) besides for inputting data.  Routine B'
does most of the arithmetic, and is called 60 times for the 5 X 5
determinant and 300 times more for the inverse.  Note that routine B' is
written "in-line", that is, it doesn't call any subroutines itself.
This is necessary because it itself is a third-level call (by E to C' to
B'), and it would run slower, even if it could be shortened with sub-
routine calls.  Note that space is saved by running it into E'.
Routine D' heads up the D' D A' A chain, and calls a part of itself four
times before running directly through it (the A' A part).  The only
conditional branch occurs as an *iferr flag at step 145 (see V2N1p4).
The flag is set with a user call to the undefined label C, and reset
with the CE at step 166.  An important output (the 5 X 5 determinant)
is created just prior to execution of step 180; yet without parentheses
it is pushed into Reg 60 with a + operator and safely preserved during
the execution of some 130 succeeding steps, until it finally emerges at
step 191 for disposition.  This is possible because no intervening
display arithmetic occurs.
     Throughout, it is careful structuring and ordering of subroutines
that saves the most space, and makes it possible for the user to
accomplish so much with a one-card program.  The program itself had to
be fit within 200 steps, since 3 program storage registers are used
for data.

SR-52 Program:  5 X 5 Determinant and Inverse; 4 x 4 Determinant and
 (with PC-100)  4 Simultaneous Equations            Barbara Osofsky/Ed

5 X 5 User Instructions:
1.  Initialize:  95 STO 66
2.  Input the 25 elements (ei) with column-wise catenation: key ei,
    press A, see 1; repeat for i=1,2, ... 25.
3.  Get the Determinant:  press B then E; see determinant displayed
    after about 2 minutes.
4.  Ignore 4 lines of print:  On printer press ADV, tear off tape,
    press PRINT, ADV.
5.  Get Inverse:  Press B then E; first column printed, see 1 displayed.
6.  Key next column number (r), press RUN, C then D then E; rth column
    printed, 1 displayed; repeat for r=2,3,4,5.

                              52-NOTES V2N2p3

5 x 5 User Instructions (con)
Notes:
      1. If elements are input with row-wise catenation, inverse
         elements are printed by rows.
      2. Before step 3 execution, the number 1 must be displayed; before
         step 5 execution, the determinant must be displayed.
      3. At step 6, do not cancel error condition caused by pressing C;
         routine D ends by flashing 5.

4 x 4 User Instructions:
1.  Initialize:  95 STO 66 1 A
2.  Input the constant column (ci):  Key ci, press A; see 1; repeat
    for i=1,2,3,4.
3.  Input coefficients (aij) by column:  Key aij, press A; see 1;
    repeat for i (row) =1,2,3,4,5 and j (column) =1,2,3,4 where aij=0
    are four dummy elements that must head each column.  a54 is the
    last coefficient, and should be in Reg 19 (following RCL 19, replace
    the 1 in the display before proceeding).
4.  Get Determinant:  Key B then *C'; determinant is printed; on printer
    key ADV.
5.  Key 0 = +/- B then E; see printed: -1, x1, x2, x3, x4; -1 displayed.
    Original input ordering of elements is returned (Reg 95-19).

Program Listing:

000:  *LBL *B' STO 68 (*IND RCL 66 x *IND RCL 68 - 1 SUM 66 +/- SUM 68
024:  *IND RCL 66 X *IND RCL 68) X *LBL *E' 1 SUM 66 *rtn *LBL *C' (8
046:  STO 66 4 *B' *E' 17 *B' +/- + 19 *B' STO 66 7 *B' -14 *B' *E' 17
072:  *B' + 19 *B' *E' 2 *B' + 9 *B' *E' 2 *B' - 4 *B' 6 STO 66 12 *B')
097:  div RCL 67 B X *prt RCL 95 + *rtn *LBL *D' 10 INV SUM 69 *LBL D
119:  95 STO 66 *A' *A' *A' *A' *LBL *A' *IND RCL 66 *IND *EXC 69
138:  *LBL A *IND STO 66 5 *iferr 150 1 SUM 69 SUM 66 *rtn *LBL B +/-
160:  STO 67 *rtn *LBL E CE 0 STO 69 *C' D *C' D *C' D *C' D *C' 5
181:  SUM 69 *D' *D' *D' *D' 0 = *pap HLT + 94 = STO 69 HLT

Magazine Review
     Members have asked for information concerning personal programming-
related periodicals.  Herewith a start.  I invite reviews of other
related periodicals from the membership.
     Byte: (the small systems journal) is aimed at the computer hobbyist,
and appears to be a fairly respectable commercial operation (total paid
circulation 30 Sep 76 of 62,280).  Published monthly by Virginia and
Manfred Peschke at 70 Main St, Feterborough, NH 03458 at $12 per year,
you'll have to scrounge for back issues.  Topics range over both hard-
ware and software aspects of building and using the class of machines
centered on the 8080 and 6800 type microprocessors, although personal
programmable calculators have occasionally been the subject of articles
and letters.
     Popular Computing: is published monthly by Fred Gruenberger (27)
at Box 272 Calabasas, CA 91302; Jan 77 is the 46th issue.  Each issue
runs 20 unreduced typewritten 8½x11 pages, with almost no advertising.
Topics generally concern numerical problems and puzzles whose solutions
are apt to require the use of large computing systems.  However, there
are problems which can be productively explored with personal programma-
bles.  On occasion computer-related philosophical topics are aired.
Subscription is $20.50 per year; back issues $2.50 each.

                              52-NOTES V2N2p4

A Fractured Digits, All Flags, Game Application (52)
     Alan Charborneau (306) found that dice rolling for the poker-like
game of Yahtzee could be mechanized for the SR-52 in such a way as to
take advantage of display variations (V1N2p5), as well as to pose a
selection requirement nicely met by using all 5 flags.  With a few
optimization revisions, Alan's program appears below.  Routine D' is
called by the main program (which starts at step 038) each time a new
die roll is required.  Dice values are temporarily stored and select-
ively changed, then integrated with a skeleton string in Reg 06 for
Reg 60 manipulation to produce the 5-dice display.  The flags "freeze"
selected dice for partial rolls.  The required flag manipulations
spotlight how nice it would be to have a function that only resets all
flags (not do everything *rset does).  Perhaps there is a "puzzling
sequence" (V2N1p1) that would do the trick.  p73 is sort of an inverse
of what is required since it causes a branch to step 000, but does not
reset flags.

SR-52 Program:  Yahtzee                        Alan Charbonneau (306)/Ed

User Instructions:

1.  Key random number seed: 0 < seed < 1, press *A'; see 9D99;
    press =, see first roll of 5 dice:  d1-d2-d3-d4-d5
2.  (Optional) Save dice by pressing one or all of A, B, C, D, E
    for corresponding dice positions
3.  Press RUN to roll remaining dice (if step 2 is omitted, all 5 dice
    are rolled); see 9D99; press =, see next dice configuration.  Go
    to step 2 for dice save, or repeat step 3 for new roll.

Program Listing:

000:  *LBL *D' RCL 98 X *pi = STO 98 - .5 = *fix 0 *D.MS INV SUM 98
022:  RCL 98 X 5.5 + 1 = *D.MS *IND STO 00 *rtn 5 STO 00 *ifflg 0 048
047:  *D' INV *stflg 0 *dsz 0 *ifflg 1 059 *D' INV *stflg 1 *dsz 0
064:  *ifflg 2 070 *D' INV *stflg 2 *dsz 0 *ifflg 3 081 *D' INV *stflg 3
084:  *dsz 0 *ifflg 4 092 *D' INV *stflg 4 1 EE 95 STO 99 5 STO 00
106:  RCL 97 STO 06 *IND RCL 00 X RCL 99 = SUM 06 100 INV *PROD 99
131:  *dsz 112 RCL 96 + STO 60 RCL 06 HLT CLR GTO 038 *LBL *A' STO 98
156:  CLR GTO 038 *LBL A CLR *stflg 0 GTO 037 *LBL B CLR *stflg 1
175:  GTO 037 *LBL C CLR *stflg 2 GTO 037 *LBL D CLR *stflg 3 GTO 037
197:  *LBL E CLR *stflg 4 GTO 037 0 0 *pap cos 6666 . *pap *ifzro
217:  90000 *ifzro *ifzro
                          - - - - - - - - -

Forum
     Sick Machine Exchange:  Robert Hausafus (431) suggests calling
your nearest TI machine exchange center before taking your machine in;
they may not have the unit you need in stock,  in which case ask them
to order one for you.  Robert's problem with a PC-100 may be a common
one:  inoperative character dots.
     Applications Topics:  Thomas Watkins (347) suggests that each
month 52-NOTES focus on one applications topic (games, surveying,
aviation/navigation, physics/chemistry, etc), emphasizing routines
that maximize user efficiency and ease.  I invite members to send me
their algorithms, routines, approaches; or a description of problems
encountered trying to get a particular applications program to work.
As info builds sufficiently on any one topic, I'll publish the material
in 52-NOTES.

                              52-NOTES V2N2p5