GO-25 SciRPN closely simulates the venerable HP-25C Programmable Pocket Scientific Calculator. The HP-25C was released in 1976 and sold for a MSRP of $195. Virtually indistinguishable from the real item in operation, GO-25 is a powerful yet simple retro calculator.
Topics
This document is not an exhaustive reference manual; rather, it's a terse outline of the calculator's function and programming
keys.
In this document normal calculator keys are shown in bold, such as +, or CHS, or 4, or Σ+.
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 g
or f,
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 arcsine function sin-1. The only
exception to this convention is when discussing programming and keycodes.
The PRGM-RUN switch (As you'll learn later there are two variants of RUN mode, for three actual calculator modes.)
The GO-25 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-25C. 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.
In RUN mode the display shows the X stack register, usually the result of the latest calculation.
Tapping the display in RUN mode
brings up the Copy / Paste menu, allowing you to export the value of X, or import a new value of X.
In GO-25, 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-25 always computes
internally
using each number as a 14-digit mantissa and a two-digit exponent of 10.
Three keys control how numbers are displayed.
FIX allows numbers to be displayed in fixed decimal point format,
SCI displays numbers in scientific notation format, and
ENG displays numbers in engineering notation,
with exponents of 10 shown in multiples of three (e.g., 103, 10-6, 109) . Display control
alters only the manner in which a number is displayed, the actual number itself is not altered by any of the display control keys.
To select a display mode press one of the display mode keys
followed by a number key to specify the number of decimal places (0-9) to which the display is to be rounded.
GO-25 switches the display from fixed point notation to full scientific notation
(SCI 7) 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.
You can key in numbers multiplied by powers of 10 by pressing EEX (enter exponent of ten). 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 CHS to make the exponent negative, then key in the power of 10.
When a number is greater than 9.9999999 x 1099 an overflow has occurred and
9.9999999+99 is displayed instead. Other illegal operations, such as a divide by zero,
display the word
Error, then set the illegal number to zero.
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 Key Codes.
It's this mode that allows you to manually enter a program into the calculator, just like an authentic HP-25C.
Tapping the display in PRGM mode
brings up the Import PRGM / Share PRGM menu, allowing you to transfer GO-25 programs
to / from the App.
Automatic storage of intermediate results is the reason that GO-25 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.
The R↓ (roll down) and X⇔Y (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 R↓ 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 R↓ key to return the contents to their original registers.
The X⇔Y (X exchange Y) key exchanges the contents of the X and Y registers
without affecting the Z and T registers.
To clear the displayed X register only, press CLX. To clear the entire automatic memory stack, including the
displayed X register, press CLEAR STK (clear stack).
This replaces all numbers in the stack with zeros.
The ENTER 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.
GO-25 provides 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 swipe-up gesture on the calculator body proper, or a double-tap on the display. If the information view is visible, a swipe-up or double-tap hides the view. If the view is not
visible, the information view appears. So a swipe-up or double-tap toggles the visibility of the auxiliary information.
Similar to the calculator display, the information that's displayed is dependent on the setting of the PRGM-RUN switch.
In RUN mode the 4 stack registers, the 10 storage registers, and the LAST X
register are displayed. Also note
in the lower-right corner a flip tab:
touching the tab flips the window and shows up to 100 lines of RUN mode key-press history.
In PRGM mode the program listing is shown. The listing displays the program name and description, and the step numbers,
opcodes and pneumonics for all program steps. Both the program listing and program description are scrollable and editable.
The current step pointer (SP) is highlighted in blue. In RUN mode this is the next instruction
to be executed via SST or R/S. In PRGM mode you edit the step following the SP unless you've turned
on GO-25 Step Editing from the Settings menu, in which case you edit the SP directly.
In PRGM mode you can also move the blue selection 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-25 opcodes described in the
section GO-25 Program Format.
(Note: unlike for iPhone
and iPod touch, which have tiny screens, on iPad both information views are by default always visible, but you can hide them
with two swipe-up gestures or two double-taps, if desired, one in PRGM mode and one in RUN mode.)
In addition to the four stack registers that automatically store intermediate results, GO-25
also contains a separate automatic register,
the LAST X register. This register preserves the value in the displayed
X register before a new function is performed.
The CLEAR PREFIX key will clear a blue prefix key, a
gold prefix key, STO, RCL, or GTO.
To clear a prefix you have mistakenly
pressed, merely press CLEAR PREFIX,
then press the correct key.
Some calculations require the absolute value, or magnitude, of a number. To obtain the absolute value of the number in the display,
press
ABS.
To extract and display the integer portion of a number, press INT.
The fractional portion of the number is
lost. The entire number, of course, is preserved in the LAST X register.
To place only the fractional portion of a number into the displayed X-register,
press FRAC.
The integer portion of the number is lost. The entire number, of course, is preserved in
the LAST X
register.
To calculate the reciprocal of a number in the displayed X register, press
1/X.
To calculate the square root of a number in the displayed X register, press
√X.
To square a number in the displayed X register, press X².
The value Π accurate to 14 places (3.14159265358979) is provided as a fixed constant in GO-25.
Merely press Π whenever
you need it in a calculation.
The % key is a two-number function that allows you to compute percentages.
To find the percentage of a number:
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 % 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.
In addition to automatic storage of intermediate results that is provided by the four-register automatic memory stack,
GO-25
also has ten addressable storage registers that are unaffected by operations within the stack. These storage registers
allow you to set aside numbers
as constants or for use in later calculations, and they can be used either manually or as part of a program.
The addresses of the storage registers are indicated by number keys 0 through 9.
To store a value appearing in the display, press STO followed by a number key 0 through 9
specifying the register address where the value is to be stored. When a number is stored, it is merely copied into the storage
register.
To copy a number from one of the storage registers into the displayed X register, press the RCL key followed
by the number key of the register address.
Recalling a number causes the stack to lift unless the preceding keystroke was ENTER, CLX or Σ+.
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 as a 10-digit
number with a two-digit exponent of 10 until you overwrite it by storing another number there, or until you clear
the storage registers.
To clear the number from a single storage register, simply store the quantity zero in the register by pressing 0 STO
followed by the number key
0 through 9 of the register address.
To clear data from all manual storage registers at once, without affecting data in other portions of the calculator,
press CLEAR REG. This places zero in all ten of the storage registers.
Arithmetic is performed upon the contents of the storage register by pressing STO, followed by the arithmetic
function key,
followed in turn by the register address.
If the magnitude of a number in any of the ten storage registers exceeds 9.999999999 x 1099, the display
immediately
shows OF (overflow) to indicate that a storage register has overflowed.
GO-25 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 DEG,
RAD or GRD to
specify the degree mode.
Note: 360 degrees = 2Π radians = 400 grads.
The six trigonometric functions provided by the calculator are:
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 keys.
The →H.MS (to hours, minutes, seconds)
key converts decimal hours to the format of hours, minutes and seconds. To see the digits for seconds, you should specify
FIX 4 display format.
Conversely, the →H (to decimal hours)
key is used to change hours, minutes, seconds into decimal hours.
The →H
and →H.MS
keys also permit you to change degrees, minutes, seconds to decimal degrees, and vice versa. The conversion is
important because trigonometric
functions in GO-25 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.
Two functions are provided for polar/rectangular coordinate conversion. 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 →P. 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 respectively)
to rectangular coordinates (x, y respectively), press →R.
Coordinate x then appears in the X register and coordinate y
is placed in the Y register.
GO-25 computes both natural and common logarithms as well as their inverse functions
(antilogarithms):
Yx permits you to raise a positive number
(either an integer or a decimal) to any power.
In conjunction with 1/X,
Yx
provides a simple way to extract roots. For example, the cube root of 5 is equivalent to 51/3.
Pressing the Σ+ 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 R3 through R8 (GO-25 extension). The
only time that information
is automatically accumulated in the storage registers is when the Σ+ key is used. Before you begin any
calculations using
the Σ+ key, you should first clear the storage registers of data by pressing
CLEAR REG.
When you press the Σ+ key each of the following operations is performed on the data in the X
and Y registers:
Thus, each press of the Σ+ key updates these summations and multiplications. The contents of the
displayed X register
and the applicable storage registers are as follows:
In addition, the Y value present before the last press of the Σ+ key is retained in the Y register,
while the X value present before Σ+ was pressed is retained in the
LAST X register.
To see any of the summations at any time, you have only to recall the contents of the desired storage register.
(In the case of the Σ+ key, recalling storage register contents or keying in a number
simply writes over the number of entries (n)
that is displayed. The stack does not lift.)
The mean (arithmetic average) of data entered and summed using the Σ+ key is available by using the
The standard deviation (a measure of dispersion around the mean) is calculated using data in the applicable storage registers
and the s (standard deviation) key.
Pressing s
uses the data in registers R3 (n),
R6 (Σx2) and R7 (Σx).
If you key in an incorrect value and have not pressed Σ+ press CLX and key in the correct value.
If one of the values is changed, or if you discover after you have pressed the Σ+ key that one of the
values is in error,
you can correct the summations by using the Σ- key as follows:
The Σ+ key can be used to sum any quantities that are in the X and Y registers.
You can even perform vector addition and subtraction using rectangular to polar coordinate conversion
and the Σ+ and Σ- keys.
Switch the PRGM-RUN switch to PRGM to enter program steps into the calculator.
Function keys are recorded in program memory. Display shows program memory step number and the keycode
(keyboard row and location in row) of the function key.
To clear program memory and reset the step pointer to the beginning of program memory press
CLEAR PRGM. (Note that
CLEAR PRGM cannot be recorded in program memory; otherwise,
there would be no way to clear program memory!)
This key, single step, also cannot be recorded in program memory in PRGM mode, as it's used to advance
the step pointer forward for
examining and/or changing program steps. (Used in automatic RUN mode, the SST key 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.)
This key, back step, also cannot be recorded in program memory in PRGM mode, as it's used to move the
step pointer backwards for
examining and/or changing program steps. (Used in automatic RUN mode, the BST key 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.)
Go to. Executed as a recorded program instruction, followed by a two-digit step number, causes the calculator to execute the
instruction at the specified step
number next, and continue program execution sequentially from there. (Used via the keyboard, positions the internal step pointer.)
Run/Stop. Executed as a recorded program instruction, stops program execution. (Use via the keyboard,
begins execution of a stored program. Stops execution if program is running.)
Pause. Executed as a recorded program instruction, stops program execution for 1 second and displays contents
of the X register, then resumes program execution.
No operation. Calculator executes no operation and continues program execution sequentially
with the instruction in the next program memory step.
Conditionals. Each 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.
There are three ways to use your GO-25 calculator:
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.
In PRGM (program) 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 three can be recorded for later execution with the PRGM-RUN switch
set to PRGM. The three operations that cannot be recorded are:
These three operations work in PRGM mode to help you write and record your programs.
GO-25 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 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.
Let's write a program to compute the volume of a sphere.
For this discussion go into Settings and ensure that GO-25 Step Editing is turned on.
First, set the PRGM-RUN switch to PRGM so that the sequence of keystrokes will be recorded for later execution.
Second, press CLEAR PRGM to clear the calculator of previous programs.
The display will show:
With 00 displayed in PRGM mode, you are ready to key in your program.
Surface area of a sphere is calculated using the formula A = Πd². The short list of keys for the area of
a sphere program is:
To conserve program memory when using prefixed functions, the keycodes for the prefix and the function are merged into one step.
For an example of this press the second key of the program, X2, and the display will change to:
The two-number code 01 on the left side of the display designates the step number of program memory
that is being displayed. The two pairs of numbers on the right side of the display indicate that the function X2
has been recorded in that step of program memory. Digits 1 and 5 denote the
g key.
Digits 0 and 2 denote the
2 key. The operation stored then, is g 2 which
is the X2 function. In every case, a single operation
uses only one step of program memory.
Before proceeding to enter the rest of the program, if you used the BST key to review step 01, now touch
the SST key to single-step back to step 02. To edit a step it must be visible in the calculator display.
The keys for finding the area of a sphere and their corresponding codes are shown below.
Press each remaining key in turn and verify the keycodes shown in the display.
Here's the program we developed in the previous section:
Programs are executed in automatic RUN mode. So first set the PRGM-RUN switch to RUN.
Next press GTO 00. This operation resets the calculator so that program execution will begin
from step 00 (pressing CLEAR PRGM in RUN mode accomplishes the same thing).
Then, key in a value for a diameter and press R/S in RUN mode to run your program.
The operations stored in program memory are executed sequentially downward from step 00. First step 01 is executed,
then step 02, then step 03, and then step 04, which now contains a special instruction, GTO 00. For example,
if you entered a diameter of 1.3, the computed surface area is 5.31.
The GTO 00 instruction in step 04 is not an instruction you keyed in yourself.
It was already there. If you press CLEAR PRGM in PRGM mode, program memory is filled with GTO 00 instructions.
The three-step program you keyed in replaced three of these instructions.
A GTO 00 instruction in the program tells the calculator to go to step 00 and execute the
automatic stop instruction there next. If R/S is pressed again in automatic RUN mode, the
calculator will begin executing instructions from step 00 as it did the first time.
Each time the calculator executes the program, it ends execution at step 00, ready to begin again.
If you had recorded a 99-step program, after executing step 99 the calculator would execute the automatic stop instruction
stored in step 00. Then you would have to press R/S to execute the program again.
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. Tapping the display in PRGM mode
brings up the Import PRGM / Share PRGM menu, allowing you to transfer GO-25 programs
to / from the App.
Additional help is available in the following sections Importing Programs and Sharing Programs.
On an actual HP-25C programs are entered using the calculator keys. That method works with
GO-25 as well, but it's often easier
to edit your programs in another App and import them into GO-25
(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-25, 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-25 programs folder.
You also have a My Programs container that uses iTunes File Sharing to sync programs between your computer and GO-25.
Alternately, 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, SurfaceAreaOfSphere-go25.txt) to GO-25, that
program's name appears in the Import PRGM window.
Finally, a small selection of programs is included in GO-25's Sample Programs container.
An HP-25C program consists of simple digits representing step numbers and opcodes.
A GO-25 program extends that by allowing comments, as well as supporting four new opcodes: DMP, BEL, SEC
and RND.
The comment character is a semi-colon. All comments appearing before the first program step 01 are collectively
called the program description 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. A CLEAR PRGM does not automatically erase the program description - you can do that by cutting the text
(touch and hold, Select All, Cut).
A GO-25 program has one convention that you are encouraged to adhere to:
the first line of descriptive text is the program name: the program name line must begin with the comment character ";",
and end with the characters "-go25.txt". If a program name cannot be found Untitled-go25.txt is used. The extension "-go25.txt" was chosen to remind humans
what the document contains, and to remind computers that it's not a binary file.
GO-25 supports four special keycodes not available on a real HP-25C, keycode 80, DMP, keycode
81, BEL, keycode 82, SEC, and keycode 83, RND.
You cannot key these instructions in, but they can be part of a program imported into the calculator. In PRGM mode,
if you touch and hold a program listing step, a contextual menu appears so you can add any extended GO-25 opcodes.
Program step zero has a special Edit button that enables insertion and removal of NOP instructions, as well as re-arrangement of program steps using gripper pads.
Touching a green plus inserts a NOP before that step, and simultaneously drops program step 99. Touching the red minus removes that NOP. Touching and dragging a gripper pad moves that program step, re-inserting it when you have reached the destination and released the gripper.
All GTO targets are automatically re-sequenced.
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 iTunes File Sharing to sync programs between your computer and GO-25.
GO-25
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-25
uses the program name to identify the program. For example, use this option to export a program to the Files App.
Unsupported programs that you may copy to the pasteboard and then import into GO-25 while in PRGM mode.
If you attempt a calculation containing an improper operation -
say, division by zero - the display will show Error. To clear, press CLX.
The following are improper operations:
Capabilities At A Glance
Introduction
controls the two basic calculator modes. In RUN mode, key presses are executed immediately and results 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.
The Calculator Display
The Stack
Auxiliary Information Views
Function Keys
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.
(mean)
key. When you press , the mean of the values of X
is calculated using the data in storage registers R3 (n) and R7 (Σx).
Programming Keys
Three Modes Of Operation
Key Codes
00
This tells you that you are at step 00, the beginning of program memory. Step 00 contains an automatic stop instruction and cannot be
used to record your program keystrokes. Program keystrokes are recorded in steps 01 through 99.
The program memory for GO-25 is separate from the four stack registers, the
LAST X register, and the ten storage registers.
g X2 ; square the diameter
g Π ; load X with Π
x ; multiply d² by Π
Press the first key of the program and the display will change to:
01 15
Since it's impossible to key anything into step 00 this first key is recorded in step 01.
The two numbers on the right of the display designate the key stored in that step. Each key on the keyboard has a two-digit keycode.
For convenience, the digit keys are coded 00 through 09. All other keys are coded by their position on the keyboard.
The first digit denotes the row of the key and the second digit the number of the key in that row.
So 15 tells you that the key is in the first row on the calculator and that it is the fifth key in that row, the
g key.
This handy matrix system allows you to easily determine the code for each instruction without using a reference table.
02 13 00
Whoa, what just happened? The calculator is smart enough the realize that program step 01 is complete, and
has stored that step into program memory and advanced its internal step pointer to step 02,
ready for you to key in the next instruction. To see step 01 just look at the program listing view if it's visible. If it's
not visible make it so with a swipe-up, or touch the BST key to back-step the step pointer so that step 01 is visible
in the calculator display. You will see this:
01 15 02
g X2 01 15 02
g Π 02 15 73
x 03 61
In this case, a program consisting of five keystrokes takes only three steps of program memory.
Running A Program
01 15 02
02 15 73
03 61
Storing and Organizing Programs
Importing Programs
GO-25 Program Format
; SurfaceAreaOfSphere-go25.txt
;
; Compute the surface area of a
; sphere using the formula:
;
; A = πd²
;
;
; ENTRY:
; X = diameter of sphere.
;
; EXIT:
; X = surface area of sphere.
;
;
01 15 02 ; X²
02 15 73 ; Π
03 61 ; x
If comments appear on individual program steps they are discarded and ignored when the program is imported.
Editing Programs Inline
Sharing Programs
User Contributed Programs
Complex Operations-go25.txt
; Complex Operations-go25.txt
; Written by Eddie Shore
; May 8, 2011
;
; V 1
;
; This program calculates the following:
; 1. (a + bi)^n. (principal power and root)
; 2. exp(a + bi)
; 3. ln(a + bi)
;
;
; Registers:
; R0 = temp
; R1 = real part
; R2 = imaginary part
; R3 = power
;
; Results:
; y stack: imaginary part
; x stack: real part
;
;
; Example:
; Find (2.8 + 2i)^4, exp(2.8 + 2i), and ln(2.8 + 2i)
;
; Store the complex number to be operated on:
; 2.8 STO 1
; 2 STO 2
; 4 STO 3
; for the power:
; 1 R/S. (-110.6944 + 86.0160i)
; for the exponential:
; 2 R/S (-6.8434 + 14.9531i)
; for the natural logarithm
; 3 R/S (1.2357 + .6202i)
01 23 00 ; STO 0
02 01 ; 1
03 14 71 ; x=y
04 13 15 ; GTO 15
05 22 ; R↓
06 02 ; 2
07 14 71 ; x=y
08 13 33 ; GTO 33
09 22 ; R↓
10 03 ; 3
11 14 71 ; x=y
12 13 45 ; GTO 45
13 22 ; R↓
14 13 00 ; GTO 00
15 24 02 ; RCL 2
16 24 01 ; RCL 1
17 15 09 ; →P
18 24 03 ; RCL 3
19 14 03 ; y^x
20 23 00 ; STO 0
21 21 ; Swap xy
22 24 03 ; RCL 3
23 61 ; X
24 31 ; ENTER
25 14 04 ; sin
26 24 00 ; RCL 0
27 61 ; X
28 21 ; Swap xy
29 14 05 ; cos
30 24 00 ; RCL 0
31 61 ; X
32 13 00 ; GTO 00
33 15 33 ; RAD
34 24 01 ; RCL 1
35 15 07 ; e^x
36 24 02 ; RCL 2
37 14 04 ; sin
38 21 ; Swap xy
39 61 ; X
40 14 73 ; LASTx
41 24 02 ; RCL 2
42 14 05 ; cos
43 61 ; X
44 13 00 ; GTO 00
45 15 33 ; RAD
46 24 02 ; RCL 2
47 24 01 ; RCL 1
48 15 09 ; →P
49 14 07 ; ln
50 13 00 ; GTO 00
Derivative-go25.txt
; Derivative-go25.txt
; Derivative Program
; Calculate the numeric derivative
;
; Instructions:
; 1. When entering the program, the function for the required derivative starts on Step 27
; 2. Use R0 as the independent variable. You can use R5, R6, and R7 for constants.
; 3. Store a tolerance level in R1. I recommend 0.01.
; 4. The last four lines of the program MUST be:
; RCL 04
; x=0
; GTO 10
; GTO 19
; The function can have at most 19 steps (for classic HP 25) or 69 steps (GO 25 App).
; The example function (listed in line 27) is ln x + 3x - 10.8074
;
; Formula (HP 67):
; [f(x+Δx/2)-f(x-Δx/2)]/Δx = f'(x)
01 00 ; 0
02 23 04 ; STO 04
03 24 00 ; RCL 00
04 24 01 ; RCL 01
05 02 ; 2
06 71 ; ÷
07 51 ; +
08 23 00 ; STO 00
09 13 27 ; GTO 27
10 22 ; R↓
11 23 02 ; STO 02
12 01 ; 1
13 23 04 ; STO 04
14 24 00 ; RCL 00
15 24 01 ; RCL 01
16 41 ; -
17 23 00 ; STO 00
18 13 27 ; GTO 27
19 22 ; R↓
20 23 03 ; STO 03
21 32 ; CHS
22 24 02 ; RCL 02
23 51 ; +
24 24 01 ; RCL 01
25 71 ; ÷
26 13 00 ; GTO 00
27 24 00 ; RCL 00
28 14 07 ; ln
29 24 00 ; RCL 00
30 03 ; 3
31 61 ; x
32 51 ; +
33 01 ; 1
34 00 ; 0
35 73 ; .
36 08 ; 8
37 00 ; 0
38 07 ; 7
39 04 ; 4
40 41 ; -
41 24 04 ; RCL 04
42 15 71 ; X=0
43 13 10 ; GTO 10
44 13 19 ; GTO 19
45 13 00 ; GTO 00
Lower Incomplete Gamma-go25.txt
; Lower Incomplete Gamma-go25.txt
; Ported from HP 65 Math PAC 2
; Similar to the Gamma function but
; γ(a,x) = Integral(e^-t t^(a-1) dt from 0 to x)
;
; a and x must be positive
;
; Instructions: a ENTER x R/S
;
; You can approximate the Gamma function by setting x high enough. According to Viktor Toth from rskey.org, for any a<50, setting x=30 gives the gamma approximation accurate from 8 to 12 digits
01 23 01 ; STO 01
02 21 ; Swap XY
03 23 02 ; STO 02
04 14 03 ; Y^X
05 24 02 ; RCL 02
06 71 ; ÷
07 23 03 ; STO 03
08 24 01 ; RCL 01
09 24 02 ; RCL 02
10 01 ; 1
11 51 ; +
12 23 02 ; STO 02
13 71 ; ÷
14 24 03 ; RCL 03
15 61 ; x
16 23 03 ; STO 03
17 51 ; +
18 14 61 ; X≠Y
19 13 08 ; GTO 08
20 24 01 ; RCL 01
21 15 07 ; e^X
22 71 ; ÷
23 13 00 ; GTO 00
Midpoint Rule-go25.txt
; Midpoint Rule-go25.txt
; Numerical Integration using the Midpoint Formula
; Property of Eddie Shore
;
; Instructions:
; 1. Store lower limit in R1
; 2. Store upper limit in R2
; 3. Store number of intervals in R3
; 4. In run mode, press f CLEAR PRGM and the R/S
;
; Input the function at Step 32. End the function with the instruction GTO 20. Registers R0 and R7 are free. The function starts with x_i on the x-stack.
;
; Registers Used
; R1 = a
; R2 = b
; R3 = n
; R4 = h = (b - a)/n
; R5 = sum
; R6 = counter
;
; The example function included in this program is:
; 2 + cos(2 sqrt(x))
; {RAD SQRT 2 x COS 2 + GTO 20}
01 01 ; 1
02 23 06 ; STO 06
03 00 ; 0
04 23 05 ; STO 05
05 24 02 ; RCL 02
06 24 01 ; RCL 01
07 41 ; -
08 24 03 ; RCL 03
09 71 ; ÷
10 23 04 ; STO 04
11 24 06 ; RCL 06
12 73 ; .
13 05 ; 5
14 41 ; -
15 24 04 ; RCL 04
16 61 ; x
17 24 01 ; RCL 01
18 51 ; +
19 13 32 ; GTO 32
20 23 51 05 ; STO + 05
21 01 ; 1
22 23 51 06 ; STO + 06
23 24 06 ; RCL 06
24 24 03 ; RCL 03
25 14 41 ; X<Y
26 13 28 ; GTO 28
27 13 11 ; GTO 11
28 24 05 ; RCL 05
29 24 04 ; RCL 04
30 61 ; x
31 13 00 ; GTO 00
32 15 33 ; RAD
33 14 02 ; √
34 02 ; 2
35 61 ; x
36 14 05 ; cos
37 02 ; 2
38 51 ; +
39 13 20 ; GTO 20
40 13 00 ; GTO 00
Sum-go25.txt
; sum-go25.txt
; Sum Program (Updated Instructions)
; Eddie Shore, 4/10/2011
; The registers used in this program are:
; R1 = initially, the user will load the lower limit. Register 1 will also act as the independent variable in the function (i)
; R2 = the upper limit, which the user loads
; R3 = the sum, calculated during the program
; The function starts at Step 16.
; Required ending commands:
; GTO 05
; Instructions:
; 1. In RUN Mode, press GTO 16
; 2. Switch to PRGM mode, enter the function. Anything previously written will be overwritten (replaced). The program loads R_1 (i) in the display. The Register for the independent variable is R_1. End the function with the command GTO 05.
; 3. Switch to RUN mode. Load the lower limit in R_0 and the upper limit in R_1.
; 4. Press f CLEAR PRGM, R/S.
; R1 = a, independent variable in f(R1)
; R2 = b
; R3 = sum
;
; Enter your function, f(R1) at line 16. The function MUST end with GTO 05.
; The function can be anything. As a example: the Zeta Function (slow converging) to calculate ζ(2).
; Preload R1 and R2 before running the program.
01 00 ; 0
02 23 03 ; STO 03
03 24 01 ; RCL 01
04 13 16 ; GTO 16
05 23 51 03 ; STO + 03
06 01 ; 1
07 23 51 01 ; STO + 01
08 24 01 ; RCL 01
09 24 02 ; RCL 02
10 14 41 ; X<Y
11 13 13 ; GTO 13
12 13 03 ; GTO 03
13 24 03 ; RCL 03
14 74 ; R/S
15 13 00 ; GTO 00
16 15 02 ; X^2
17 15 22 ; 1/X
18 13 05 ; GTO 05
19 15 74 ; NOP
20 15 74 ; NOP
21 15 74 ; NOP
22 15 74 ; NOP
23 15 74 ; NOP
24 15 74 ; NOP
25 15 74 ; NOP
26 15 74 ; NOP
27 15 74 ; NOP
28 13 00 ; GTO 00
Improper Mathematical Operations
where n <= 0
Gesture Summary
.
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