GO-29 SciRPNclosely simulates the venerable HP-29C Programmable Pocket Scientific
Calculator.
The HP-29C was released in 1977 and sold for a MSRP of $195.
Virtually indistinguishable from the real item in operation, GO-29 was created in 2019 as a powerful yet
simple programmable retro calculator.
Topics
Prologue
1. Capabilities At A Glance
RPN (Reverse Polish Notation)
10-digit LED calculator display, 10-99 to 10+99
Four stack registers with roll down, labelled X, Y, Z, T
Thirty storage registers with arithmetic memory operators:
10 primary registers R0 - R9
6 statistical registers R.0 - R.5
14 indirect registers R(16) - R(29)
Math, trigonometric, polar⇔rectangular, sexagesimal⇔decimal, logarithmic, statistical, power and other miscellaneous functions
Programmable, with labels, subroutines, branching, conditionals, indirect addressing, annotated program listing, and memory for 198 program steps
Library of Sample Programs
Fast, slow or single step program execution
Program import via pasteboard or from other Apps (except Apple TV)
Program export via printer, email, pasteboard or to others Apps (except Apple TV)
Program File Sharing (except Apple TV)
Two additional windows with views of:
stack/storage registers
paper tape keystroke log
program source code
program documentation
Copy-from and Paste-to the calculator display (except Apple TV)
Use the OFF - ON switch and ensure the calculator is powered-on.
This document — also available as a PDF download GO-29 Help — is not an exhaustive reference manual; rather, it's a terse outline of the calculator's operation, and function and programming
keys. The information is structured so that prerequisite material generally comes first, thus, you are encouraged to read the topics sequentially.
In this document normal calculator keys are shown in bold, such as +, or x, or 4, or g.
Most keys can perform two other functions, however, one labeled in blue and and one labeled in gold. To execute one of these functions
you first touch the corresponding colored prefix key,
either r
or t,
followed by the desired function key.
So to compute the sine of a number
you'd touch two keys, the f prefix key followed by the 4 key.
However, this document will simply show the key as sin: the font color
implies which prefix character is used. Similarly, touching the two keys g
and 4 executes the inverse sine function sin-1. The only
exception to this convention is when discussing programming and keycodes.
The PRGM - RUN switch
controls the two basic calculator modes. In RUN mode, key presses are executed immediately and results are shown
in the calculator display area. In PRGM mode, key presses are stored in program memory for later execution.
It's important to realize which mode the calculator is in, as it has ramifications that affect other operational characteristics
of the device.
(As described later there are two variants of RUN mode, for three actual calculator modes.)
To get the feel of your new calculator, try a few simple calculations. First, perform these operations:
Set the OFF - ON switch to ON.
Set the PRGM - RUN switch to RUN.
Press Q2 so the display will match the examples.
To calculate the surface area of a sphere, the formula `A_(surface)=pid^2` can be used, where
d is the diameter of the sphere.
Ganymede, one of Jupiter's 12 moons, has a diameter of 3,200 miles. You can use the calculator to manually compute the area of Ganymede in square miles. Merely press the following keys in order:
After calculating the surface area of Ganymede, one of Jupiter's 12 moons, suppose you decided you wanted the surface area of each moon. You could repeat the procedure you used for Ganymede 12 times, using a different diameter d each time; however, an easier and faster method is to create a program that will calculate the surface area of any sphere from its diameter rather than pressing all the keys for each moon.
To calculate the area of a sphere using a program, you should first write the program, then you must load the program into the calculator, and finally you run the program to calculate each answer.
Writing the Program
You have already written it! A program is nothing more than the series of keystrokes you would execute to solve the same problem manually . Two additional operations, a label and a return are used to define the beginning and end of the program.
Loading the Program
To load the keystrokes of the program into the calculator:
Slide the PRGM - RUN switch to PRGM.
Press _X to clear the calculator.
Press these keys in order. (When you are loading a program, the display gives you information that you will find useful later, but which you can ignore for now.)
The calculator will now remember this keystroke sequence.
Running the Program
To run the program to find the area of any sphere from its diameter:
Slide the PRGM - RUN switch to RUN.
Key in the value of the diameter.
Press ¦0 to run the program.
When you press ¦0, the sequence of keystrokes you loaded is automatically executed by
the calculator, giving you the same answer you would have obtained manually.
So now, in short order, you can calulate the surface areas of Io (2310 miles), Europa (1950 miles) and Callisto (3220 miles):
The GO-29 LED window acts as a display area, as well as a touch sensitive input area
that initiates further activities not available on an actual HP-29C. The calculator display is also modal, so what it displays
and how it reacts to touches depends on the setting of the PRGM - RUN switch.
A similar concept exists for Apple TV, based on focus navigation rather than touch, see the section
Apple TV Particulars for details.
LED Display (RUN Mode)
In RUN mode the display shows the X stack register, usually the result of the latest calculation.
Single tapping the display in RUN mode
brings up the Copy / Paste / Paper Tape menu, allowing you to export the value of X, import a new value of X,
or annotate the paper tape (Copy / Paste unavailable on Apple TV).
In GO-29, numbers in the display normally appear rounded to only two decimal places.
For example, the fixed constant π, which is actually in the calculator as 3.14159265358979, normally
appears in the display as 3.14 (unless you tell the calculator to show you the number
rounded to a greater or lesser number of decimal places).
Although a number is normally shown to only two decimal places, GO-29 always computes
internally
using each number as a 14-digit mantissa and a two-digit exponent of 10.
Display Control Keys: Q, W, E
A Display Key allows you to control the manner
in which a number is displayed — the number itself is not altered
by the key.
You can choose one of three ways to display
a number: Fixed Decimal Point, Scientific or Engineering notation.
No matter what notation you choose, these rounding options
affect the display only, GO-29 always calculates internally
with the entire number.
These key sequences control how numbers are displayed:
Qn
Selects Fixed Decimal Point notation where n specifies the number
of decimal places (0 - 9) to which the display is rounded.
The number begins
at the left side of the display and includes trailing zeros to fill the width, if needed.
Wn
Selects Scientific notation where n specifies the number of decimal places
(0 - 7) to which
the display is rounded. Again, the number is left-justified
and includes trailing zeros to fill the width, if needed.
The exponent
occupies the rightmost
two digits.
En
Selects Engineering notation where
the first digit of a number is
always present, n specifies the number of
additional digits (0 - 7) displayed after the first, and
exponents of ten that are multiples of three (e.g., 103, 10-6, 109).
This is particularly useful in scientific and engineering calculations, where units of measure are often specified in multiples of
three. Otherwise ENG behaves similarly to SCI.
Multiplier
Prefix
Symbol
1012
tera
T
109
giga
G
106
mega
M
103
kilo
k
10-3
milli
m
10-6
micro
µ
10-9
nano
n
10-12
pico
p
10-15
femto
f
10-18
atto
a
Automatic Display Switching
GO-29 switches the display from fixed point notation to scientific notation
with the same number of decimal places as previously set by FIX whenever the number is too large or too small to be seen with a
fixed decimal point.
This feature keeps you from missing unexpectedly large or small answers.
After automatically switching from fixed to scientific, when a
new number is keyed in or v is pressed the display automatically reverts back to the fixed point display originally
selected.
Keying In Exponents of Ten
You can key in numbers multiplied by powers of 10 by pressing EEX (enter exponent of ten)
followed by number keys to specify the exponent of 10.
You can save time when
keying in exact powers
of 10 by merely pressing EEX and then pressing the desired power of 10.
To key in negative exponents of 10, key in the number,
press EEX, press x to make the exponent negative, then key in the power of 10.
Calculator Overflow and Underflow
When a number is greater than 9.9999999 x 1099 an overflow has occurred and
9.9999999+99 is displayed instead.
For numbers 10-100 and smaller an underflow has occurred and
0.000000000 is displayed instead.
Error Display
Illegal operations such as a divide by zero and taking the square root of a negative number
display the word
Error. Use v to clear the display.
Low Power Display
A GO-2+ SciRPN calculator App blinks its decimal point when the host device is running on battery
and the power level is ≤ 1.1%.
LED Display (PRGM Mode)
In PRGM mode the calculator display shows the current program step. The left-most two digits are the actual program step number, and the
remaining digits represent the step's instruction opcodes, fully described in the section GO-29 Keycodes.
It's this mode that allows you to manually enter a program into the calculator, just like an authentic HP-29C.
Single tapping the display in PRGM mode
brings up the Import PRGM / Share PRGM menu, allowing you to transfer GO-29 programs
to / from the App (for Apple TV only Sample Programs are available for import).
Automatic storage of intermediate results is the reason that GO-29 slides so
easily through the most complex equations. The displayed X register, which is the only visible register
in the calculator display,
is one of four registers inside the calculator that are positioned to form the automatic memory stack.
We label these registers X, Y, Z, and T. They are "stacked" one on top of the other with the
displayed X register on the bottom and T at the top.
T
4.00
Z
3.00
Y
2.00
X
1.00
Automatic Memory Stack
Manipulating Stack Contents
The s (roll down) and a (X exchange Y) keys allow you to
review the stack contents or to shift data within the stack for computation at any time. Each time you press the s key
the stack contents shift downward one register, with the contents of X rotating up to the T register.
Notice that the contents of the registers are shifted - the registers themselves maintain their positions.
Always remember, though, that it takes four presses of the s key to return the contents to their original registers.
The a key exchanges the contents of the X and Y registers
without affecting the Z and T registers.
The z key lifts the stack, by copying the contents of Z into T, Y into Z, X
into Y,
hence losing the contents of T and duplicating the contents of X.
The opposite of lifting the stack is called dropping the stack. When the stack drops, Y is copied to X,
Z is copied to Y, and T is copied to Z, hence losing the contents of X and duplicating the
contents of T.
To clear the displayed X register only, press v. Any new number then writes over the zero in X. To clear the entire stack press v
followed by z three times.
Functions and the Stack
One-number functions such as m execute upon the number in the X-register only, and the answer writes over that number. No other stack registers are affected by executing a one-number function.
Two-number functions such as p, or arithmetic operations such as /, execute upon two stack registers, X and Y.
Obviously, for the power function first enter the base followed by z to lift it into Y, then enter the power into X and press p to perform the function.
For arithmetic operations imagine the stack as an old-fashioned sheet of paper, where in the case of division, the divedend (Y) is written on top of the divisor (X), then the / operation is executed.
Addition, subtraction and muliplication work the same way, both numbers are positioned in the stack in the natural order, there are no exceptions to this rule.
You can use s and a as required to re-order the operands. In all cases after the function or operation is executed the stack drops and the answer is written over X (the old Y before the stack drop).
In addition to the automatic storage of intermediate results that is provided by the four-register automatic memory stack,
the calculator
also has 30 addressable data storage registers that are unaffected by operations within the stack. These storage registers
allow you to manually store and recall constants or to set aside numbers
for use in later calculations. Like all functions, you can use these storage registers either from the keyboard or as part of a program. All 30 storage registers reside contiguously in Continuous Memory and maintain their contents even when the calculator is off.
The diagram below shows all storage registers. The addresses of the primary storage registers are indicated by the numbers 0 through 9 and by .0 through .5. The addresses of the indirect storage registers are indicated by the numbers (16) through (29).
Storing and recalling numbers in the 14 indirect storage registers is explained in section Using the R₀ Register for Indirect Control.
Primary
Indirect
R₀
R₍₁₆₎
R₁
R₍₁₇₎
R₂
R₍₁₈₎
R₃
R₍₁₉₎
R₄
R₍₂₀₎
R₅
R₍₂₁₎
R₆
R₍₂₂₎
R₇
R₍₂₃₎
R₈
R₍₂₄₎
R₉
R₍₂₅₎
R.₀
R₍₂₆₎
R.₁
R₍₂₇₎
R.₂
R₍₂₈₎
R.₃
R₍₂₉₎
R.₄
R.₅
Storage Registers
Manipulating Storage Registers
Store
To store the X value appearing in the display into any of the storage registers R₀ through R₉, press STO followed by a number key 0 through 9
specifying the register address where the value is to be stored.
To store X into any of the storage registers R.₀ through R.₅, press d followed by the decimal point key . followed by
the number key of the applicable register address 0 through 5.
When a number is stored, it is merely copied into the primary storage
register, and remains in the displayed X register.
Recall
Numbers are recalled from one of the sixteen primary storage registers back into the displayed X register in much the same way as they are stored. Press the RCL key followed
by:
either the register number key 0 through 9.
or the decimal point . then the register number key 0 through 5.
Recalling a number causes the stack to lift unless the preceding keystroke was z, v or g.
When you recall a number, it is copied from the storage register into X, and it also remains in the storage register.
You can recall a number from a storage register any number of times without altering it; the number will remain in the storage
register until you overwrite it by storing another number there, or until you clear
the storage registers.
Clear
To clear the number from a single storage register, simply store the quantity zero in the register by pressing 0 STO
followed by the register number
0 through 9 or .0 through .5.
To clear data from all manual storage registers at once, without affecting data in other portions of the calculator,
press _C. This places zero in all thirty of the storage registers.
You can also clear storage registers R.₀ through R.₅ while leaving the remaining storage registers and the stack intact by using the _¥function.
Remember that because of the Continuous Memory of the calculator the primary storage registers retain their contents even though the calculator is off.
Storage Register Arithmetic
Arithmetic is performed upon the contents of a primary storage register by pressing STO, followed by the arithmetic
function key,
followed in turn by the register address R₀ through R.₅.
STO + 1 (Contents of storage register R₁ plus X, and sum placed into R₁.)
STO - 2 (Contents of storage register R₂ minus X, and difference placed
into R₂.)
STO x . 3 (Contents of storage register R.₃ multiplied X, and product
placed into R.₃.)
STO ÷ . 4 (Contents of storage register R.₄ divided by X, and quotient placed
into R.₄.)
When storage register arithmetic operations are performed, the answer is written into the selected storage register,
while the contents of the displayed X register and the rest of the stack remain unchanged.
If the magnitude of a number in any of the storage registers exceeds 9.999999999 x 1099, the display
immediately
shows Error (overflow) to indicate that a storage register has overflowed.
When you then press any key, the error condition is cleared and the last value in the X register before the error is again displayed. The storage registers all contain the values they held before the error-causing operation was attempted.
GO-29 provides two distinct, scrollable, views of the calculator's internal state unavailable on the real hardware.
This makes using the calculator, and programming and debugging code much easier. Access to this additional information is
controlled by a double tap on the calculator display. If the information view is visible, a double tap hides the view. If the view is not
visible, the information view appears. So a double tap of the calculator display toggles the visibility of the available auxiliary information.
If you eschew gestures and prefer buttons, enable the Accessibility setting Auxiliary Views Assist.
Similar to long-pressing the calculator display, the information that's displayed in response to a double tap is dependent on the setting of the PRGM - RUN switch.
(Note: unlike for iPhone
and iPod touch, which have tiny screens, on Mac and iPad both information views are by default always visible, but you can hide them
with two double taps, if desired, one in PRGM mode and one in RUN mode. For Apple TV the information views are always visible and cannot be hidden.)
Both auxiliary information views include this
touch point that toggles what the view shows, detailed in the following two sections.
Auxiliary Information Views (RUN Mode)
In RUN mode the 4 stack registers, the 30 storage registers, and the Y
register are displayed in the scrollable stack and register window.
Touching the switch-views control
transitions to the paper tape window and shows up to 200 lines of key-press history to help you make sense of the values you see in the stack-register window.
Flippable Switch Views: left Registers, right Paper Tape
Auxiliary Information Views (PRGM Mode)
In PRGM mode the program listing is shown. The listing displays the program name and description, and the step numbers,
opcodes and mnemonics for all program steps. Both the program listing and program description are scrollable and editable.
The current step pointer (SP) is highlighted by a right pointing double arrow. In RUN mode this is the next instruction
to be executed via q or R/S. In PRGM mode you edit the step following the SP. More on this in the programming sections of these notes.
In PRGM mode you can also move the arrow pointer to any step by just touching the step. If you touch and hold a program listing step,
a contextual menu appears so you can add any extended GO-29 opcodes described in the
section Special 8* Opcodes.
Finally note there is a touchable switch-views control that controls how to display your program's description: either plain Text or full HTML. The default is Text with semi-colon as the comment character. But HTML allows for rich text and cool things like mathematical equations. This is explained in the section Naming and Documenting Your Program.
Press x to change the sign of the mantissa or exponent of the X register.
Recovering From Mistakes
In addition to the four stack registers that automatically store intermediate results, the calculator
also contains a separate automatic register,
the Y register. This register preserves the value in the displayed
X register before a new function is performed.
Prefix Clear
The _Z key will clear a blue prefix key t, a
gold prefix key r
, d, RCL, or GTO.
To clear a prefix you have mistakenly
pressed, merely press _Z,
then press the correct key.
Absolute Value
Some calculations require the absolute value, or magnitude, of a number. To obtain the absolute value of the number in the display,
press
@.
Integer Portion
To extract and display the integer portion of a number, press n.
The fractional portion of the number is
lost. The entire number, of course, is preserved in the Y register.
Fractional Portion
To place only the fractional portion of a number into the displayed X-register,
press M.
The integer portion of the number is lost. The entire number, of course, is preserved in
the Y
register.
Reciprocals
To calculate the reciprocal of a number in the displayed X register, press
O.
Square Roots
To calculate the square root of a number in the displayed X register, press
m.
Squaring
To square a number in the displayed X register, press !.
Using Pi
The value % accurate to 14 places (3.14159265358979) is provided as a fixed constant in GO-29.
Merely press % whenever
you need it in a calculation.
Percentages
The I key is a two-number function that allows you to compute percentages.
To find the percentage of a number:
key in the base number
press z
key in the number representing percent rate
press I
For example, to calculate the sales tax on a purchase, the purchase price is the base number and the sales tax is the percentage rate.
When I is pressed, the
calculated answer writes over the percentage rate in the X register, and the base number is preserved in the Y register.
Since the purchase price is now in the Y register and the amount of tax is in the X register, the total
amount can be obtained by simply adding.
Trigonometric Functions
The calculator provides you with six trigonometric functions. It also calculates angles in decimal
degrees,
radians, or grads; and it converts between decimal degrees and degrees, minutes, seconds.
Use P, { or }
to
specify the degree mode.
Note: 360 degrees = 2π radians = 400 grads.
The six trigonometric functions provided by the calculator are:
j (sine)
K (inverse sine)
k (cosine)
L (inverse cosine)
l (tangent)
B (inverse tangent)
Each trigonometric function assumes angles in decimal degrees, radians, or grads. Trigonometric functions are one-number
functions,
so to use them you key in the number, then press the function key.
The T(to hours (or degrees), minutes, seconds)
key converts decimal hours to the format of hours, minutes and seconds, or
converts angles specified in decimal degrees to degrees, minutes, seconds. These hour and degree values are based on the sexagesimal (base 60) number system.
When a time (or angle) is displayed in hours (or degrees), minutes, seconds format, the digits specifying hours (or degrees) occur to the left of the decimal point, while the digits specifying minutes, seconds, and fractions of seconds occur to the right of the decimal point. To see all these digits you should specify
Q5 display format. For example, the decimal number 89.29047° displays
as 89°, 17′, 25.7″ in H.MS format:
Conversely, the $(to decimal hours (or degrees))
key is used to change hours (or degrees), minutes, seconds into decimal hours (or degrees).
The $
and T
keys are
important because the calculator's trigonometric
functions operate on angles in decimal degrees, but not in degrees,
minutes, seconds.
In order to calculate any trigonometric function of an angle given in degrees, minutes, seconds, you must first convert
the angle to decimal degrees.
Polar/Rectangular Coordinate Conversion
Two functions
H and
o
are provided for polar/rectangular coordinate conversions.
Polar angle θ is assumed in decimal degrees, radians, or grads, depending upon the trigonometric mode selected by P, {, or }.
To convert values in the X and Y
registers
representing rectangular (x, y) coordinates, respectively, to polar (r, θ) coordinates, magnitude and angle,
respectively,
press H. Magnitude r then appears in the X register
and angle θ
is placed in the Y register.
Conversely, to convert values in the X and Y registers representing polar (r, θ) coordinates, respectively,
to rectangular coordinates (x, y), press o.
Coordinate x then appears in the X register and coordinate y
is placed in the Y register.
Logarithm and Exponential Functions
The calculator computes both natural and common logarithms as well as their inverse functions
(antilogarithms):
u is loge (natural log). It takes the log of the
value in X to base e (2.718...).
F is antiloge (natural antilog).
It raises e (2.718...) to the power of the value in X. (To display the value of e, press
1F.)
i is log10 (common log). It computes the log of the
value in the X register to base 10.
G is antilog10 (common antilog). It raises 10
to the power of the value in the X
register.
Raising Numbers to Powers
The p key is used to raise numbers to powers. This function raises a positive real number to any real power; that is, the power may be positive or negative, and it may be an integer, a fraction, or a mixed number. p also permits you to raise any negative real number to the power of any integer within the calculating range of the calculator.
In conjunction with O,
p
provides a simple way to extract roots. For example, the cube root of 5 is equivalent to 51/3 e.g.:
5 z
3 O
p
Statistical Functions
Accumulations
Pressing the g key automatically gives you several different
sums and products of the values in the X and Y registers at once. In order to make these values accessible
for sophisticated statistics problems,
they are automatically placed by the calculator into storage registers R.₀ through R.₅ . The
only time that information
is automatically accumulated in the storage registers is when the g (or D) key is used. Before you begin any
calculations using
the g key, you should first clear the storage registers of data by pressing
_¥.
When you press the g key each of the following operations are performed on the data in the X
and Y registers:
The number in X is added to the contents of storage register R.₁.
The square of the number in X is added to the contents of storage register R.₂.
The number in Y is added to the contents of storage register R.₃.
The square of the number in Y is added to the contents of storage register R.₄.
The number in X is multiplied by the contents of the Y register, and the product added to storage register R.₅.
The number 1 is added to storage register R.₀, and the total number in R.₀ is
then written into the display. The stack does not lift.
The number that you keyed into the X register is preserved in the Y register, while the number in the stack Y register remains in the Y register.
Thus, each press of the g key updates these summations and multiplications. The contents of the
displayed X register
and the applicable storage registers are as follows:
R.₀ = X is n, the number of entries.
R.₁ is Σx, summation of x values.
R.₂ is Σx2, summation of x2 values.
R.₃ is Σy, summation of y values.
R.₄ is Σy2, summation of y2 values.
R.₅ is Σxy, summation of products of x and y values.
Again, before you begin any
calculations using
the g key, you should first clear the storage registers of data by pressing
_¥.
There is a special flavor of storage register recall
fg
that summons only Σx and Σy, and stores them in X and Y, respectivfely, overwriting the contents of those two registers. The stack does not lift. (This feature is particularly useful when performing vector arithmetic, discussed shortly.)
To recall any of the summations individually at any time, you can recall the contents of the desired storage register into the X register by pressing
f
followed the number key of the storage register address .₀ though .₅. After you have pressed g, recalling storage register contents or keying in another number writes over the number of entries (n) that is displayed. The stack does not lift.
Mean
The A key calculates the arithmetic average of x and y accumulated in registers R.₁ and R.₃, respectively, according to these formulae:
The resultant values for x̄ and ȳ are available on the stack, in the X and Y registers, respectively.
Standard Deviation
The S key computes a measure of dispersion around the mean by using data accumulated in the storage registers R.₀ through R.₅, according to these formulae:
The resultant values vaues for sx and sy are available on the stack, in the X and Y registers, respectively.
Note: a population standard deviation is computed from the sample standard deviation by:
`sigma=ssqrt(frac{n-1}{n})`
Deleteing and Correcting Summation Data
If you key in an incorrect value and have not pressed g, press v and key in the correct value.
If one of the values is changed, or if you discover after you have pressed the g key that one of the
values is in error,
you can correct the summations by using the
D key as follows:
Key the incorrect data pair into the X and Y registers. (You can use
Y
to return a single incorrect data value to the X register.)
Press D to delete the incorrect data.
Key in the correct values for x and y. (If one value of an
X,Y data pair is incorrect, both values must be deleted and reentered.)
Press g.
The correct values for mean and standard deviation are now obtainable by pressing
A and
S.
Vector Arithmetic
You can add or subtract vectors by combining the polar/ rectangular conversion functions (the
H and
o
keys) with the summation functions (the
g and
D
keys).
For an example of this, examine the Sample Program
Apeneck Sweeney
as he flies the Swordfish into a crossing headwind.
There are three ways to use your GO-29 calculator:
Manual RUN Mode
The functions and operations you have learned about in previous sections are
performed manually one at a time with the PRGM - RUN switch set to RUN.
These functions combined with the automatic register stack enable you to calculate any problem with ease.
PRGM Mode
In PRGM mode the functions and operations you
have learned about are not executed, but instead are recorded in a part of the calculator called program memory
for later execution. All operations on the keyboard except the following can be recorded for later execution while in PRGM mode:
q - single-step foreward through program memorey
w - backward-step through program memory
e .n nor the GO-29 extension e + n n n - position step pointer to designated step number
¬ - deletes current step from program memory
_X - clears all 198 steps of program memory
_Z - cancels r, t, d, RCL or GTO
These operations work in PRGM mode to help you write, record and edit your programs from the keyboard.
Automatic RUN Mode
The calculator can also be used to automatically execute a list of operations with
the PRGM - RUN switch set to RUN
if they have previously been recorded in program memory. Instead of your having to press each key manually, the
recorded operations are executed sequentially in automatic RUN mode when you press GTO, GSB or R/S (run /stop). You press
only one key and the entire list of recorded operations is executed much more quickly than you could have executed them yourself.
A program is nothing more than a series of calculator keystrokes that you would press to solve a problem manually. The calculator remembers these keystrokes when you key them in, then executes them, in order, whenever you wish. You've already seen this demonstrated in the section
Programmed Problem Solving, which you may wish to review.
All HP-29C programming techniques work with GO-29, although this App has some useful extensions. The first
is the amount of program memory available for storing the keystrokes that define your program, now increased to 198 steps.
When you set the calculator to PRGM mode you can examine the contents of program memory; logically, here is how the surface area program `A_(surface)=pid^2` is stored:
You can tell from the display what keystrokes are loaded into each step of program memory by means of the keycodes for those keys. Let's look at some keycodes now.
If you have cleared the surface area of a sphere
program illustrated in the section
Programmed Problem Solving, please reenter it now before continuing.
With the calculator in PRGM mode, press the 4 keys
e . 0 0
(go to step number 00) to return the calculator to the beginning of program memory. The number that you see on the left side of the display indicates the step number of program memory to which the calculator is set. You should be set at step 00, indicated by a display of 00. Now we'll use the
q
(single-step) key to examine the next step of program memory. q
lets you step through program memory, one program step at a time.
Press
Display
SST
01 15 13 00
The calculator is now set to step 01 of program memory, as indicated by the number 01 that you see on the left side of the display. The other numbers in the display are as many as three two-digit keycodes for the keystrokes that have been loaded into that step of program memory.
Each key on the calculator has a keycode. For each keycode, the first digit denotes the row of the key on the keyboard and the second digit identifies the column of the key in that row (there are 7 rows of keys, and 4-5 columns of keys per row). Always count from the top down, and from left to right. Each key, even the double-wide
z key, counts as one keystroke.
For convenience, digit keys are identified by two digit keycodes of 00 through 09, except when prefixed by
r or
t. When preceeded by either of these prefix keys the digit keys are identified by the row-column keycode.
Now use the q key again to examine the keycodes in the next step of the program:
GO-29 provides four extended keycodes, the 8* series, named because they assume the existence of an 8th row of calculator keys.
Because there are no such keys, these opcodes are inserted using a contectual menu activated from the program listing auxiliary view. The new instructions, DMP,
BEL, SEC and RND are explained in the section Special 8* Opcodes.
The programming keys described in this section help you write, edit and run programs. Specifics depend upon which of the three calculator modes
you are using.
PRGM Mode
Reminder, these six keys are non-recordable in PRGM mode:
q - single-step foreward through program memorey for
examining and/or changing program steps.
w - backward-step through program memory for
examining and/or changing program steps.
e .n nor the GO-29 extension e + n n n - position step pointer to designated step number
¬ - deletes current step from program memory. All subsequent instructions move up one step in program memory.
_X - clears all 198 steps of program memory to R/S instructions and resets the step pointer to step 00.
_Z - cancels r, t, d, RCL or GTO.
Manual RUN Mode
e . n nor the GO-29 extension e + n n n
Goto positions the internal step pointer to an explicit step number without executing instructions.
Goto searches downward through program memory to first designated label and sets step pointer without executing instructions.
GSB followed by a label number 0 through 9, or indirect label ¤
(described in section Using the R₀ Register for Indirect Control)
Goto subroutine searches downward through program memory to first designated label and starts executing instructions.
§
Return sets the step pointer to 00 without executing instructions.
q
Single step displays the step
number and keycode of the current program memory step when pressed; executes instruction, displays result, and moves
to next step when released.
w
Back step displays the step
number and keycode of the previous program memory step when pressed; moves
to previous step when released - the program is not run in reverse.
,
Run/Stop. Begins execution of a stored program from the current step pointer. Stops execution if program is running.
Goto subroutine searches downward through program memory to first designated label and executes that section of memory as a subroutine.
§
Return. If executed as a result of pressing GSB
and a label designator or execution of a GTO instruction, stops execution and returns control to keyboard. If executed as a result of a GSB instruction, returns control to next step after the GSB instruction.
U
Pause. Stops program execution for 1 second and displays contents
of the X register, then resumes program execution.
,
Run/Stop. Stops program execution.
¯®bR [°N#
Conditionals. These instructions make tests and branch instruction flow accordingly, and are discussed in the section
Branching.
The section Programmed Problem Solving provided a concise overview of how to write, load and run our surface area of a sphere program. Let's delve deeper into those topics.
To define the end of a program, you should use a § instruction. When the calculator is executing a program and encounters a § instruction in program memory, it stops (unless executed as part of a subroutine - more about subroutines later). Another instruction that will cause a running program to stop is R/S. When a running program executes a R/S instruction in program memory, it stops just as it does when it executes §. Good programming practice, however, dictates that you normally use § rather than R/S to define the end of your program.
Run the Program
To run the surface area of a sphere program you have only to set the calculator to RUN mode, key in any needed
data, then press ¦ and the number key (0 - 9) that labels your program. What is the surface area of Mercury, in kilometers?
Each of the memory label markers (0 - 9) can be used as many times as you wish. In fact, you can label each of several programs and subroutines with the same number.
You can see that it is possible to have many different programs or parts of a program loaded in the calculator at any time. You can run anyone of these programs by pressing GSB followed by the number key 0 - 9 that corresponds with its label.
Debugging a program on an actual HP-29C can be very difficult because you cannot easily see the state of the calculator's storage registers without recalling them individually to the stack. On the other hand, GO-29's auxiliary information views, Settings, and 8* series of new instructions give an unparalleled view of the registers and stack, making debugging much easier.
Running One Step at a Time If all you need is to see the stack registers, then the q single step command works beautifully. To use this method, do not start program execution with GSB or R/S, rather, position the step pointer to the first program step using GTO then press q. This runs that step and only that step. Then you can manipulate the stack and check the contents of the four registers for sanity. Repeat as required.
Running in Slow Motion The Settings option Program Run Speed controls how fast a program runs by varying the time delay before running subsequent program steps.
Running Full Speed with DMP Inserting opcode 80 in your program dumps the calculator's internal state to the paper tape. Here we see the calculator's register values after computing the surface area of the unit sphere.
Editing a program in PRGM mode consists of four basic maneuvers: clearing stuff, positioning the step pointer to an instruction of interest, deleting instructions at the step pointer, and inserting new instructions after the step pointer. GO-29 adds "full screen" editing to the mix, which deletes and rearranges instructions.
Clearing stuff
In PRGM mode, _X clears all 198 program memory steps to R/S instructions and resets the step pointer to step 00.
_Z cancels r, t, d, RCL or GTO.
Positioning the Step Pointer
e . n nor the GO-29 extension e + n n n
q single step
q back step
RTN in RUN mode sets the step pointer to step 00
Deleting Instructions The ¬ key erases the instruction at the current step of program memory, and all subsequent instructions
in program memory move upward one step. An R/S instruction drops in to fill the vacated step 198.
Inserting Instructions If you press a recordable operation, it will be loaded in the next step of program memory, and all subsequent instructions will be "bumped" down one step in program memory. Program step 198 is lost off the end of program memory. You should always view the contents of the last few steps of program memory before adding instructions to a program to ensure that no vital instructions disappear.
Editing the Program Listing (unavailable on Apple TV)
The program listing auxiliary window has a special Edit (Done) button on step 00 that enables removal and re-arrangement of program steps.
Touching the red minus removes that program step and adds a R/S at step 198. Touching and dragging a gripper pad moves that program step, re-inserting it when you have reached the destination and released the gripper.
We have used e . n nor the GO-29 extension e + n n n to help edit our programs. This form of GTO cannot
be recored as part of program, but there is a variant which can: GTO followed by a label designator 0 - 9, or the indirect label
¤ (described in section Using the R₀ Register for Indirect Control).
Conditional
Each conditional operator tests the value in the X register against that in the Y register or 0 as indicated.
If true, the calculator executes the instruction in the next program memory step. If false, the calculator skips the next step
and continues execution after the skipped program step. This is the "Do if TRUE" rule, and GTO is the most commonly done instruction after one of these tests.
This will branch program
execution to another section of program memory if the conditional test is true:
There may be occasions when you want a program to halt during execution so that you can key in data, or to pause so that you can quickly view results before the program automatically resumes running. Other interruptions may be an overt keyboard action on your part, or even a runtime error such as divsion by zero or arithmetic overflow.
R/S The run/stop function can be used either as an instruction in a program or pressed
from the keyboard.
When pressed from the keyboard, if a program is running, R/S stops the program.
If a program is stopped or not running and the calculator is in RUN mode, R/S starts
the program running beginning with the current location in program memory. You can use these features to stop a running program at points where you want to key in data. After the data has been keyed in, restart the program using the R/S key from the keyboard.
U
The pause function suspends program execution for one second. You can stack multiple pauses to lengthen the delay time, or use the Program Run Speed Settings option to delay between every program step.
Error Stop
If the calculator attempts to execute any error-causing operation during a running program, execution immediately halts and the calculator displays the word Error. To see the step number and keycode of the error-causing instruction, you can briefly set the calculator to PRGM mode, or simply examine the program listing window.
Press v to clear the error. You can then resume program execution by pressing R/S from the keyboard in RUN mode.
Often, a program contains a certain series of instructions that are executed several times throughout the program. When the same set of instructions occurs more than once in a program, it can be executed as a subroutine. A subroutine is selected by the ¦ operation, followed by a label designator 0 - 9, or the indirect label
¤ (described in section Using the R₀ Register for Indirect Control).
Subroutine Overview
A ¦ instruction transfers execution to the routine specified by the label address, just like a e instruction . However, after a ¦ instruction has been executed, when the running program then executes a §, execution is transferred back to the next instruction after the ¦. Execution then continues sequentially downward through program memory.
The illustration below should make the distinction between e and ¦ clearer.
As you can see, the only difference between a subroutine and a normal branch is the transfer of execution after the §. After the e, the next § halts a running program; after a ¦, the next § returns execution back to the main program, where it continues until another § (or R/S) is encountered. The same routine may be executed by e and ¦ any number of times in a program.
For example, a quadratic equation of the form `ax^2+bx+c = 0` has two roots found by the formula:
Subroutines give you extreme versatility in programming. A subroutine can contain a loop, or it can be executed as part of a loop. Another common and space-saving trick is to use the same routine both as a subroutine and as part of the main program.
The program Dice shows this trick in action, read the program's comments for complete details.
Part of the program is a home-grown pseudo random number generator, which, since it's not a native instruction, occupies several steps of valuable program memory. GO-29 provides a RND instruction, part of the the 8* series of extended keycodes, which generates really random numbers, and saves program memory as well. The program DiceRND demonstrates how to retrofit RND into Dice.
Subroutine Limits
A subroutine can call up another subroutine, and that subroutine can call up yet another. Subroutine branching is limited only by the number of §s that can be held pending by the calculator. Three subroutine returns can be held pending at any one time in the HP-29C, although GO-29 doubles that to 6 nested subroutine calls.
The calculator can return to the main program from subroutines that are 6 deep; however, if you attempt to call up subroutines that are more than 6 deep, the calculator will execute only 6 returns, and execution will stop prematurely. To illustrate this and to keep the diagram simple, let's assume that only two subroutine returns are allowed:
The step numbers that §s return to are kept in an ordered list known as a Last In First Out (LIFO) queue. What this means is that as GSBs are processsed, they push their return address on the end the LIFO queue, and as §s are executed they pop the most recent return address off the end of queue. As long as there is room at the end of the LIFO queue for GSB to attach its return address, a § can grab it and transfer control appropriately. When a § is executed and the LIFO queue is empty, the program has nowhere to go and simply ends.
To understand the diagram above, it's very important to realize then when a GSB is executed from the keyboard (i.e. to start the Main Program) the LIFO queue is first emptied, all § information is erased. This means that the GSB 1 instruction creates the first LIFO queue entry, which contains the return step number after the GSB 1.
Now follow the blue numbered arrows: when GSB 2 is processed it pushes the second return entry onto the LIFO queue. But when GSB 3 is processed the LIFO § queue is full, so the first entry is discarded to make room for the current entry. At this point the calculator only knows how to return from GSB 3 and GSB 2, the return information for GSB 1 has been lost.
It's easy enough to probe the calculator and determines its § nesting depth: write a program, as above, with many nested subroutine calls, and keep replicating subroutine after subroutine until the program fails to return to the main program. This could work if you are ambitious and the nesting level is small, or you might never succeeed in any reasonable amount of time. But there is a clever way to accomplish this using a recursive subroutine, a subroutine that calls itself. So instead of writing `n_29` subroutines, write one and have it call itself `n_29` times. Visit the Sample Program Recursive Test Of Subroutine Limits to see how this is done.
The R₀ register is special. Using R₀ in conjunction with other instructions, you can specify the storage register addresses of d and RCL,
and the label addresses of GTO and GSB. By storing a negative number in R₀, you can even transfer execution to any step number of program memory.
The «
and ª
instructions permit you to increment (add 1 to) or decrement (subtract 1 from) the current value in R₀.
These are features that you will find extremely useful in controlling loops.
The ª (decrement R₀, skip if zero) instruction subtracts 1 from the contents of the R₀, then tests to see if the register is 0. (A number between +1 and -1 tests as zero.) If R₀ is greater than zero, execution continues with the next step of program memory. If R₀ is zero, the calculator skips one step of program memory before resuming execution.
« works similarly except, of course, it increments R₀. For an example, see Manhattan.
You have seen how the value in R₀ can be altered using the d, « and ª operations. But the value contained in R₀ can also be used to control other operations. The indirect function ¤, combined with certain other functions allows you to control those functions using the current number in R₀. ¤ uses the number stored in R₀ as an address.
Summary of Indirect Operations
The indirect operations that can be controlled by R₀ are:
d¤,
when the number in R₀ is 0 through 29, stores the value that is in the displayed X register into the primary or indirect storage register addressed by the integer portion of the absolute value of the current number in R₀.
f¤,
when the number in R₀ is 0 through 29, recalls the contents of the primary or indirect storage register addressed by the current number in R₀.
d +¤,
d -¤,
d ?¤,
and d /¤,
when the number in R₀ is 0 through 29, perform storage register arithmetic upon the contents of the primary or indirect storage register addressed by the current number in R₀.
e¤,
when the number in R₀ is 0 or a positive 1 through 9, transfers execution of a running program sequentially downward through program memory to the next label specified by the current number in R₀.
e¤,
when the number in R₀ is a negative number between -1 and -198, transfers execution of a running program back in program memory the number of steps specified by the current negative number in R₀.
¦¤,
when the number in R₀ is 0 through 9, transfers execution of a running program to the subroutine specified by the current number in R₀. Like a normal subroutine, when a § is then encountered, execution transfers and continues with the step following the ¦¤.
¦¤,
when the number in R₀ is a negative number between -1 and -198, transfers execution of a running program back in program memory the number of steps specified by the current negative number in R₀. Execution from that point is like a normal subroutine, so if a § instruction is then encountered, execution is transferred once again, this time to the next instruction after the ¦¤.
Note that you can use the ¤ key with the above functions with or without using the
t
prefix key. That is, pressing d¤ is the same as pressing dt¤.
If the number in R₀ is outside the specified limits when the calculator attempts to execute one of these operations, the display will show Error. When using ¤, the calculator
uses for an address only the integer portion of the number currently stored in R₀. Thus, 25.99998785 stored in R₀ retains its full value there, but when used as address ¤, it is read as 25 by the calculator.
Store and Recall
You can use the number in R₀ to address the 30 storage registers that are in your calculator. When you press d¤, the value that is in the display is stored in the storage register addressed by the number in R₀. f¤ addresses the storage registers in a like manner, as do the storage register arithmetic operations d +¤,
d -¤,
d ?¤,
and d /¤.
When using d¤, f¤,
or any of the storage register arithmetic operations utilizing the ¤ function, R₀ can contain numbers positive or negative from 0 through 29. The numbers 0 through 15 address primary storage registers R₀ - R₉ and R.₀ - R.₅, while numbers from 16 through 29 will address indirect storage registers R₍₁₆₎ - R₍₂₉₎.
The only way to access an indirect storage register is via the ¤ function. Notice that with the number 0 in R₀, ¤ addresses R₀ itself!
Remember that the numbers in R₀ must be positive or zero (negative numbers cause rapid reverse branching, which we discuss next), and that the calculator looks at only the integer portion of the number in R₀ when using it for an address.
Rapid Reverse Branching
Using e¤
and ¦¤, with a negative number stored in R₀, you can actually branch to any step number of program memory. The calculator does not search for a label, but instead transfers execution backward the number of steps specified by the negative number in R₀. This is advantageous because the branch is faster than searching for a label, and because you can thus transfer execution even though all labels in the calculator have been used for other purposes.
Rapid reverse branching can be specified with numbers from -1 through -198. If you attempt to execute an indirect control transfer when the magnitude of the integer portion of the negative number in R₀ is greater than 198, the calculator displays Error.
Suppose the step pointer is at 2, then a rapid reverse branch (RRB) of:
GO-29 supports six special opcodes not available on a real HP-29C. These are collectively known as the 8* series of instructions, named because they exist on a theoretical 8th row of calculator keys having an infinite number of columns.
You cannot key these instructions in, but they can be typed as part of a program imported into the calculator. Or, in PRGM mode,
if you touch and hold a program listing step, a contextual menu appears so you can add extended GO-29 opcodes.
See the section on keycodes for background information.
DMP (80) dumps the step pointer and the stack and memory registers to the paper tape for debugging.
A GO-29 program can exist by itself, a simple stream of step numbers and instructions, just like an HP-29C program, or it can be bundled with its documentation in a structure called a Program Package. These descriptive comments can be simple Text, or expressive HTML markup.
A Program Package is really easy to maintain, it's just a file (ASCII or UTF-8 Unicode), and consists of two parts: the documentation at the top / beginning, immediately followed by the program. That's it. Simple enough to manage in most any editor you choose.
Generally, it's useful to associate a name with a program, and GO-29 tries to extract the name from the documentation as the program is being read into memory. If you provide no documentation at all, or do not adhere to the following prescribed naming rule, then Untitled-go29.txt is used.
While the program is being read into memory GO-29 is also scanning the documentation to determine if it's plain Text or rich HTML,
by searching for a case-insensitive <html> / </html> tag pair. This defines the start and end of the HTML documentation; if those two strings are not found then the documentation is assumed plain Text.
Finally, the prescribed program naming rule is:
you get to pick the actual name of the program, even including spaces
you must suffix the characters "-go29" to the chosen program name
and you must suffix an extension, either ".txt" or ".html"
e.g. Einstein Tensor-go29.html
The extension simply reminds humans of the documentation type, and reminds computers that the program is an editable file.
Text Documentation
Lacking <html> / </html> marker strings, program documentation is assumed plain Text, with the semi-colon as the comment character.
All comments appearing before the first program step 01 are gathered together
and appear in the top
of the program listing window. This window is editable, and the descriptive text is saved with the program steps when
the program is exported.
By definition the very first documentation line specifies the program name, excluding the semi-colon, of course.
e.g. ; Einstein Tensor-go29.txt
For example:
HTML Documentation
If <html> / </html> marker strings are present, program documentation is assumed to be HTML.
The HTML is rendered and displayed in the top of the program listing window.
Program step 01 immediately follows the </html> tag. This HTML window is not editable - touch the switch-views
control to toggle into Text mode to view and edit the raw HTML source.
The descriptive text is saved with the program steps when
the program is exported.
By definition a <title> / </title> tag pair surrounds the program name.
e.g. <title>Einstein Tensor-go29.html</title>
The title tag is contained in the document's <head> section.
Note: For Apple TV this section is not applicable.
Beginning with iOS 11 managing your programs is relatively easy using Apple's Files App. Files not only provides a storage location for your programs such as iCloud Drive or Dropbox, but also allows you to create subfolders and maneuver between them, which means you can setup a file hierachy that is meaningful to you. To take advantage of theses capabilities, incorporate Files in your import and export workflows.
If you have iCloud Drive configured then GO-29 creates a folder similar to this for Files
to store and retrieve your programs. Tapping the display in PRGM mode
brings up the Import PRGM / Share PRGM menu, allowing you to transfer programs
between GO-29 and Files.
To export a program to Files select Share PRGM from this menu:
Open In Another App
Save to Files, which runs Files
Navigate to the destination folder
Save
To import a program from Files:
First run the Files App
Naviagte to the desired folder
Long touch the desired program to display the Action menu
Share
Touch the App's icon (previously Copy to GO-29), which runs GO-29
This displays the standard Import PRGM menu with your desired program as one of the items, select the program
Additional help is available in the following sections Importing Programs and Sharing Programs.
If you enable the Settings option Persist Program Registers, when a program is shared (saved) all the device register values are saved with it.
Subsequently, when you import (open) that program device registers are restored to their previously saved values. This behavior is implemented via a
special comment in the program's documentation of the form:
<Registers>stack,lastX,memory</Registers>
Inside the Registers element is a list of comma-separated
double precision numbers: 4 for the stack X, Y, Z and T registers, 1 for the LAST X register, and n numbers for the memory registers, where n = 10 for GO-25 and n = 30 for GO-29.
Of course, nothing prevents you from editing the registers list manually; for instance, this list for GO-25
If there are registers you do not want to preset then leave their value in the list empty; for instance this list initializes all registers excluding the 4 stack registers:
<Registers>,,,,-5,0,1,2,3,4,5,6,7,8,9</Registers>
Notes:
A number is a signed integer or float, with or without a signed exponent, e.g. -1.23e-45, 3.1415, -21, etcetera.
The case-insensitive Registers element is a single line in the form of a comment, thus must occur after a semicolon for text documentation, or be part of an HTML comment for HTML documentation.
If multiple Registers elements are encountered then the last takes precedence.
Note: For Apple TV this section is not applicable, see Apple TV Particulars.
On an actual HP-29C programs are entered using the calculator keys. That method works with
GO-29 as well, but it's often easier
to edit your programs in another App and import them into GO-29
(activate the Import menu by touching the calculator's display in PRGM mode). For
instance, you can use Mail to write your program,
then copy the program to the pasteboard, switch to GO-29, and import the pasteboard data.
As a bonus, when you are finished editing the program simply email it to yourself for
later filing in your GO-29 programs folder.
You also have a My Programs container that uses File Sharing to sync programs between your computer and GO-29.
Preferably, Apps like Files use the iOS Document Model and have a menu to open their
documents in another App (labelled variously as Add to appName, Copy to appName, Open in appName, or Save to appName). If such an App
sends a program (named, say, Surface Area Of Sphere-go29.txt) to GO-29, that
program's name appears in the Import PRGM window.
Finally, a small selection of programs is included in GO-29's Sample Programs container.
For macOS, in PRGM mode, you can also import a program using the File menu item Open.
Note: For Apple TV this section is not applicable.
You can export a program in various ways using the Share PRGM menu item (activate the Share menu by touching the calculator's display in PRGM mode).
Besides the pasteboard, email
and printing, you also have a My Programs container that uses File Sharing to sync programs between your computer and GO-29.
Preferably, GO-29
also supports the iOS Document Model and allows other Apps to open its program files via the Open In Another App menu item. When sending a program to another App,
GO-29
uses the program name to identify the program. For example, use this option to export a program to the Files App.
For macOS, in PRGM mode, you can also export a program using the File menu item Save.
Programs you may copy to the pasteboard and then import into GO-29 while in PRGM mode.
Also, do check out the more complex and extensive repertoire of Sample Programs available from the Import PRGM menu.
; Dice-go29.txt
;
; This program simulates the throwing
; of a pair of dice, pausing to
; display first the value of one die
; (an integer from 1 to 6) ; and then
; pausing to display the value of the
; second die (another integer from 1
; to 6). Finally the values of the two
; dice are added together to give the
; total value of the throw.
;
; The heart of the program is a
; pseudo random number generator that
; is executed first as a subroutine
; and then as part of the main
; program. When you key in a first
; number, called a seed and press
; GSB 1, the digit for the
; first die is generated and displayed
; using the LBL 2 routine as a
; subroutine. Then the digit for the
; second die is generated using the
; same routine as part of the main
; program. The program then uses the
; generated number as a new seed for
; successive throws of the dice.
;
01 15 13 01 ; LBL 1
02 14 11 02 ; FIX 2
03 23 00 ; STO 0
04 15 13 00 ; LBL 0
05 00 ; 0
06 23 01 ; STO 1
07 12 02 ; GSB 2
08 15 13 02 ; LBL 2
09 24 00 ; RCL 0
10 09 ; 9
11 09 ; 9
12 07 ; 7
13 61 ; X
14 15 62 ; FRAC
15 23 00 ; STO 0
16 06 ; 6
17 61 ; X
18 01 ; 1
19 51 ; +
20 14 62 ; INT
21 14 11 00 ; FIX 0
22 14 74 ; PAUSE
23 23 51 01 ; STO + 1
24 24 01 ; RCL 1
25 15 12 ; RTN
26 13 00 ; GTO 0
27 15 12 ; RTN
28 74 ; R/S
DiceRND-go29.txt
; DiceRND-go29.txt
;
; Just like Dice-go29.txt, this program
; uses a pseudo random number generator
; to simulate throwing a pair of dice.
; Please read the program documenttion
; for the real Dice to learn how this
; program flows.
;
; The salient difference is DiceRND uses
; GO-29's builtin RND function rather
; than rolling its own, hence reducing
; the memory footprint.
;
; RND step 09 replaces Dice steps 9-17.
;
01 15 13 01 ; LBL 1
02 14 11 00 ; FIX 0
03 15 13 00 ; LBL 0
04 00 ; 0
05 23 01 ; STO 1
06 12 02 ; GSB 2
07 15 13 02 ; LBL 2
08 06 ; 6
09 83 ; RND replaces Dice steps 09-17
10 01 ; 1
11 51 ; +
12 14 62 ; INT
13 14 74 ; PAUSE
14 23 51 01 ; STO + 1
15 24 01 ; RCL 1
16 15 12 ; RTN
17 13 00 ; GTO 0
18 15 12 ; RTN
19 74 ; R/S
; Pythagorean Theorem-go29.txt
;
; Computes the hypotenuse of any right
; triangle, given the other two sides.
; The formula used is:
;
; c = √( a² + b² )
;
; Usage:
; Y = length of one side
; X = length of other side
; GSB 9
;
01 15 13 09 ; LBL 9
02 15 63 ; x^2
03 21 ; Swap xy
04 15 63 ; x^2
05 51 ; +
06 14 63 ; √
07 15 12 ; RTN
08 74 ; R/S
Theory
In GO-29's documentation, Part II - Programmatic Usage, the section Subroutines
describes the nature and limits of the calculator's ¦
and § mechanism. In particular we learned
that on an actual HP-29C, subroutine calls could be nested to a depth of three, although GO-29
extends that number. If the new, larger, subroutime call depth `n_29` had not been documented, how could you determine it?
With the aid of this diagram we discovered that if you wrote and called enough nested subroutines the LIFO
§ queue would lose its earliest entries
and that the program would terminate prematurely before returning to the Main Program:
As it happens, we can couple this observation of early program termination along
with a recursive subroutine to discover `n_29`, GO-29's subroutine call depth,
or § queue size.
Recursion is pretty opaque until you wrap your head around it, then it's amazingly awesome - search the web and read
up on the topic! A recursive subroutine typically contains in its definition instructions that do stuff, then a call to itself
to do similar stuff based upon what it just did. Makes perfect sense, right?
The big problem here (ignoring the fact that R₈ hasn't been initialized) is that the count-up goes on forever, there is no test to exit the virtual loop! If you manually key GSB 9, the subroutine calls itself an infinite number of times. A recursive
subroutine always needs a way out, a testable condition that can activate a clean exit from the subroutine. Here, two things should be obvious:
Corollary: We assume that nesting level 0 represents the Main Program.
Let's examine these two observations in greater detail. For this experiment we are probing the calculator to find `n_29` by repeatedly making nested subroutine calls
until we exceed the size of the call depth queue.
The essential idea is to count-up as we
¦ deeper and create LIFO queue entries,
then reverse course and count-down as we §
and consume LIFO queue entries. If the call queue becomes truncated then there is no longer a one-to-one correspondence between
¦s and
§s (too many
¦s and not enough
§ information),
thus the count-down will stop too soon, and the final subroutine nesting level in R₈ will not be zero.
The R₈ rule says always increment before ¦ 9, always decrement afterwards.
Instructions
Enter the proposed subroutine call depth to probe, `n_p` >= 1.
Press GSB 0.
The program ¦s and counts-up from 0 until the proposed call depth value is reached.
The program §s and counts-down until either:
✓ the program ends with a non-zero value `n_f` in the display, signifying it has terminated early without reaching the Main Program,
∴`n_29=n_p-n_f`
× the display shows 0 and the Main Program is reached. The value of `n_29` cannot be determined, go to step 1 and probe again using a larger value of `n_p`.
; Surface Area Of Sphere-go29.txt
;
; Compute the surface area of any
; sphere using the formula:
;
; A = π d²
;
; ENTRY:
; X = diameter of sphere.
; GSB 0
;
; EXIT:
; X = surface area of sphere.
;
01 15 13 00 ; LBL 0
02 15 63 ; x²
03 15 73 ; π
04 61 ; X
05 15 12 ; RTN
Settings are built into the calculator, except Apple TV where they are part of the tvOS Settings App. Available Settings options are device dependant - here are their default values:
Reminder: There are no gestures on Apple TV thus this section is not applicable, see the section Apple TV Particulars for details.
On macOS taps/touches are pointer clicks, pans/swipes/scrolls are pointer drags.
Shake to clear X. Not available on macOS.
Single tap the calculator display for Copy / Paste / Paper Tape in RUN mode.
Single tap the calculator display for Import PRGM / Share PRGM in PRGM mode.
Double tap the calculator display to show/hide the stack, memory and paper tape views in RUN mode.
Double tap the calculator display to show/hide the program description and listing views in PRGM mode.
Two-finger pan for iPad to reposition the stack, program and calculator views.
Touch and hold q or q in RUN mode to display the next or previous step, respectively.
Touch a program listing line to make it the current SP.
Touch a program listing line to dismiss the keyboard while editing the program description.
Touch and hold for 1.0 second (long touch) a program listing step to add special opcodes.
Long touch for iPad/Mac on the program documentation window to toggle between the docked and floating views. The gripper handles resize and move the floating window: on iPad use a two-finger pan, for macOS drag using your pointing device.
Touch switch-views control to alternate between two views.
Swipe up and down to scroll program description, program listing and sample programs views.
Swipe left and right to manipulate slide switches, if activated in Settings. Not available on macOS.
Flick left on the calculator display to erase last mantissa character entered.
Triple tap the calculator display to show/hide the Info button .
All calculator capabilites are supported on macOS.
Mac Window Mechanics
The App has a single window with the three standard window control buttons in the top-left corner:
The red button closes the window and quits the App.
The yellow button minimizes the window to the Dock.
The green button toggles the window between two size states: a minimalist size and the window's previous size.
When zooming to its minimalist size all Auxiliary Information Views are hidden, which are then restored when zooming back to the previous window size.
Mac Menu Actions
Some App actions have been duplicated in the macOS menus:
Application : Settings opens the Settings view.
File : Open imports a program.
File : Save exports a program.
File : Print prints current program.
Edit : Paper Tape manipulates the paper tape.
Edit : Copy exports the value of X to the pasteboard.
Edit : Paste imports a new value of X from the pasteboard.
Help : Help shows the documentation in a Help Book.
Most calculator capabilites are supported on Apple TV, with these notable exceptions:
Only the Sample Programs are available for import, you enter all other programs manually, just like in 1977.
No fancy Program editing, you do it all manually, just like in 1977.
No fancy Program sharing, you write it down on a piece of paper, just like in 1977.
No Copy / Paste.
Enjoy your trip in the WABAC Machine!
ATV Focus Navigation
Use the Apple TV remote to move the screen focus left, right, up and down until the desired object is highlighted, then click. The calculator keys are arranged in a regular grid so focus navigation is easy. But to reach the Info button and either of the two switch-views controls there is a special path passing through a focus portal key that you must follow in order to move the screen focus in and out of the calculator:
Left focus portal key q From the left portal key, focus left once to reach the stack and paper tape, focus left a second time to reach the Info button. Simply reverse your path to return to the calculator.
Right focus portal key t From the right portal key, focus right once to reach the program, and reverse your path to return to the calculator.
You may rightly view this focus ordering as if the following objects exist in their own logically horizontal row that you can freely traverse left and right:
Stack
q
GSB
GTO
r
t
Program
A focused, clickable object is highlighted: calculator keys with a translucent white overlay, and other objects with a light gold background. When the calculator first starts the initial screen focus is on the Info button for quick access to Help and Settings, as seen in this picture. Note that the OFF - ON switch can never receive the focus because the calculator is always on.
The Info button actually identifies with both switch-views controls, this means that the focus order is really a ring that you may circle in either direction:
As with iOS and macOS, you can view and scroll the paper tape and program listing on tvOS. Move the focus to the appropriate switch-views control ,
tap the control until the scrollable view of interest is visible, then pan up and down to scroll the contents. When you are finished, pan left or right to move the screen focus to the next object in the focus ring. Remember that
a view is only scrollable when it has the light gold focus.
Note: when a scrollable view is visible it inserts itself into the focus ring.
ATV LED Display Focus Actions
Similarly to iOS and macOS, after moving the screen focus up from the focus ring to the calculator's display area you can initiate context sensitive actions unavailable on a real device:
In RUN mode Paper Tape Actions... allows you to erase or annotate the paper tape.
In PRGM mode Import Sample Program... shows a list of programs you may run. After making a selection the calculator returns to RUN mode and the program inserts itself into the focus ring.
GO-21, GO-25 and GO-29
all provide support for hardware keyboards. You can enter digits and a decimal point into the
X register by simply typing those characters, even from a numeric keypad.
Use delete instead of a flick left in the display to delete the last character typed, and
return instead of z
to push the completed number onto the stack.
To enter an exponent of 10 for a floating point number
type e instead of c.
To change the sign of a mantissa or exponent
type c instead of x.
To perform any of the four basic arithmetic operations
-+?/
on these numbers type - + * /, respectively.
So the keyboard works rather well for simple calculator operations, but it's non-trivial to do more because there are no
familiar mappings between keyboard and calculator keys.
However, all 30 keys and the 2 slide switches of these calculators have a keyboard equivalent, with 27 keys common to all devices and 6 keys specific to an individual model:
27 Common
6 Specific
GO-21
orange t
green
GO-25
orange t
r violet (except ¦)
GO-29
orange t
r violet (except w)
Mappings by color (see below)
Additionally,
⌘? shows the Info view for Help and Settings
keys colored red map to virtual calculator keys
on tvOS there are even keys to mimic an Apple TV remote:
Many thanks to Namir Clement Shammas for convincing me to write this simulation, for his testing, and for all his wonderful Sample Programs.
Also thanks to my far-away-friend, David Marriott of Melbourne, Australia, whose calculator
artwork, GO-Regular font and other contributions to GO-25 played key roles in the development of this App.
Thank you Willy Kunz of Zurich, Switzerland, for showing me how to support international keyboards.
controls the two basic calculator modes. In RUN mode, key presses are executed immediately and results are shown
in the calculator display area. In PRGM mode, key presses are stored in program memory for later execution.
It's important to realize which mode the calculator is in, as it has ramifications that affect other operational characteristics
of the device.
touch point that toggles what the view shows, detailed in the following two sections.
In this example when you press GSB 1, the calculator searches sequentially through program memory from wherever it was located until it encounteres the first © 1 instruction. The calculator then executes instructions until it executes a § or a R/S instruction and stops.
Execution falls through step 00, too. You can load instructions into steps 01 through 198 of program memory, but you cannot load an instruction into step 00. In fact, step 00 merely acts as a kind of origin in program memory, a beginning point for the loading of a program. When step 00 is encountered by a running program, execution continues without a halt from step 198 to step 01, just as if step 00 were not there.
As you can see, the only difference between a subroutine and a normal branch is the transfer of execution after the §. After the e, the next § halts a running program; after a ¦, the next § returns execution back to the main program, where it continues until another § (or R/S) is encountered. The same routine may be executed by e and ¦ any number of times in a program.
The step numbers that §s return to are kept in an ordered list known as a Last In First Out (LIFO) queue. What this means is that as GSBs are processsed, they push their return address on the end the LIFO queue, and as §s are executed they pop the most recent return address off the end of queue. As long as there is room at the end of the LIFO queue for GSB to attach its return address, a § can grab it and transfer control appropriately. When a § is executed and the LIFO queue is empty, the program has nowhere to go and simply ends.
As it happens, we can couple this observation of early program termination along
with a recursive subroutine to discover `n_29`, GO-29's subroutine call depth,
or § queue size.
.
