RPN83P User Guide

RPN calculator app for the TI-83 Plus and TI-84 Plus inspired by the HP-42S.

Version: 0.9.0 (2024-01-06)

Project Home: https://github.com/bxparks/rpn83p

Introduction

RPN83P is an RPN calculator app for the TI-83 Plus (including the Silver Edition) and the TI-84 Plus (including the Silver Edition). The app is inspired mostly by the HP-42S calculator, with some significant features from the HP-12C and the HP-16C.

The RPN83P is a flash application written in Z80 assembly language that consumes 2 pages (32 kiB) of flash memory. Since it is stored in flash, it is preserved if the RAM is cleared. It consumes about 735 bytes of TI-OS RAM through 3 AppVars: RPN83REG (496 bytes), RPN83STK (116 bytes), and RPN83SAV (123 bytes).

Summary of features:

traditional 4-level RPN stack (X, Y, Z, T), with LastX register
8-line display showing all stack registers
hierarchical menu system similar to HP-42S
quick reference HELP menu
storage registers
- store and recall:STO nn, RCL nn
- storage arithmetics: STO+ nn, STO- nn, STO* nn, STO/ nn, RCL+ nn, RCL- nn, RCL* nn, RCL/ nn
- 25 storage registers: nn = 00..24
all math functions with dedicated buttons on the TI-83 Plus and TI-84 Plus
- arithmetic: /, *, -, +
- algebraic: 1/X, X^2, SQRT, ^ (i.e. Y^X)
- transcendental: LOG, 10^X, LN, e^X
- trigonometric: SIN, COS, TAN, ASIN, ACOS, ATAN
- constants: pi and e
additional menu functions
- arithmetic: %, %CH, GCD, LCM, PRIM (prime factor), IP (integer part), FP (fractional part), FLR (floor), CEIL (ceiling), NEAR (nearest integer), ABS, SIGN, MOD, MIN, MAX
- algebraic: X^3, 3RootX
- transcendental: XRootY,2^X, LOG2, LOGB, E^X- (e^x-1), LN1+ (log(1+x))
- trigonometric: ATN2
- hyperbolic: SINH, COSH, TANH, ASNH, ACSH, ATNH
- probability: PERM, COMB, N!, RAND, SEED
- angle conversions: >DEG, >RAD, >HR, >HMS, >REC, >POL
- unit conversions: >C, >F, >hPa, >inHg, >km, >mi, >m, >ft, >cm, >in, >um, >mil, >kg, >lbs, >g, >oz, >L, >gal, >mL, >floz, >kJ, >cal, >kW, >hp
statistics and curve fitting, inspired by HP-42S
- statistics: Sigma+, Sigma-, SUM, MEAN, WMN (weighted mean), SDEV (sample standard deviation), SCOV (sample covariance), PDEV (population standard deviation), PCOV (population covariance)
- curve fitting: Y>X, X>Y, SLOP (slope), YINT (y intercept), CORR (correlation coefficient)
- curve fit models: LINF (linear), LOGF (logarithmic), EXPF (exponential), PWRF (power)
base conversion and bitwise operations, inspired by HP-16C and HP-42S
- base conversions: DEC, HEX, OCT, BIN
- bitwise operations: AND, OR, XOR, NOT, NEG, REVB (reverse bits), CNTB (count bits)
- integer arithmetics: B+, B-, B*, B/, BDIV (divide with remainder)
- shift and rotate: SL, SR, ASR, RL, RR, RLC, RRC, SLn, SRn, RLn, RRn, RLCn, RRCn
- carry flag and bit masks: CCF, SCF, CF?, CB, SB, B?
- word sizes: WSIZ, WSZ?: 8, 16, 24, 32 bits
time value of money (TVM), inspired by HP-12C, HP-17B, and HP-30b
- N, I%YR, PV, PMT, FV, P/YR, BEG, END, CLTV (clear TVM)
complex numbers, inspired by HP-42S and HP-35s
- stored in RPN stack registers (X, Y, Z, T, LastX) and storage registers R00-R24
- computation modes: RRES (real results), CRES (complex results)
- display modes: RECT, PRAD (polar radians), PDEG (polar degrees)
- linking/unlinking: 2ND LINK (convert 2 reals to 1 complex, same as COMPLEX on HP-42S)
- number entry: 2ND i (rectangular), 2ND ANGLE (polar degrees), 2ND ANGLE 2ND ANGLE (polar radians)
- extended regular functions: +, -, *, /, 1/x, x^2, SQRT, Y^X, X^3, 3RootY, XRootY, LOG, LN, 10^x, e^x, 2^x, LOG2, LOGB
- complex specific functions: REAL, IMAG, CONJ, CABS, CANG
- unsupported: trigonometric and hyperbolic functions (not supported by TI-OS)
various modes (MODE)
- floating display: FIX, SCI, ENG
- trigonometric: RAD, DEG
- complex computation: RRES, CRES
- complex display: RECT, PRAD, PDEG
- SHOW (2ND ENTRY): display all 14 internal digits

Missing features (partial list):

vectors and matrices
keystroke programming

Why?

Short Answer

This project helped me relearn Z80 assembly language programming using TI calculators. It also produced a scientific RPN app that can run on calculators which are easily and cheaply obtainable. There are no scientific RPN calculators currently in production from HP. The prices for many HP calculators in the used market are unreasonably high, so RPN83P may fill a gap for some people in some cases.

Long Answer

When I was in grad school, I used the HP-42S extensively. After graduating, I sold the calculator, which I have regretted later. The old HP-42S calculators now sell for $200-$300 on eBay, which is a sum of money that I cannot justify spending.

I finished my formal school education before graphing calculators became popular, so I didn't know anything about them until a few months ago. I did not know that the early TI graphing calculators used the Z80 processor, and more importantly, I did not know that they were programmable in assembly language.

I realized that I could probably create an app that could turn them into passable, maybe even useful, RPN calculators. The debate over RPN mode versus algebraic mode has probably been going on for 40-50 years, so I probably cannot add more. Personally, I use algebraic notation for doing math equations on paper or writing high-level computer programs. But when I do numerical computation on a hand-held device, I am most comfortable using the RPN mode.

There are many RPN calculator apps for the smartphone, but the touchscreen of a phone can become tedious for calculations that require large number of keystrokes. For those cases, a physical device is more convenient and less error prone.

The RPN83P app is inspired by the HP-42S. It is the RPN calculator that I know best. It also has the advantage of having the Free42 app (Android, iOS, Windows, MacOS, Linux) which faithfully reproduces every feature of the HP-42S. This is essential because I don't own an actual HP-42S anymore to verify obscure edge cases which may not be documented.

The RPN83P app cannot be a clone of the HP-42S for several reasons:

The keyboard layout and labels of the TI-83 and TI-84 calculators are different. As an obvious example, the TI calculators have 5 menu buttons below the LCD screen, but the HP-42S has 6 menu buttons.
The RPN83P does not implement its own floating point routines, but uses the ones provided by the underlying TI-OS. There are essential differences between the two systems. For example, the HP-42S supports exponents up to +/-499, but the TI-OS supports exponents only to +/-99.

Although the HP-42S may be close to "peak of perfection for the classic HP calcs", I think there are features of the HP-42S that could be improved. For example, the HP-42S has a 2-line LCD display which is better than the single-line display of earlier HP calculators. But the TI-83 and TI-84 LCD screens are big enough to show the entire RPN stack as well as the hierarchical menu bar at all times, so it makes sense to take advantage of the larger LCD screen size.

The purpose of the RPN83P project was to help me learn Z80 programming on a TI calculator, and to convert an old TI calculator into a scientific RPN calculator that I can actually use. The host calculator hardware is readily and cheaply available, so I hope other people find it useful.

Installation

Obtaining the Program File

The RPN83P app is packaged as a single file named rpn83p.8xk. There are at least 2 ways to obtain this:

RPN83P release page on GitHub
- go to the latest release
- click and download the rpn83p.8xk file
Compile the binary locally
- See Compiling from Source section below

Uploading

The rpn83p.8xk file must be uploaded to the calculator using a "link" program from a host computer. There are a number of options:

Linux: Use the tilp program. On Ubuntu Linux 22.04 systems, the precompiled package can be installed using $ apt install tilp2. (I'm not actually sure if the tilp2 binary is actually compiled from the tilp_and_gfm source code mentioned above)
Windows or MacOS: Use the TI Connect software and follow the instructions in Transferring FLASH Applications.

Warning: If you are upgrading from a previous version of RPN83P, you may need to manually remove the RPN83P app from the calculator, before uploading the new rpn83p.8xk file. I don't know why, but sometimes the calculator gets stuck at the Defragmenting... step and never finishes uploading the file. To manually remove, go to 2ND MEM, 2 (Mem Mgmt/Del), ALPHA A (Apps), scroll down to the RPN83P, hit DEL, press 2 (Yes).

Starting

After installing rpn83p.8xk file, go to the calculator:

Press the APPS key
Scroll down to the RPN83P entry
Press the ENTER key

The RPN83P starts directly into the calculator mode, no fancy splash screen. You should see a screen that looks like:

Quitting

The RPN83P application can be quit using:

2ND QUIT: to exit to normal TI calculator
2ND OFF: to turn the calculator off (the RPN registers and storage registers will be preserved)

Upon exit, the state of the RPN83P app will be saved in an AppVar named RPN83SAV. When the app is restarted, the calculator will resume from exactly where it left off, including the exact cursor position of any pending input. When restarted, if the RPN83SAV variable does not pass validation (e.g. does not exist; was archived; is wrong size; contains an incompatible schema version; does not pass a CRC checksum) then the application starts from a clean slate.

Supported Hardware

This app was designed for TI calculators using the Z80 processor:

TI-83 Plus (6 MHz Z80, 24 kB accessible RAM, 160 kB accessible flash)
TI-83 Plus Silver Edition (6/15 MHz Z80, 24 kB accessible RAM, 1.5 MB accessible flash)
TI-84 Plus (6/15 MHz Z80, 24 kB accessible RAM, 480 kB accessible flash)
TI-84 Plus Silver Edition (6/15 MHz Z80, 24 kB accessible RAM, 1.5 MB accessible flash)

The app configures itself to run at 15 MHz on supported hardware, while remaining at 6 MHz on the TI-83+.

I have tested it on the following calculators that I own:

TI-83 Plus, OS v1.19
TI-83 Plus Silver Edition, OS v1.19
TI-84 Plus Silver Edition, OS v2.55MP

It should work on the TI-84 Plus, but I have not actually tested it.

The following calculators are not supported because their internal hardware is too different:

TI-84 Plus C Silver Edition
TI-84 Plus CE

Basic Usage

This guide assumes that you already know to use an RPN calculator. In particular, the RPN83P implements the traditional RPN system used by Hewlett-Packard calculators such as the HP-12C, HP-15C, and the HP-42S. (The RPN83P does not use the newer RPN system used by the HP-48 series and other similar HP calculators.)

It is beyond the scope of this document to explain how to use an RPN calculator. One way to learn is to download the Free42 emulator for the HP-42S (available for Android, iOS, Windows, MacOS, and Linux) and then download the HP-42S Owner's Manual.

Screen Areas

Here are the various UI elements on the LCD screen used by the RPN83P app:

The LCD screen is 96 pixels (width) by 64 pixels (height). That is large enough to display 8 rows of numbers and letters. They are divided into the following:

1: status line
2: (currently unused)
3: error code line
4: T register line
5: Z register line
6: Y register line
7: X register/input line
8: menu line

The X register line is also used as the input line when entering new numbers. It is also used to prompt for command line argument, for example FIX _ _ to set the fixed display mode.

Input and Editing

The following buttons are used to enter and edit a number in the input buffer:

0-9: digits
.: decimal point
(-): enters a negative sign, or changes the sign (same as +/- or CHS on HP calculators)
DEL: Backspace (same as <- on many HP calculators)
CLEAR: Clear X register, same as CLX; or clear the input buffer
CLEAR CLEAR CLEAR: Clear the stack, same as CLST
2ND EE: adds an E to allow entry of scientific notation exponent (same as E or EEX on HP calculators)
,: same as 2ND EE, allowing the 2ND to be omitted for convenience

The following keys are related to complex numbers and are explained in more detail in the Complex Numbers section below:

2ND LINK: convert X and Y into a complex number in X, or the reverse
2ND ANGLE: enter a complex number in polar degree form
2ND ANGLE 2ND ANGLE: enter a complex number polar radian form
2ND i: enter a complex number in rectangular form

The (-) button acts like the +/- or CHS button on HP calculators. It toggles the negative sign, adding it if it does not exist, and removing it if it does.

The DEL key acts like the backspace key on HP calculators (usually marked with a LEFTARROW symbol. This is different from the TI-OS where the DEL key removes the character under the cursor. In RPN83P, the cursor is always at the end of the input buffer, so DEL is programmed to delete the right-most digit. If the X line is not in edit mode (i.e. the cursor is not shown), then the DEL key acts like the CLEAR key (see below).

The CLEAR key performs slightly different actions depending on the context:

If the X register is normally displayed, CLEAR goes into edit mode with an empty input buffer.
If the X register is already in edit mode, CLEAR clears input buffer.
If the X register is in edit mode and the input buffer is already empty, then CLEAR shows a message to the user: CLEAR Again to Clear Stack.
If the CLEAR button is pressed immediately again, the RPN stack is cleared. This is the same functionality as the ROOT > CLR > CLST menu button.

In an RPN system, it is generally not necessary to clear the RPN stack before any calculations. However, many users want to see a clean slate on the display to reflect their mental state when starting a new calculation. The CLST menu function provides this feature, but is nested under the ROOT > CLR > CLST menu hierarchy. If you are deeply nested under another part of the menu hierarchy, it can be cumbersome to navigate back up to the ROOT, invoke the CLST button, then make your way back to the original menu location. To solve this problem, the RPN83P app will invoke CLST function when CLEAR is hit 3 times. (The TI-OS does not support 2ND CLEAR, it returns the same code as CLEAR.)

An empty string will be interpreted as a 0 if the ENTER key or a function key is pressed.

The comma , button is not used in the RPN system, so it has been mapped to behave exactly like the 2ND EE button. This allows scientific notation numbers to be entered quickly without having to press the 2ND button repeatedly.

Emulating the input system of the HP-42S was surprisingly complex and subtle, and some features and idiosyncrasies of the HP-42S could not be carried over due to incompatibilities with the underlying TI-OS. But some features were deliberately implemented differently. For example, on the HP-42S, when the input buffer becomes empty after pressing the <- backspace button multiple times, or pressing the CLEAR > CLX menu button, the cursor disappears and the X register is shown as 0.0000. But internally, the HP-42S is in a slightly different state than normal: the Stack Lift is disabled, and entering another number will replace the 0.0000 in the X register instead of lifting it up to the Y register. In RPN83P, when the DEL key or the CLEAR key is pressed, the X register always enters into Edit mode with an empty input buffer, and the cursor will always be shown with an empty string. The presence of the cursor indicates that the Edit Mode is in effect and that the Stack Lift is disabled.

I'm not sure that documenting all the corner cases would be useful in this document because it would probably be tedious to read. I hope that the input system is intuitive and self-consistent enough that you can just play around with it and learn how it works.

RPN Stack

The RPN83P tries to implement the traditional 4-level stack used by many HP calculators as closely as possible, including some features which some people may find idiosyncratic. There are 4 slots in the RPN stack named X, Y, Z, and T. The LCD screen on the TI calculators is big enough that all 4 RPN registers can be shown at all times. (For comparison, the HP-12C and HP-15C have only a single line display. The HP-42S has a 2-line display, with the bottom line often commandeered by the menu line so that only the X register is shown.)

These are the buttons which manipulate the RPN stack:

(: rolls RPN stack down (known as R(downarrow) on HP calculators)
): exchanges X and Y registers
ENTER: saves the input buffer to the X register
2ND ANS: recalls the last X

This mapping of the ( and ) to these stack functions is identical to the mapping used by the HP-30b when it is in RPN mode. (The HP-30b supports both algebraic and RPN entry modes.)

When a new number is entered (using the 0-9 digit keys), the press of the first digit causes the stack to lift, and the calculator enters into the edit mode. This mode is indicated by the appearance of an underscore _ cursor.

A stack lift causes the previous X value to shift into the Y register, the previous Y value into the Z register, and the previous Z value into the T register. The previous T value is lost.

The ENTER key performs the following actions:

if the X register was in edit mode, the input buffer is closed and the number is placed into the X register,
the X register is then duplicated into the Y register,
the stack lift is disabled for the next number.

This is consistent with the traditional RPN system used by HP calculators up to and including the HP-42S. It allows the user to press: 2 ENTER 3 * to multiply 2*3 and get 6 as the result, because the second number 3 does not lift the stack.

The parenthesis ( and ) buttons are not used in an RPN entry system, so they have been repurposed for stack manipulation:

( key rolls the stack down, exactly as the same as the R(downarrow) or just a single (downarrow) on the HP calculators.
) key performs an exchange of the X and Y registers. That functionality is usually marked as X<>Y on HP calculators.

The 2ND ANS functionality of the TI-OS algebraic mode is unnecessary in the RPN system because the X register is always the most recent result that would have been stored in 2ND ANS. Therefore, the 2ND ANS has been repurposed to be the LastX functionality of HP calculators. The LastX is the value of the X register just before the most recent operation. It can be used to bring back a number that was accidentally consumed, or it can be used as part of a longer sequence of calculations.

Menu System

Menu Hierarchy

The menu system of the RPN83P was directly inspired by the HP-42S calculator. There are over 150 functions supported by the RPN83P menu system, so it is convenient to arrange them into a nested folder structure. There are 5 buttons directly under the LCD screen so it makes sense to present the menu items as sets of 5 items corresponding to those buttons.

The menu system forms a singly-rooted tree of menu items and groups, which look like this conceptually:

There are 4 components:

MenuGroup: a folder of 1 or more MenuRows
MenuRow: a list of exactly 5 MenuNodes corresponding to the 5 menu buttons below the LCD
MenuNode: one slot in the MenuRow, can be either a MenuGroup or a MenuItem
MenuItem: a leaf-node that maps directly to a function (e.g. ASNH) when the corresponding menu button is pressed

Menu Buttons

The LCD screen always shows a MenuRow of 5 MenuItems. Here are the buttons which are used to navigate the menu hierarchy:

F1- F5: invokes the function shown by the respective menu
UP_ARROW: goes to previous MenuRow of 5 MenuItems, within the current MenuGroup
DOWN_ARROW: goes to next MenuRow of 5 MenuItems, within the current MenuGroup
ON: goes back to the parent MenuGroup (similar to the ON/EXIT button on the HP-42S)
MATH: goes directly to the root MenuGroup no matter where you are in the menu hierarchy

The appropriate key for the "menu back to parent" function would have been an ESC button. But the TI-83 and TI-84 calculators do not have an ESC button (unlike the TI-92 and TI Voyager 200 series calculators), so the ON button was recruited for this functionality. This seemed to make sense because the HP-42S uses the ON key which doubles as the EXIT or ESC key to perform this function.

The HOME button is useful to go directly to the top of the menu hierarchy from anywhere in the menu hierarchy. The TI-83 and TI-84 calculators do not have a HOME button (unlike the TI-92 and TI Voyager 200 series again), so the MATH button was taken over to act as the HOME key. This choice was not completely random:

The HOME button on the TI-89 series calculator is located exactly where the MATH is.
The RPN83P app does not need the MATH button as implemented by the TI-OS, which opens a dialog box of mathematical functions. In the RPN83P app, that functionality is already provided by the menu system.
When the menu system is at the root, the first menu item on the left is a menu group named MATH, which may help to remember this button mapping.

HP-42S Compatibility Note: As far I can tell, the menu system of the HP-42S is multiply rooted and pressing a given menu button (e.g. BASE) activates the menu hierarchy of that particular button. I think this works because the menu bar on the HP-42S is not displayed by default, so there is no single ROOT node of its menu system. Some of the HP-42S menu bars can stack on top of each other, so that the EXIT button goes back to the previous menu bar. But some menu bars do not. I have never figured out the rhyme and reason for this behavior. The RPN83P app, on the other hand, always displays its menu bar, so it was simpler for the user (and the programmer of this app) to create a singly rooted menu hierarchy with the menu bar always starting from the implicit ROOT menu node.

Menu Indicator Arrows

There are 3 menu arrows at the top-left corner of the LCD screen. The downarrow indicates that additional menu rows are available:

When the DOWN button is pressed, the menu changes to the next set of 5 menu items in the next menu row, and the menu arrows show both an uparrow and a downarrow to indicate that there are more menu items above and below the current menu bar:

Pressing DOWN goes to the last set of 5 menu items, and the menu arrows show only the uparrow to indicate that this is the last of the series:

You can press UP twice goes back to the first menu row, or you can press DOWN from the last menu row to wrap around to the beginning:

Pressing the F2/WINDOW button from here invokes the NUM menu item. This menu item is actually a MenuGroup, so the menu system descends into this folder, and displays the 5 menu items in the first menu row:

Pressing the DOWN arrow button shows the next menu row:

Pressing the DOWN arrow button goes to the final menu row:

Notice that inside the NUM menu group, the menu arrows show a back arrow. This means that the ON button (which implements the "BACK", "EXIT", or "ESC" functionality) can be used to go back to the parent menu group:

Menu Shortcuts

Some menu groups can be accessed quickly through dedicated keys on the TI calculator which happen to have the same label as the menu item:

MODE: bound to ROOT > MODE
STAT: bound to ROOT > STAT
MATH: repurposed to be HOME (aka ROOT)

The MATH button is slightly different. It is not bound to ROOT > MATH. Rather it has been repurposed to be the HOME button which goes to the top of the menu hierarchy ROOT.

Menu Shortcut Jump Back

Normally when the ON/EXIT/ESC button is pressed, the menu bar goes up to the parent of the current MenuGroup. That makes sense because the user normally must travel through the parent to reach the child MenuGroup. But the keyboard shortcuts break this rule.

When the MODE button is pressed, the menu bar goes directly to the ROOT > MODE MenuGroup from anywhere in the menu hierarchy. Since the MODE functions involve quick changes to the floating point display or the trigonometric angle units, it seems likely that the user would want to go back to the original menu bar after making the MODE changes. Therefore, the ON/EXIT/ESC button has been programmed to jump back to the previous menu bar if the ROOT > MODE menu was invoked through the MODE button.

The STAT shortcut, however, does not implement the jump back feature. Instead, the ON/EXIT/ESC acts normally and the menu goes up to the parent of the STAT MenuGroup to the ROOT of the menu system. This behavior was chosen because it seemed more likely that the user would spend a significant amount of time inside the STAT menu functions. The more time spent inside the STAT menu, the less likely it seemed the user would remember where the original menu bar was, and unlikely to want to go back there using the ON/EXIT/ESC key.

Built In Help

Pressing the HELP menu button at the root menu activates the Help pages:

The contents of these pages are updated frequently so the screenshots below may not be identical to the current version:

The Help pages are intended to capture some of the more obscure tidbits about the RPN83P app which may be hard to remember. Hopefully it reduces the number of times that this User Guide needs to be consulted.

The message at the bottom of each page is not completely honest. A number of navigational keys are recognized by the Help system:

UP, LEFT: previous page with wraparound
DOWN, RIGHT: next page with wraparound
DEL, MATH, CLEAR, ON: exit Help
any other button: next page without wraparound, exiting on the last page

Error Codes

The RPN83P supports all error messages from the underlying TI-OS which are listed in the TI-83 SDK. The SDK unfortunately does not describe how these errors are actually triggered. By trial-and-error, I could reverse engineer only a few of them as described below:

Err: Argument: incorrect number of arguments
Err: Bad Guess
Err: Break
Err: Domain: invalid argument or argument outside range
Err: Data Type: invalid argument type (e.g. complex number)
Err: Invalid Dim: list index larger than list size
Err: Dim Mismatch
Err: Divide By 0: divide by 0
Err: Increment
Err: Invalid
Err: Iterations
Err: In Xmit
Err: Memory
Err: Non Real (I could never reproduce this, the TI-OS seems to use Err: Domain or Err: Data Type instead)
Err: Overflow: result exceeds 9.99999999E99
Err: No Sign Change
Err: Singularity
Err: Stat
Err: StatPlot
Err: Syntax: incorrect math expression syntax
Err: Tol Not Met
Err: Undefined

These are shown in the Error Code line on the screen. For example, if we try to divide 1 / 0, a division by 0 error is shown:

If a TI-OS function returns an internal error code outside of the ones documented in the SDK, RPN83P will print an error message in the form of Err: UNKNOWN (##) like this:

The number in parenthesis is the internal numerical value of the error code. If the error is reproducible, please file a bug report containing the numerical error code and the steps needed to reproduce it so that I can add it to the list of error messages supported by RPN83P.

Functions

This section contains a description of all functions implemented by the RPN83P app, accessed through buttons or through the menu system.

Direct Functions

All mathematical functions that are exposed through physical buttons are supported by the RPN83P app.

arithmetic
- /, *, -, +
algebraic
- X^-1, X^2, sqrt, ^ (i.e. Y^X)
trigonometric
- SIN, COS, TAN
- 2ND SIN^-1, 2ND COS^-1, 2ND TAN^-1
transcendental
- LOG, 10^X, LN, e^X
constants
- pi, e

Menu Functions

These functions are accessed through the hierarchical menu, using the 5 menu buttons just under the LCD screen. Use the UP, DOWN, ON (EXIT/ESC), and MATH (HOME) keys to navigate the menu hierarchy.

ROOT (implicit)
ROOT > MATH
- $MATH MenuRow 1$
- $MATH MenuRow 2$
- X^3: cube of X
- 3RootX: cube root of X
- XRootY: X root of Y
- ATN2: atan2(X, Y) in degrees or radians, depending on current mode
  - Y: y-component, entered first
  - X: x-component, entered second
  - (order of Y and X is the same as the >POL conversion function)
- 2^X: 2 to the power of X
- LOG2: log base 2 of X
- LOGB: log base X of Y
- E^X-: e^x-1 accurate for small x
- LN1+: log(1+x) accurate for small x
ROOT > NUM
- %: X percent of Y, leaving Y unchanged
- %CH: percent change from Y to X, leaving Y unchanged
- GCD: greatest common divisor of X and Y
- LCM: lowest common multiple of X and Y
- PRIM: prime factor of X
  - returns 1 if prime
  - returns the smallest prime factor otherwise
  - See Prime Factors section below.
- IP: integer part of X, truncating towards 0, preserving sign
- FP: fractional part of X, preserving sign
- FLR: the floor of X, the largest integer <= X
- CEIL: the ceiling of X, the smallest integer >= X
- NEAR: the nearest integer to X
- ABS: absolute value of X
- SIGN: return -1, 0, 1 depending on whether X is less than, equal, or greater than 0, respectively
- MOD: Y mod X (remainder of Y after dividing by X)
- MIN: minimum of X and Y
- MAX: maximum of X and Y
ROOT > PROB
- COMB: combination C(n,r) = C(Y, X)
- PERM: permutation P(n,r) = P(Y, X)
- N!: factorial of X
- RAND: random number in the range [0,1)
- SEED: set the random number generator seed to X
ROOT > CPLX
- REAL: extract the real component of the complex number
- IMAG: extract the imaginary component of the complex number
- CONJ: calculate the complex conjugate
- CABS: calculate the magnitude of the complex number
- CANG: calculate the angle (i.e. argument) of the complex number
ROOT > HELP: display the Help pages
- use arrow keys to view each Help page
ROOT > BASE
- DEC: use decimal base 10
- HEX: use hexadecimal base 16
  - display register values as 32-bit unsigned integer
- OCT: use octal base 8
  - display register values as 32-bit unsigned integer
- BIN: use binary base 2
  - display register values as 32-bit unsigned integer
- AND: X bit-and Y
- OR: X bit-or Y
- XOR: X bit-xor Y
- NOT: one's complement of X
- NEG: two's complement of X
- SL: shift left logical one bit
- SR: shift right logical one bit
- ASR: arithmetic shift right one bit
- SLn: shift left logical Y by X bits
- SRn: shift right logical Y by X bits
- RL: rotate left circular one bit
- RR: rotate right circular one bit
- RLC: rotate left through carry flag one bit
- RRC: rotate right through carry flag one bit
- RLn: rotate left circular Y by X bits
- RRn: rotate right circular Y by X bits
- RLCn: rotate left through carry flag Y by X bits
- RRCn: rotate right through carry flag Y by X bits
- CB: clear bit X of Y
- SB: set bit X of Y
- B?: get bit X of Y as 0 or 1
- REVB: reverse bits of X
- CNTB: count number of 1 bits of X (same as #B on HP-16C)
- B+: add X and Y using unsigned 32-bit integer math
- B-: subtract X from Y using unsigned 32-bit integer math
- B*: multiply X and Y using unsigned 32-bit integer math
- B/: divide X into Y using unsigned 32-bit integer math
- BDIV: divide X into Y with remainder, placing the quotient in X and the remainder in Y
- CCF: clear carry flag
- SCF: set carry flag
- CF?: return carry flag state as 0 or 1
- WSIZ: set integer word size (supported values: 8, 16, 24, 32)
- WSZ?: return current integer word size (default: 32)
ROOT > HYP
- SINH: hyperbolic sin()
- COSH: hyperbolic cos()
- TANH: hyperbolic tan()
- ASNH: hyperbolic asin()
- ACSH: hyperbolic acos()
- ATNH: hyperbolic atan()
ROOT > STAT
- See Chapter 15 of the HP-42S User's Manual
- Sigma+: add Y and X data point to STAT registers
- Sigma-: remove Y and X data point from STAT registers
- ALLSigma: collect statistical sums for all curve fit models
- LINSigma: collect statistical sums for the linear curve fit model
- CLSigma: clear STAT registers [R11,R16] (if LINSigma selected) or [R11,R23] (if AllSigma selected)
- SUM: return Sum of Y and Sum of X in the Y and X registers
- MEAN: return average <Y> and <X> in the Y and X registers
- WMN: return the weighted mean of Y and weighted mean of X in the Y and X registers
  - weighted mean Y = Sum(XY)/Sum(X)
  - weighted mean X = Sum(XY)/Sum(Y)
- N: return the number of data items entered
- SDEV: sample standard deviation of Y and X
  - sdev(X) = sqrt(N/(N-1)) pdev(X)
  - sdev(Y) = sqrt(N/(N-1)) pdev(Y)
- SCOV: sample covariance
  - scov(X,Y) = (N/(N-1)) pcov(X,Y)
- PDEV: population standard deviation of Y and X
  - pdev(X) = <X^2> - <X>^2
  - pdev(Y) = <Y^2> - <Y>^2
- PCOV: population covariance
  - pcov(X,Y) = <XY> - <X><Y>
- ROOT > STAT > CFIT
  - See Chapter 15 of the HP-42S User's Manual
  - Y>X: forecast X from Y
  - X>Y: forecast Y from X
  - SLOP: slope of curve fit model, i.e. m parameter
  - YINT: y-intercept of curve fit model, i.e. b parameter
  - CORR: correlation coefficient of the least square curve fit
  - LINF: linear fit model, y = mx + b
  - LOGF: logarithmic fit model, y = m ln(x) + b
  - EXPF: exponential fit model, y = b e^(mx)
  - PWRF: power fit model, y = b x^m
  - BEST: automatically select the best model, i.e. the one with the largest absolute value of the correlation coefficient. The CORR value is returned in the X register for reference.
ROOT > CONV
- >DEG: convert radians to degrees
- >RAD: convert degrees to radians
- >REC: polar to rectangular
  - input: Y=y, X=x
  - output: Y=theta, X=r
  - (consistent with HP-42S)
- >POL: rectangular to polar
  - input: Y=theta, X=r
  - output: Y=y, X=x
  - (consistent with HP-42S)
- >HR: convert HH.MMSSssss to HH.hhhh
- >HMS: convert HH.hhhh to HH.MMSSssss
ROOT > TVM (time value of money)
- N: set or calculate Number of payment periods
- I%YR: set or calculate Interest Percent per Year
- PV: set or calculate Present Value
- PMT: set or calculate Payment per period
- FV: set or calculate Future Value
- P/YR: set number of payments per year
- BEG: payment occurs at the Beginning of each period
- END: payment occurs at the End of each period
- CLTV: clear TVM variables and parameters
- IYR1: set I%YR guess 1 for TVM Solver
- IYR2: set I%YR guess 2 for TVM Solver
- TMAX: set iteration max for TVM Solver
- RSTV: reset TVM Solver parameters to factory defaults
ROOT > CLR
- CLX: clear X stack register (stack lift disabled)
- CLST: clear all RPN stack registers
- CLRG: clear all storage registers R00 to R24
- CLSigma: clear STAT storage registers [R11, R16] or [R11, R23]
- CLTV: clear TVM variables and parameters
ROOT > MODE
- FIX: fixed mode with N digits after the decimal point
  - set N to 99 for floating number of digits
  - status line indicator is FIX(N)
- SCI: scientific notation with N digits after the decimal point
  - set N to 99 for floating number of digits
  - status line indicator is SCI(N)
- ENG: engineering notation with N digits after the decimal point
  - set N to 99 for floating number of digits
  - status line indicator is ENG(N)
- RAD: use radians for trigonometric functions
- DEG: use degrees for trigonometric functions
- RRES: real results only from real arguments
- CRES: complex results allowed from real arguments
- RECT: display complex number in rectangular form
- PRAD: display complex number in polar radian form
- PDEG: display complex number in polar degree form
ROOT > STK
- R(up): roll stack up
- R(down): roll stack down, also bound to ( button
- X<>Y: exchange X and Y, also bound to ) button
ROOT > UNIT
- >C: Fahrenheit to Celsius
- >F: Celsius to Fahrenheit
- >hPa: hectopascals (i.e. millibars) to inches of mercury (Hg)
- >iHg: inches of mercury (Hg) to hectopascals (i.e. millibars)
- >km: miles to kilometers
- >mi: kilometers to miles
- >m: feet to meters
- >ft: meters to feet
- >cm: inches to centimeters
- >in: centimeters to inches
- >um: mils (1/1000 of inch) to micrometers
- >mil: micrometers to mils (1/1000 of inch)
- >kg: pounds to kilograms
- >lbs: kilograms to pounds
- >g: ounces to grams
- >oz: grams to ounces
- >L: US gallons to liters
- >gal: liters to US gallons
- >mL: fluid ounces to milliliters
- >foz: milliliters to fluid ounces
- >kJ: kilo calories to kilo Joules
- >cal: kilo Joules to kilo calories
- >kW: horsepowers (mechanical) to kilo Watts
- >hp: kilo Watts to horsepowers (mechanical)

Advanced Usage

Auto-start

For convenience, you may choose to auto-start the RPN83P application as soon as you turn on the calculator.

Download the Start-Up application from TI
Press APPS, then scroll down to Start-up
Configure:
- Display: ON
- Type: APP
- Name: RPN83P (hit ENTER and scroll down to select this)
Select FINISH and hit ENTER

The LCD screen should look like this before hitting FINISH:

Turn off the calculator and turn it back on. It should directly go into the RPN83P application.

Input Limits and Long Numbers

The input buffer is rendered using the Large Font which means that only 14 characters can be displayed on a single line. Entering numbers longer than 14 characters is now (v0.9) supported by scrolling excess characters off the screen to the left. When a leading digit scrolls off, an ellipsis character appears on the left to indicate that some digits are hidden.

For example, if the number "123456.78901234" is entered, the input buffer look normal after 14 characters (see left), then when the 15th character is entered, some digits scroll off to the left (see right):

In normal mode, the input system is configured to accept up to 20 digits because a TI-OS floating point number in scientific notation requires 20 digits to enter in full precision (14 significant digits plus 6 digits of notation overhead).

In BASE mode, the digit limit is a variable that depends on the WSIZ and the base number (DEC, HEX, OCT, BIN). As shown in [Base Input Digit Limit](#base-input-digit-limit), the input system will accept as many as 32 digits for a BIN` binary number.

When the input system detects a complex number in inlined entry mode, through the presence of a 2ND i or 2ND ANGLE delimiter, the maximum number of characters is increased to 41 to allow 2 floating point numbers to be entered with full precision.

Floating Point Display Modes

The RPN83P app provides access to the same floating point display modes as the original TI-OS. For reference, here are the options available in the TI-OS when the MODE button is pressed:

In RPN83P, the MODE button presents a menu bar instead:

HP-42S Compatibility Note: The HP-42S uses the DISP button to access this functionality. For the RPN83P, it seemed to make more sense to the follow the TI-OS convention which places the floating display modes under the MODE button.

The NORMAL mode in TI-OS is named FIX in RPN83P following the lead of the HP-42S. It is also short enough to fit into the menu label nicely, and has the same number of letters as the SCI and ENG modes which helps with the top-line indicator.

Suppose the RPN stack has the following numbers:

Pressing the FIX menu item shows a FIX _ _ prompt for the number of digits after the decimal point, like this:

Type 4 then ENTER. The display changes to this:

(You can also press FIX 04 which will automatically invoke the ENTER to apply the change.)

Notice that the floating point mode indicator at the top of the screen now shows FIX(4).

Try changing to scientific notation mode, by pressing: SCI 04 to get this:

The top-line indicator shows SCI(4).

You can change to engineering notation mode, by pressing: ENG 04, to get this:

The top-line indicator shows ENG(4).

To set the number of digits after the decimal point to be dynamic (i.e. the equivalent of FLOAT option in the TI-OS MODE menu), type in a number greater than 9 when prompted for FIX _ _, SCI _ _, or ENG _ _. I usually use 99, but 11 would also work. For example, to use scientific notation mode with a variable number of fractional digits, press SCI 99 to get this:

Notice that the top-line floating point indicator now shows SCI(-).

Finally, type FIX 99 to go back to the default floating point mode.

HP-42S Compatibility Note: The RPN83P uses the underlying TI-OS floating point display modes, so it cannot emulate the HP-42S exactly. In particular, the ALL display mode of the HP-42S is not directly available, but it is basically equivalent to FIX 99 on the RPN83P.

SHOW Mode

Many HP RPN calculators have a display mode that shows all significant digits that are stored internally. On the HP-42S and HP-16C, the button that activates this is labeled SHOW. On the HP-12C and HP-15C, the button is labeled Prefix.

The RPN83P app implements the SHOW functionality using the 2ND ENTRY key sequence (just above the ENTER button). This key was selected because ENTRY is unused in our RPN system, and because it is located close to the ENTER key. The Show mode reverts back to the normal display mode when any key is pressed (exception OFF and QUIT). Unlike the HP-42S which automatically reverts back to the normal mode after a 2-3 second delay, the TI calculator must wait for a keyboard event from the user.

Normally, the Show mode displays all 14 digits of the internal floating point format of the X register in scientific notation. For example, sqrt(2) is normally displayed with 10 significant digits as 1.414213562, but in Show mode it looks like this:

If the X value is an exact integer internally, then the value is printed in integer form instead of scientific notation. For example 2^46 is an exact integer that will normally appear as 7.036874418E13, but in Show mode looks like this:

The Show mode has a slight variation in BASE mode. For DEC, HEX, and OCT modes, the SHOW function behaves as before, showing the internal floating point number in scientific or integer notation. However, in BIN mode, the SHOW function displays the X value in binary notation, allowing all digits of the binary number to be shown. This behavior is consistent with the SHOW function on the HP-42S. For example, the hex number 01D62BB7 in normal BIN mode looks like ...011 1011 0111 because only 12 digits can be displayed on a single line. But in Show mode, all 32 digits (assuming WSIZ was 32) will be displayed like this:

Trigonometric Modes

Just like the TI-OS, the RPN83P uses the radian mode by default when calculating trigonometric functions. The top status line shows RAD:

If we calculate sin(pi/6) in radian mode, by typing PI 6 / SIN, we get 0.5 as expected.

Press the DEG menu button to change to degree mode. The top status line shows DEG:

We can calculate sin(30deg) by typing: 30 SIN to get 0.5.

Warning: The polar to rectangular conversion functions (>REC and >POL) are also affected by the current Trig Mode setting.

HP-42S Compatibility Note: The RPN83P does not offer the gradian mode GRAD because the underlying TI-OS does not support the gradian mode directly. It is probably possible to add this feature by intercepting the trig functions and performing some pre and post unit conversions. But I'm not sure if it's worth the effort since gradian trig mode is not commonly used.

Storage Registers

Similar to the HP-42S, the RPN83P provides 25 storage registers labeled R00 to R24. They are accessed using the STO and 2ND RCL keys. To store a number into register R00, press:

STO 00

To recall register R00, press:

2ND RCL 00

To clear the all storage registers, use the arrow keys for the menu system to get to:

Press CLR to get
Press CLRG

The message REGS cleared will be displayed on the screen.

Similar to the HP-42S and the HP-15C, storage register arithmetic operations are supported using the STO and RCL buttons followed by an arithmetic button.

For example:

STO + 00: add X to R00
STO - 00: subtract X from R00
STO * 00: multiply X to R00
STO / 00: divide X into R00

Similarly:

RCL + 00: add R00 to X
RCL - 00: subtract R00 from X
RCL * 00: multiply R00 to X
RCL / 00: divide R00 into X

Indirect storage registers, the STO IND nn and RCL IND nn functionality from the HP-42S, are not supported (as of v0.9.0).

Prime Factors

The PRIM function calculates the lowest prime factor of the number in X. The result will be 1 if the number is a prime. Unlike almost all other functions implemented by RPN83P, the PRIM function does not replace the original X. Instead it pushes the prime factor onto the stack, causing the original X to move to the Y register. This behavior was implemented to allow easier calculation of all prime factors of a number as follows.

After the first prime factor is calculated, the / can be pressed to calculate the remaining factor in the X register. We can now press PRIM again to calculate the next prime factor. Since the PRIM preserves the original number in the Y register, this process can be repeated multiple times to calculate all prime factors of the original number.

For example, let's find the prime factors of 119886 = 2 * 3 * 13 * 29 * 53:

Press 119886
Press PRIM to get 2
Press / to divide down to 59943
Press PRIM to get 3
Press / to divide down to 19981
Press PRIM to get 13
Press / to divide down to 1537
Press PRIM to get 29
Press / to divide down to 53
Press PRIM to get 1, which makes 53 the last prime factor.

For computational efficiency, PRIM supports only integers between 2 and 2^32-1 (4 294 967 295). This allows PRIM to use integer arithmetic, making it about 7X faster than the equivalent algorithm using floating point routines. Any number outside of this range produces an Err: Domain message. (The number 1 is not considered a prime number.)

If the input number is a very large prime, the calculation may take a long time. However, testing has verified that the PRIM algorithm will always finish in less than about 33 seconds on a TI-83+ (running at 6 MHz) or 13 seconds on a TI-83+SE, TI-84+, or TI-84+SE (running at 15 MHz), no matter how large the input number. During the calculation, the "run indicator" on the upper-right corner will be active. You can press ON key to break from the PRIM loop with an Err: Break message.

BASE Functions

The BASE functions are available through the ROOT > BASE hierarchy:

These functions allow conversion of integers into different bases (10, 16, 8, 2), as well as performing bitwise functions on those integers (bit-and, bit-or, bit-xor, etc). They are useful for computer science and programming. Many of the BASE mode functions were inspired by the HP-16C, which has more extensive functions in this area compared to the HP-42S.

All menu functions under the BASE menu operate on unsigned integer values instead of floating point values. The following word sizes have been implemented: 8, 16, 24, and 32 bits. Any floating point values on the RPN stack (e.g. X or Y registers) are converted into an unsigned integer before being passed into a logical, bitwise, or arithmetic function. This includes the DEC (base 10) mode.

The maximum value that can be represented when in BASE mode is 2^WSIZ-1, which is (255, 16383, 16777215, 4294967295) for (8, 16, 24, 32) bit integers respectively.

Base Modes

When the BASE menu is selected, one of the base number menu items will be activated: DEC, HEX, OCT, BIN. Normally the default is DEC, but the BASE menu remembers the last base number that was used.

The numbers on the RPN stack are not modified internally when the BASE menu is selected, but they are displayed on the screen differently to emphasize that they are intended to be treated as unsigned integers.

Let's start with the RPN stack containing the following numbers: -1, 17.1, 9E9, and 1234567, like this:

DEC (decimal)

The DEC (decimal) mode is the default when the BASE menu is selected. All numbers on the RPN stack are displayed as an integer, as if they were converted to an unsigned integer, but the RPN stack values are not modified. For the values given above, the display now looks like this:

If the value on the RPN stack is negative, a single - sign is shown. If the value is greater than or equal to 2^WSIZ, then 3 dots ... are shown to indicate that the number is too large. If the floating point value is within the range of [0, 2^WSIZ) but has non-zero fractional value, a decimal point is shown after the integer part of the unsigned integer.

HEX (hexadecimal)

The HEX (hexadecimal) mode displays all numbers on the RPN stack using base 16. Only the integer part is rendered as if the RPN stack values were converted to an unsigned integer.

If the value on the RPN stack is negative, a single - sign is shown. If the value is greater than or equal to 2^WSIZ, then 3 dots ... are shown to indicate that the number is too large. If the floating point value is within the range of [0, 2^WSIZ) but has non-zero fractional value, a decimal point is shown after the integer part of the unsigned integer.

On the keyboard, the hexadecimal digits A through F are entered using ALPHA A, through ALPHA F. You can lock the ALPHA mode using 2ND A-LOCK, but that causes the decimal buttons 0 to 9 to send letters instead which prevents those digits to be entered, so it is not clear that the Alpha Lock mode is actually useful in this context.

OCT (octal)

The OCT (octal) mode displays all numbers on the RPN stack using base 8. Only the integer part is rendered as if the RPN stack values were converted to an unsigned integer.

If the value on the RPN stack is negative, a single - sign is shown. If the value is greater than or equal to 2^WSIZ, then 3 dots ... are shown to indicate that the number is too large. If the floating point value is within the range of [0, 2^WSIZ) but has non-zero fractional value, a decimal point is shown after the integer part of the unsigned integer.

On the keyboard, the button digits 0 through 7 are entered normally. The button digits 8 and 9 are disabled in octal mode.

BIN (binary)

The BIN (binary) mode displays all numbers on the RPN stack using base 2. Only the integer part is rendered as if the RPN stack values were converted to an unsigned integer.

If the value on the RPN stack is negative, a single - sign is shown. If the value is greater than or equal to 2^WSIZ, then 3 dots ... are shown to indicate that the number is too large. If the floating point value is within the range of [0, 2^WSIZ) but has non-zero fractional value, a decimal point is shown after the integer part of the unsigned integer.

Binary numbers are displayed in groups of 4 digits to help readability. That means that maximum number of digits that can be displayed is 12 digits. If WSIZ is 16, 24 or 32, then a number may have non-zero digits which are cutoff after the 12 digits. When that happens, a small ellipsis character will be shown on the left most digit to indicate truncation, as shown above.

The SHOW function (bound to 2ND ENTRY on the TI calculators) can be used to reveal all digits of the binary number, in groups of 4, using as many 4 lines of text like this:

We can now see that the number 1234567 in Base 2 is 0000 0000 0001 0010 1101 0110 1000 0111.

On the keyboard, only the button digits 0 and 1 are active in the binary mode. The rest are disabled.

Shift and Rotate

The RPN83P supports most of the common shift and rotate operations implemented by modern microprocessors, including the Z80 processor used in the TI-83 Plus and TI-84 Plus calculators. Unfortunately, there seems to be no standard mnemonics for these shift and rotate operations, and different processors and calculators use conflicting names. The RPN83P follows the conventions of the HP-16C for consistency, even though the conventions are sometimes contrary to the conventions of the Z80 processor:

SL - shift left logical
- named SLA on the Z80 (see Note below regarding SLL instruction)
- named SL on the HP-16C
SR - shift right logical
- named SRL on the Z80
- named SR on the HP-16C
ASR - arithmetic shift right
- named SRA on the Z80
- named ASR on the HP-16C
SLn - shift left logical of Y for X times
- no equivalent on Z80 or HP-16C
SRn - shift right logical of Y for X times
- no equivalent on Z80 or HP-16C
RL - rotate left circular
- named RLC on the Z80
- named RL on the HP-16C
RR - rotate right circular
- named RRC on the Z80
- named RR on the HP-16C
RLC - rotate left through carry flag
- named RL on the Z80
- named RLC on the HP-16C
RRC - rotate right through carry flag
- named RR on the Z80
- named RRC on the HP-16C
RLn - rotate left circular of Y for X times
- no equivalent on Z80
- named RLn on the HP-16C
RRn - rotate right circular of Y for X times
- no equivalent on Z80
- named RRn on the HP-16C
RLCn - rotate left through carry flag of Y for X times
- no equivalent on Z80
- named RLCn on the HP-16C
RRCn - rotate right through carry flag of Y for X times
- no equivalent on Z80
- named RRCn on the HP-16C

For all XXn operations, if the n value (i.e. X register) is 0, the operation does not change the value of Y, but the RPN stack collapses by one position so the X value disappears. If the n value is >= to the BASE word size (WSZ?), normally 32, an error message will be displayed.

Note: The Z80 apparently has an undocumented instruction named shift left logical which is shortened to SLL or SL1. It places a 1 into bit 0 of the register, instead of a 0. It is unfortunate that term "logical" is used in the exact opposite to the meaning that I would have expected.

Base Arithmetic

Similar to the HP-42S, activating the BASE hierarchy of menus changes the behavior of keyboard arithmetic functions. Specifically, the buttons +, -, *, / are re-bound to their integer counterparts B+, B-, B*, B/ which perform 32-bit unsigned arithmetic operations instead of floating point operations. The numbers in the X and Y registers are converted into 32-bit unsigned integers before the integer subroutines are called.

The BDIV menu function performs the same integer division operation as B/ but returns both the quotient (in X) and the remainder (in Y). With the quotient in X, it becomes easy to recover the original X value by using the LastX function (2ND ANS), then pressing the * button, then the + button to add back the remainder.

HP-42S Compatibility Note: The HP-42S calls these integer functions BASE+, BASE-, BASE*, and BASE/. The RPN83P can only display 4-characters in the menu bar so I had to use shorter names. The HP-42S function called B+/- is called NEG on the RPN83P. Early versions of the RPN83P retained the keyboard arithmetic buttons bound to their floating point operations, but it became too confusing to see hex, octal, or binary digits on the display, but get floating point results when performing an arithmetic operation such as /. The RPN83P follows the lead of the HP-42S so that the arithmetic keyboard buttons trigger the integer operations instead of floating point operations.

For example, suppose the following numbers are in the RPN stack before entering the BASE menu:

Entering the BASE menu shows this (assuming that the default base number was DEC):

Changing to HEX mode shows this:

Pressing the + button adds the X and Y registers, converting the values to 32-bit unsigned integers before the addition:

Changing back to DEC mode shows that the numbers were added using integer functions, and the fractional digits were truncated:

Carry Flag

The RPN83P supports the Carry Flag implemented by most (all?) microprocessors. The Carry Flag is supported by the HP-16C but not by the HP-42S. When the flag is off, a dash - is shown (left). When the Carry Flag is set, a small C letter appears (right):

The Carry Flag can be explicitly cleared, set, and retrieved using the following menu items:

CCF: clear carry flag
SCF: set carry flag
CF?: get carry flag

Many operations affect the Carry Flag (CF). All shift and rotate operations affect the CF:

SL: bit 31 shifted into CF
SR: bit 0 shifted into CF
ASR: bit 0 shifted into CF
SLn: bit 31 shifted into CF after shifting n positions
SRn: bit 0 shifted into CF after shifting n positions
RL: bit 31 shifted into CF
RR: bit 0 shifted into CF
RLC: CF into bit 0; bit 31 into CF
RRC: CF into bit 31; bit 0 into CF
RLn: bit 31 shifted into CF after rotating n positions
RRn: bit 0 shifted into CF after rotating n positions
RLCn: CF into bit 0; bit 31 into CF after rotating n positions
RRCn: CF into bit 31; bit 0 into CF after rotating n positions

All integer arithmetic functions affect the CF:

B+: CF set on overflow
B-: CF set on borrow
B*: CF set on overflow
B/: CF always set to 0
BDIV: CF always set to 0

On most microprocessors, the bitwise operations clear the Carry Flag to zero. However the RPN83P follows the lead of the HP-16C calculator where these operations do not affect the Carry Flag at all:

AND, OR, XOR, NEG, NOT, REVB, CNTB

Bit Operations

Specific bits can be cleared or set using the CB and SB menu items.

CB: clear the X bit of Y
SB: set the X bit of Y
B?: get the X bit of Y as 1 or 0

The range of X must be between 0 and 31, or an error code will be generated.

This menu row contains a couple of additional bit manipulation functions:

REVB: reverse the bit patterns of X
CNTB: count the number of 1 bits in X

None of these bit operations affect the Carry Flag.

Base Word Size

The HP-42S uses a 36-bit signed integer for BASE rendering and operations. To be honest, I have never been able to fully understand and become comfortable with the HP-42S implementation of the BASE operations. First, 36 bits is a strange number, it is not a multiple of 8 as used by most modern microprocessors (8, 16, 32, 64 bits). Second, the HP-42S does not display leading zeros in HEX OCT, or BIN modes. While this is consistent with the decimal mode, it is confusing to see the number of displayed digits change depending on its value.

The RPN83P deviates from the HP-42S by using unsigned integers internally, and rendering the various HEX, OCT, and BIN numbers using the same number of digits regardless of the value. The word size of the integer can be changed using the WSIZ menu item (see below). The following word sizes are supported: 8, 16, 24, and 32 bits. This means that HEX mode with a word size of 32 always displays 8 digits, OCT mode always displays 11 digits, and BIN mode always displays 12 digits (due to size limitation of the LCD screen). I find this less confusing when doing bitwise operations (e.g. bit-and, bit-or, bit-xor).

Since the internal integer representation is unsigned, the (-) (change sign) button is disabled. Instead, the menu system provides a NEG function which performs a two's complement operation which turns a 00000001 hex number into FFFFFFFF. The NEG function is closely related to the NOT function which performs a one's complement operation where the 00000001 becomes FFFFFFFE.

If we want to see the decimal value of a hex number that has its sign-bit (the most significant bit) turned on (so it would be interpreted as a negative number if it were interpreted as a signed integer), we can run the NEG function on it, then hit the DEC menu item to convert it to decimal. The displayed value will be the decimal value of the original hex number, without the negative sign.

The word size, defaulting to 32 bits, can be changed using the WSIZ menu function. Pressing it displays WSIZ _ _ and waits for the argument, just like the FIX and STO commands. To simplify the implementation code, only the following word sizes are supported: 8, 16, 24, and 32, corresponding to 1, 2, 3, and 4 bytes respectively:

If an unsupported word size is entered, for example 9, then the error code Err:Argument will be displayed:

Note: The RPN83P app represents all numbers internally using the TI-OS floating point number format which supports 14 decimal digits. This corresponds to 46.5 bits. Therefore, the largest word size that could be supported in the current architecture is 40. Supporting a 64-bit word size would require a major rearchitecture of the application.

Every BASE operation respects the current WSIZ value, truncating the X or Y integers to the word size, before performing the BASE operation, then truncating the result to the word size. For example, if the word size is 16, then the RR (rotate right circular) operation rotates bit 0 to bit 15, instead of bit 31 if the word size was 32.

The current WSIZ value can be retrieved using the WSZ? menu function.

HP-42S Compatibility Note: The original HP-42S does not support the WSIZ command. Its word size is fixed at 36 bits. The Free42 app however does support it as the WSIZE command which I suspect was borrowed from WSIZE command on the HP-16C. Keen observers will note a UI discrepancy: On the HP-16C and HP-42S, the WSIZE command uses the value of X register to set the word size, but the RPN83P prompts the user to enter the size using a WSIZ _ _ prompt similar to the FIX and STO commands. This decision was made to solve a major usability problem on the RPN83P: The X register value in the BASE menu hierarchy is shown using the currently selected base mode (e.g. DEC, HEX, etc). If the mode was something other than DEC, for example HEX, then the user needs to type 10 WSIZ to set the WSIZ to 16 bits, because 10 is the base-16 representation of 16. Even worse, if the base mode was BIN, then the user must type in 100000 WSIZ to set the word size to 32 because 100000 is the base-2 representation of 32. I find this far too confusing. Instead, the RPN83P uses the command argument prompt WSIZ _ _ to obtain the word size from the user in normal base-10 format. The prompt is not affected by the current base mode so the user can type 8, 16, 24, or 32 to select the new word size without confusion. The WSZ? command returns the current word size in the X register and will be displayed using the current base mode. I could not think of any way around this, but I assume that this will not cause as much usability problems as the WSIZ command.

Base Input Digit Limit

The maximum number of digits allowed to be entered into the input buffer is determined by a function which depends on both the WSIZ and the current base number (HEX 16, DEC 10, OCT 8, BIN 2). Adding a limit during input hopefully reduces the likelihood that the user will enter a number that is greater than the maximum number of bits allowed in by the current WSIZ and base number.

Here are the limits:

+------+------+-------------+------------+
| Base | WSIZ |  Max Number | Max Digits |
|------+------+-------------+------------|
|  DEC |    8 |         255 |          3 |
|  DEC |   16 |       65535 |          5 |
|  DEC |   24 |    16777215 |          8 |
|  DEC |   32 |  4294967295 |         10 |
|------+------+-------------+------------|
|  HEX |    8 |          FF |          2 |
|  HEX |   16 |        FFFF |          4 |
|  HEX |   24 |      FFFFFF |          6 |
|  HEX |   32 |    FFFFFFFF |          8 |
|------+------+-------------+------------|
|  OCT |    8 |         377 |          3 |
|  OCT |   16 |      177777 |          5 |
|  OCT |   24 |    77777777 |          8 |
|  OCT |   32 | 37777777777 |         10 |
|------+------+-------------+------------|
|  BIN |    8 |         255 |          8 |
|  BIN |   16 |       65535 |         16 |
|  BIN |   24 |    16777215 |         24 |
|  BIN |   32 |  4294967295 |         32 |
+------+------+------------ +------------+

Limiting the number of digits during input does not completely prevent the user from entering a number which is immediately out-of-bounds of the WSIZ limit. That's because in certain bases like OCT, the maximum number of allowed bits falls inside a single digit. In other bases, like DEC, the number of binary bits does not correspond exactly to the representation in decimal. (A future enhancement may be to parse the input buffer upon ENTER and refuse to accept the number if it is greater than the maximum allowed by the WSIZ.)

The longest binary number that can be displayed on a single line in edit mode is 14 digits. If the WSIZ is greater than 14 (i.e. greater than 8), then a binary number in BIN can exceed this limit and entering more digits will cause the left digits to scroll off the screen.

Base Number Retention

The DEC, HEX, OCT and BIN modes are useful only within the BASE hierarchy of menus. When the menu leaves the BASE hierarchy, the numbers on the RPN stack revert back to using floating points. This is similar to the HP-42S. However, unlike the HP-42S, the RPN83P remembers the most recent base number and restores its setting if the BASE menu hierarchy is selected again.

STAT Functions

The RPN83P implements all statistical and curve fitting functionality of the HP-42S, as described in Ch. 15 of the HP-42S User's Manual. Additional reference material can be found at:

https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
https://en.wikipedia.org/wiki/Simple_linear_regression
https://en.wikipedia.org/wiki/Covariance_and_correlation

Most of the menu names are the same as the HP-42S. Here are some of the differences:

The organization of the menu items is different because the TI calculator has only 5 menu buttons instead of 6 on the HP-42S. I also did not like the complexity of the HP-42S menus for the STAT functions; it is nested unnecessarily deeply. I have simplified the menu hierarchy for the RPN83P to just 2-levels instead of 3.
The HP-42S WMN (weighted mean) returns only the weighted mean of X. If you wanted the weighted mean of Y instead, you are forced to re-enter the data points by swapping the X and Y values, or manually calculate it from the raw summation registers. The RPN83P calculates both weighted means so that you can choose the appropriate value.
The RPN83P contains an N menu item that simply returns the number of data points entered for convenience. This value can be retrieved using 2ND RCL 16, but it is unreasonable to expect users to remember this storage register number.
The HP-42S calculates only the sample standard deviation SDEV. The RPN83P supports both the sample standard deviation SDEV or the population standard deviation PDEV. The ratio of SDEV/PDEV is sqrt(N/(N-1)) but it is convenient to have both types available in the menu.
The RPN83P supports the calculation of the covariance in 2 forms, the sample covariance SCOV and population covariance PCOV. They are needed internally for least square curve fitting, so it seemed appropriate to expose them to the user through the menu buttons. The ratio of SCOV(X,Y)/PCOV(X,Y) is N/(N-1).

The curve fit models under the CFIT menu group are identical to the HP-42S. The linear curve fit LINF is available with either LINSigma or ALLSigma selected. The other models (LOGF, EXPF, PWRF) are available only when the ALLSigma option is selected, because they require additional summation registers to be active and updated.

On the HP-42S, the clear menu item CLSigma is available only under the CLEAR menu hierarchy. On the RPN83P, the CLSigma menu appears in 2 places for convenience, under the CLR hierarchy and under the STAT hierarchy. The number of storage registers that are cleared depends on whether LINSigma or ALLSigma are selected, just like the HP-42S.

There are a few STAT features which are not implemented on the RPN83P:

The storage registers allocated to the STAT functions are hardcoded to be R11-R23. On the HP-42S, the register allocation can be changed.
RPN83P does not (yet) support vectors and matrices, so it is not possible to enter the data into a matrix first, then perform the STAT functions over the matrix.

Example

Let's enter the data points given in the HP-42S manual, the "maximum and minimum monthly winter rainfall values in Corvallis, Oregon".

Month   Y(max)  X(min)
-----   ----    ----
Oct      9.70   0.10
Nov     18.28   0.22
Dec     14.47   2.33
Jan     15.51   1.99
Feb     15.23   0.12
Mar     11.70   0.43

We would enter these data points like this:

Press STAT to see
Press ALLSigma (select all curve fit models)
Press CLSigma to clear the summation registers. You should see a status message STAT cleared.
Enter the data points in pairs, with the Y value first, then X:
- 9.70 ENTER 0.10 Sigma+. You should see a 1.
- 18.28 ENTER 0.22 Sigma+. You should see a 2.
- 14.47 ENTER 2.33 Sigma+. You should see a 3.
- 15.51 ENTER 1.99 Sigma+. You should see a 4.
- 15.23 ENTER 0.12 Sigma+. You should see a 5.
- 11.70 ENTER 0.43 Sigma+. You should see a 6.

(Note that the "stack lift" is disabled by the Sigma+ and Sigma- buttons, similar to the ENTER key. So the N values will be replaced by the next Ymax value.)

Let's calculate the basic statistics measures:

Press DOWN arrow key to see
Press SUM to get Y:84.89 and X:5.19
Press MEAN to get Y:14.14833333 and X:.865
Press WMN to get Y:14.72643545 and X:.9003439746
Press N to get X:6
Press DOWN arrow key to see
Press SDEV to get Y:3.032500069 and X:1.015613115
Press SCOV to get X:.60007
Press PDEV to get Y:2.768281155 and X:.9271236883
Press PCOV to get X:.5000583333

Let's perform some curve fits. It is not obvious that the maximum rainfall for a given month is correlated with the minimum rainfall for the same month. We can use the CFIT routines to figure this out:

Press CFIT to see
Press the DOWN arrow to see
Verify that the LINF (linear fit) is selected
Press the UP arrow to get back to the main CFIT row.
Press SLOP to get X:.5817619514. This is the slope variable m.
Press YINT to get X:13.64510925. This is the y-intercept variable b.
Press CORR to get X:.1948376107. This is the correlation coefficient r. A value of 0.19 means that the correlation between min and max rainfall is fairly weak. A high correlation would be close to 1.0.

Let's see if a different curve fit model does better.

Press DOWN arrow to get to
Press BEST button to request the app to automatically determine the best curve model. You should see X:.2963586116 and the menu should have changed to select PWRF, like this:

HP-42S Compatibility Note: Unlike the HP-42S, BEST menu on the RPN83P returns the CORR value of the best curve fit model. It seemed like a useful bit of information to see, and it provides visual feedback that the BEST function has finished, since the RPN83P seems significantly slower than the HP-42S, at least on the emulators.

The RPN83P app has determined that the best curve fit model for the data is the power curve y = b x^m, with a correlation coefficient r = .2963586116. It is still a weak correlation, but better than the linear model.

You can perform forecasting with the Y>X and X>Y menus:

Enter 1.5 (min rainfall) then press X>Y. It predicts a maximum rainfall of 14.75.
Enter 12 (max rainfall) then press Y>X. It predicts a minimum rainfall of 0.02188.

These predictions should be regarded with suspicion because the correlation coefficient of r=.29635 is quite low, and the power fit may not be a good model for this data. For example, typing 20 Y>X (max rainfall of 20.0) gives an X=752.098 (a minimum rainfall of 752) which is not reasonable.

TVM Functions

The Time Value of Money (TVM) functionality is inspired by RPN financial calculators such as the HP-12C, HP-17B, and the HP-30b. They are available through the ROOT > TVM menu:

This User Guide assumes that you are already know the theory of the Time Value of Money, and that you are familiar with TVM functions of RPN financial calculators. Some introductory information can be found in the manuals of these calculators:

HP-12C User's Guide: Section 3: Basic Financial Functions
HP-30b User's Guide: Chapter 3: Time Value of Money

TVM Menu Buttons

There are 5 menu items that correspond to the 5 variables in the TVM equation:

N: number of payment periods
I%YR: interest percent per year
PV: present value
PMT: payment per period
FV: future value

When 4 variables are known, the 5th variable can be calculated from the other 4. Just like the HP-12C and HP-30b, each menu button performs a dual function: it can either store a value to the corresponding TVM variable, or it can calculate the TVM variable from the other 4 variables. The rules that determine the course of action are:

If a value has been entered into the X register, then the next press of a TVM menu button stores the X value to the corresponding variable.
If the most recent action was another TVM menu button, then the next press of a TVM menu button calculates that variable from the other 4, and returns the result in the X register.

Since each button has a dual-function, it can sometimes be confusing to remember which action a given TVM menu button has performed. This is definitely true on the HP-12C and the HP-30b which provide no feedback regarding the two different actions. The RPN83P solves this problem by displaying different status messages after a TVM menu button has completed. The message will read:

TVM Stored if the menu button stored the X value into the TVM variable,
TVM Calculated if the menu button calculated the given TVM variable from the other 4 variables.

TVM Payments Per Year

On the HP-12C, the interest rate button is labeled with an i and represents the interest percentage for each payment period. On the HP-30b and most modern financial calculators, the i button has been replaced with I%YR (or I/YR) which accepts the interest rate as a nominal annual percentage rate. The RPN83P app follows the modern convention and the interest rate menu button is named I%YR.

The relationship between the i button (as implemented on the HP-12C) and the I%YR button as implemented on the RPN83P is:

i = IYR / PYR

where PYR is the number of payments per year. In math equations and inside computer programs, the quantity i is usually represented as a fractional rate instead of a percentage, so there is an addition division by 100.

The RPN83P app allows the PYR quantity to be modified using the P/YR menu button. PYR is an input-only parameter, not an output parameter, so the P/YR is not a dual-action button. It performs only a store function. By default, the P/YR value is set to 12, which makes it easy to calculate monthly mortgage payments whose rates are given as yearly percentages.

TVM BEG and END

The BEG and END menu buttons act in the same way as the equivalent buttons on the HP-12C and HP-30b. The BEG button specifies that the payments are made at the beginning of the payment term. The END button specifies that the payments are made at the end of the payment term. A little dot on the menu button indicates the currently selected option. Both of these are input-only buttons. The default value is END.

TVM Solver Control

It is well-known that the N, PV, PMT, and FV variables can be solved using analytical equations. However, there is no closed-form solution for the I%YR quantity, so it must be solved using iterative methods. The TVM Solver is the submodule that implements the iterative method to solve for I%YR.

It can be mathematically deduced that the root-solving equation for I%YR can fall into 3 categories:

0 solution, or
1 unique solution, or
0 or 2 solutions.

The TVM Solver tries to handle the various cases as follows:

If the TVM Solver can determine immediately that the equation has 0 solution, it will return a TVM No Solution error message.
The TVM Solver can fail to find a solution, even though the math says that a solution must exist. The TVM Solver will return a TVM Not Found error message.
If the equation has 2 solutions, but the TVM Solver finds only one of the 2 solutions, the solver currently (v0.9.0) does not notify the user that another solution may exist. A normal TVM Calculated will be returned.
If there are 2 solutions, but the solver finds neither solution, a TVM Not Found message will be returned.
To prevent excessive execution time, the number of iterations performed by the TVM Solver has a maximum limit. The default is 15 iterations. If exceeded, the message TVM Iterations is displayed.

Due to the complexity of the numerical algorithm and the number of iterations required, calculating the I%YR will take noticeably longer than the other variables. Somewhere between 1-3 seconds on the TI-84 Plus model has been observed.

The RPN83P currently (v0.9.0) uses the Newton-Secant method to solve for I%YR. For the purpose of debugging and to allow extra control for advanced users, three parameters that affect the progression and termination of the algorithm are exposed:

IYR1: first guess percent per year (default: 0%; allowed: IYR1 > -PYR*100)
IYR2: second guess percent per year (default: 100%; allowed: IYR2 > -PYR*100)
TMAX: iteration maximum (default: 15; allowed: 0-255)

For most TVM problems representing real-life situations, the default values should be sufficient to find a solution. You can override the defaults of these values by entering a value and pressing the appropriate menu button. A small dot will be appended to the menu name to indicate that the default value has been overridden:

We might choose to override IYR1 and IYR2 when 2 solutions are known to exist, but the TVM Solver is unable to find either of them due to the default initial values. If we know the approximate value of one of the solutions, we can override the initial guesses to be closer to the solution of interest. This will help the TVM Solver converge to that solution.

(TODO: Maybe add a menu item to control the convergence error tolerance? Currently, it is set to 1e-8. Some HP calculators use the number of digits in the FIX, SCI or ENG display modes to determine the value of the error tolerance. TI calculators are usually kept in "floating" (aka "display all digits") mode FIX(-), so I'm not sure it would be useful to use the display mode to extract size of the tolerance.)

These control parameter can be restored to their default factory values by pressing the RSTV menu. The "overridden" dot on the menu buttons should disappear.

TVM Clear

There are 2 reset or clear menu buttons under the TVM menu hierarchy:

RSTV: Reset the TVM Solver control parameters to factory defaults
CLTV: Clear all TVM variables and parameters, including RSTV parameters

The RSTV clears only the 3 parameters related to the TVM Solver which calculates the interest rate. The factory default values are:

IYR1: 0%
IYR2: 100%
TMAX: 15

The CLTV clears everything in the TVM submenu, including the RSTV parameters. The following additional variables are cleared or reset to their factory values:

N, I%YR, PV, PMT, FV: 0
P/YR: 12
BEG, END: END

TVM Variable Recall

Remember that most of TVM menu buttons are dual-action:

number + button: sets the TVM variable to X value, and
button: calculates the TVM variable from the other 4 variables.

Other TVM menu buttons (i.e. P/YR, IYR1, IYR2, TMAX) are single-action buttons and support only the storing of their values. There is no ability to calculate those parameters from other parameters. This convention used by most (all?) HP financial calculators.

The RPN83P app provides a mechanism to retrieve a TVM variable without performing a calculation. This was useful for debugging during development, but the functionality was innocuous enough that I retained it for general use. The recall functionality is available through the 2ND key:

2ND N: recall the N variable
2ND I%YR: recall the I%YR variable
2ND PV: recall the PV variable
2ND PMT: recall the PMT variable
2ND FV: recall the FV variable
2ND P/YR: recall the P/YR variable
2ND IYR1: recall the IYR1 variable
2ND IYR2: recall the IYR2 variable
2ND TMAX: recall the TMAX variable

As a rule of thumb, the RPN83P does not use the 2ND button for its menu buttons. Usually if a menu button sets an internal variable, the equivalent read functionality is implemented by another menu button with a name similar to the original menu with the addition of a question mark (e.g. WSIZ and WSZ?). This helps with discovery because each function is directly shown through the menu system, with no hidden features. But there are so many TVM variables and parameters, that adding the ? variant of all those menu buttons would have made the menu rows too cluttered and hard to navigate. Currently (v0.9.0), the TVM submenu is the only place where the 2ND button is used for hidden menu functionality.

TVM Examples

Example 1: Calculate the monthly payment on a 30-year, $500,000 mortgage at 7.5%

Press CLTV
Press 360 N (30 years * 12 payments/year)
Press 7.5 I%YR
Press 500000 PV
Press 0 FV
Press PMT
Answer: -$3496.072543 (should see TVM Calculated)

The sign convention of the TVM equation is such that +'ve represents inflow of cash, and -'ve represents outflow of cash.

Example 2: Assuming Example 1, calculate the amount that can be borrowed if the payment is $3000/month instead of $3496/month

(Building on Example 1)
Press -3000 PMT (should see TVM Stored)
Press PV (should see TVM Caculated)
Answer: $429052.882

Example 3: Assuming Examples 1 and 2, calculate the interest rate required to get a $500,000 mortgage with a $3000/month payment

(Building on Examples 1 and 2)
Press 500000 PV (should see TVM Stored message). This resets the current PV which became modified by the calculation in Example 2.
Press I%YR (should see TVM Calculated)
Answer: 6.00699%

Example 4: If Susan got paid $0.01 per second, compounded every second, at a 10% per annum rate, what is her bank balance after 365 days?

Press CLTV
Press 3600 ENTER 24 * 365 * (should see 31536000)
Press N
Press DOWN to next menu row
- Press P/YR (set payments per year to the same 31536000)
- Press UP to return to the TVM menu row
Press 10 I%YR
Press 0 PV (bank balance starts at 0)
Press -0.01 PMT (negative to indicate outward cash flow to bank)
Press FV (should see TVM Calculated)
Answer: $331667.0067

Note that the answer is accurate to all displayed digits because we avoided roundoff errors by using the new E^X- and LN1+ functions internally.

Source:

A Penny for your Thoughts (1983)
Looking for TVM formulas (2014)

Example 5: Multiple Solutions

The following contrived example has 2 solutions for I%YR 14.44% and 53.17%. We can persuade the TVM module to give us 2 solutions using the IYR1 and IYR2 menu buttons:

Press CLTV
Press 10 N
Press 50 PV
Press -30 PMT
Press 400 FV
Press 1 P/YR
Press I%YR (should see TVM Not Found)
Modify the TVM Solver initial guesses to get the first solution
- Press 10 IYR1
- Press 20 IYR2
Press I%YR (should see TVM Calculated)
Answer: 14.43587133%
Modify the TVM Solver initial guesses to get the second solution
- Press 40 IYR1
- Press 60 IYR2
Press I%YR (should see TVM Calculated)
Answer: 53.17221327%

Source:

Solving the TVM equation for the interest rate (2012)

Complex Numbers

Complex numbers can be entered in rectangular form a+bi, polar radian form r e^(i theta), or polar degree form (theta in degrees). They can be also be displayed in all three forms. The entry modes and the display modes are independent of each other. For example, a complex number can be entered in rectangular form, even if the current display mode is polar form.

Internally, complex numbers are always stored in rectangular format. They can be displayed in 3 different formats. They can be entered in 3 different formats regardless of the display mode.

Complex Numbers and Screen Size

Complex numbers are rendering using the Small Font of the TI-83 and 84 calculators instead of the Large Font. With the Large Font, we are limited to 16 digits on a single line (including the stack label), which are not sufficient to display the 2 floating point numbers of a complex number. The Small Font allows us to display about 24 digits on a single line, which allows us to allocate 10 digits for each component of a complex number.

Here is what the screen looks like with just Large Font (left), and a mix of Small and Large Fonts (right):

Readability suffers a bit using the small font, but it seems reasonable.

Complex Number Entry

There are 2 ways to enter complex numbers on the RPN83P app:

linking two real numbers in the X and Y registers into a single complex number
inlining both components on a single line into the X register

Linking (2ND LINK)

The linking method borrows from the HP-42S which provides a COMPLEX key. It takes the Y and X registers and combines them into a complex number Y + Xi. By convention, the real part is entered first, ENTER is pressed, then the imaginary part is entered second. (Interestingly, this is the opposite order compared to the semantically related ATN2 function or the >POL conversion function.) If the COMPLEX key is pressed again on a complex number, the reverse happens. The complex number is broken up into 2 real numbers, with the Y register containing the real part, and the X register containing the imaginary part.

The TI-83 Plus and TI-84 Plus calculators do not have a COMPLEX button. The closest alternative key seems to be the 2ND LINK button which is otherwise unused in RPN83P.

For example, the number 1-2i would be entered like this:

1
ENTER
2
(-)
2ND LINK

The display before and after the 2ND LINK looks like this:

Notice that the RPN83P follows the convention used by the HP-35s in rendering the complex number with an imaginary i delimiter between the two components. The negative sign on the -2 appears after the i, because it is a delimiter not a multiplier of the number -2.

Pressing 2ND LINK on a complex number performs the reverse operation. The complex number is broken up into its real components, with the real part going into Y and the imaginary part going into X.

Inlining (2ND i, 2ND ANGLE)

The inlined entry method borrows from the HP-35s which allows a complex number to be entered in its entirety on a single line. The 2ND i button (above the . button), and the 2ND LINK button (above the x,t,theta,n button) are used to delimit the 2 components of a complex number.

To enter 1-2i in rectangular mode, we would type:

1
2ND i
2
(-)
ENTER

The display before and after the ENTER looks like this:

To enter 2 e^(i 60deg) in polar-degree mode, we would type:

2
2ND ANGLE
60
ENTER

The display before and after the ENTER looks like this:

Notice that the complex number separator is the combination of an Angle symbol and a Degree symbol, which indicates that the input is expecting the angle to be entered in degrees. After the ENTER, the input buffer is parsed and a complex number is pushed into the X register of the RPN stack.

Note also that the number was entered in polar form, but the number is displayed in rectangular form. That is because the rendering of complex number is controlled by the Complex Display Mode, currently set to RECT, which is independent of how the complex number is entered.

We can enter complex numbers using angles in radians by typing 2ND ANGLE twice. For example, to enter 2 Angle 1.047, use the following keystrokes:

2
2ND ANGLE
2ND ANGLE
1.047
ENTER

The display before the ENTER looks like this, where the Angle symbol appears without the Degree symbol:

The polar-degree mode was chosen to be the default, and the polar-radian mode available with an extra keystroke, because it seemed like the degree mode would be more useful when a complex number is inlined. For example, a three-phase electric power supply has three lines, each 120 degrees out of phase with each other. In contrast, the same angle in radians would involve a factor of Pi (120 deg = pi/3 = 2.094395102 radians) so would be easier to enter using the 2ND LINK functionality.

Special Case for Solitary 2ND i

A solitary 2ND i should be interpreted as 0 i 0 (0+0i) if the parsing rules were strictly followed, because the empty string on both sides of the 2ND i delimiter should be interpreted as a 0. However it seemed convenient to make a exception for a solitary 2ND i so that it is parsed as 0 i 1 instead. This makes it easier to enter the pure imaginary number i. Here are screenshots after a solitary 2ND i and an ENTER:

This special rule is triggered only by a solitary 2ND i. If there is any digit before or after the 2ND i, regular parsing rules are used. For example, 1 2ND i is interpreted to be 1+0i not 1+1i.

HP-35s Compatibility Note 1: The HP-35s uses a Theta symbol to display complex numbers in polar notation. The problem with the Theta symbol is that in the Small Font of the TI calculators, it looks too similar to the digit 0. The Angle symbol seemed like a better choice as a delimiter because it is visually distinct from other digit characters. It is also the symbol used by the HP-42S.

HP-35s Compatibility Note 2: The HP-35s uses SHIFT Theta button to enter complex numbers in polar notation. The Theta symbol is available on a TI calculator as ALPHA Theta. However, the ALPHA shift key is used for no other functionality in the RPN83P app, and I found switching from 2ND and ALPHA to invoke this function was too confusing for the muscle memory. The 2ND ANGLE key, on the other hand, was previously unused in the RPN83P app, and it matches the Angle symbol used to display complex numbers in polar notation.

Complex Display Modes

Just as there are 3 modes that complex numbers can be entered, there are 3 modes that complex numbers can be displayed. The complex display modes are: RECT, PRAD, and PDEG. These are available in row 2 of the MODE menu group, under ROOT > MODE, but the fastest way to reach this menu row is to use the MODE button shortcut on keyboard:

Pressing the RECT, PRAD, and PDEG menu buttons will change the display into the following:

Note that unlike most calculators with complex number support, the trigonometric modes (DEG, RAD) do not affect the rendering of complex numbers. The trigonometric modes affect only the computation of trigonometric functions. The complex display modes (RECT, PRAD, PDEG) are independent of the trigonometric modes.

This is also a good place to note that the 2ND LINK function is the only complex functionality that is affected by the display mode. The 2ND LINK function merges 2 real numbers from Y and X registers using the display mode that is currently in effect. (It did not make sense for it to do anything else.)

In other words:

if RECT: the resulting number is Y+Xi
if PRAD: the resulting number is Y e^(i X)
if PDEG: the resulting number is Y e^(i * X*pi/180), where X has been converted from degrees to radians

For example, let's set the display mode to PDEG, and enter the following:

1
ENTER
60
2ND LINK

The display before and after the 2ND LINK looks like this:

The unlinking process is also affected by the complex display mode. Let's change the display mode to RECT, then hit 2ND LINK to perform the unlinking. The display before and after the 2ND LINK looks like this:

Complex Polar Mode Overflow

When a large complex number is converted to polar form, the magnitude value in the polar form, i.e. the r term, may overflow the usual floating point limit of the calculator. That's because r=sqrt(a^2+b^2). For example,

(9e99 + 9e99i) = 1.2728e100 e^(i 0.785398163)

The number 1.2728e100 would normally generate an overflow error, but through a quirk in the underlying TI-OS, the PRAD and PDEG display modes will display these polar forms correctly, like this:

However, if we try to unlink the 2 components using the 2ND LINK function, an Err: Overflow code will be generated, because the magnitude 1.2728e100 is too large to be stored in the RPN register:

Complex SHOW

The SHOW functionality (implemented by 2ND ENTRY) supports complex numbers. All 14 internal digits of both the real and imaginary parts will be shown, using the current display mode (RECT, PRAD, PDEG).

Here is the number 1+i in 3 different modes using the SHOW function:

Complex FIX, SCI, ENG

The floating point formatting modes FIX, SCI, and ENG can be applied to complex numbers. Here are screenshots of a complex number using FIX(4), SCI(4), and ENG(4):

Complex Functions

The TI-OS provides versions of many functions that support complex numbers. Almost all of those functions have been implemented in the RPN83P app, and are transparently invoked by using a complex number argument. The following RPN83P functions have been extended to support complex numbers:

arithmetic: +, -, *, /
algebraic: 1/X, X^2, SQRT, X^3, 3RootX, Y^X, XRootY
transcendental: LOG, 10^X, LN, e^X, LOG2, 2^X, LOGB

Trigonometric and hyperbolic functions do not support complex numbers because the underlying TI-OS functions do not support them.

Additional functions specific to complex numbers are under the ROOT > CPLX menu:

They are:

REAL: extract the real part of a complex number
IMAG: extract the imaginary part of a complex number
CONJ: compute the complex conjugate of complex number
CABS: compute the magnitude r=sqrt(a^2+b^2) of complex number
CANG: compute the angle (i.e. "argument") of the complex number

The CANG function returns the angle of the complex number in polar form. In mathematics, this function is normally called the "argument". But the word "argument" has too many other meanings in software and computer science. Therefore, this function is named CANG (complex angle) to be more self-descriptive.

Since CANG returns the angle, it uses the trigonometric mode (RAD, DEG) to determine the unit of that angle. It is currently the only complex function that is affected by the trigonometric mode. An alternative was to use the complex display mode (RECT, PRAD, PDEG) to determine the unit of CANG, but it was too confusing for 2 reasons: 1) When the complex number is displayed in RECT format, there is no obvious reason why it should pick RAD over DEG, especially when, 2) The trigonometric mode is shown on the screen and can indicate one unit (e.g. DEG) but the CANG function could return another unit (e.g. radians).

Example 1: Arithmetic

Here is an example of adding the 3 complex numbers as described in p. 9-6 of the HP-35s User's Guide, shown in the following diagram:

We can add them like this:

185 2ND ANGLE 62 ENTER
170 2ND ANGLE 143 +
100 2ND ANGLE 261 +

RECT # shows -64.559244 i 166.885025
PRAD # shows 178.937161 Angle 1.93991416
PDEG # shows 178.937161 AngleDeg 111.148894

The result can be viewed in the 3 complex display formats by clicking on the RECT, PRAD, and PDEG menu buttons:

Example 2: Y^X, SQRT

In this contrived example, we compute an expression involving all three representations of complex numbers:

# ignore the following comment line, comments are not supported by MarkDown
\[ \sqrt{(1+i)^{(3 \angle 45^{\circ})} + (1 \angle 2)} \]

The keystrokes can be:

1 2ND i 1
ENTER
3 2ND ANGLE 45
^
1 2ND ANGLE 2ND ANGLE 2
+
2ND SQRT

RECT # shows .576363737 i 1.01949228
PRAD # shows 1.17113606 Angle 1.05624914
PDEG # shows 1.17113606 AngleDeg 60.518618

Example 3: CANG, CABS

In this example, we calculate the magnitude and angle of the complex number 1+i. We want the angle in degrees, so we have to first set the trigonometric mode to DEG (using MODE DEG), just like trigonometric functions. Enter the complex number in rectangular format, it does not matter what the complex display mode (RECT, PRAD, PDEG) is:

MODE DEG # trig mode to DEG
MATH CPLX # CPLX menu
1 2ND i 1 # (1+i)
CANG # shows 45, determined by DEG mode
2ND ANS # LastX
CABS # shows 1.414213562

The complex display mode (RECT, PRAD, PDEG) does not affect the value returned by CANG.

If you want the angle value as shown on the screen, use the 2ND LINK function to unlink the 2 components of the complex number. The value in the X register will be the angle value shown on the screen.

Complex Computation Modes

There are 2 computation mode settings under the MODE menu group which affect whether some functions return complex values or real values when the argument to the functions are real:

RRES (real results): return only real results for real arguments
CRES (complex results): allow complex results for real arguments

These are available on row 2 of the MODE menu group, under ROOT > MODE, but the fastest way to reach this menu row is to use the MODE button shortcut:

Note that these settings do not affect how functions evaluate complex arguments. If the argument is complex, all functions that support complex numbers will return complex results.

There are currently only a few functions which are affected by these settings:

SQRT, for arguments < 0
LOG, for arguments < 0
LN, for arguments < 0
LOG2, for arguments < 0
LOGB, for arguments < 0
Y^X, for Y<0 and non-integer values of X
XRootY, for Y<0 and non-integer values of X

If RRES is selected, then these functions will return an Err: Domain error message. If CRES is selected, these functions will return a complex value.

For example, if we try to take the sqrt(-1), in RRES mode, an error will be printed like this:

But if we change the computation mode to CRES, we get a complex result:

Complex Numbers and Trigonometric Modes

In the MODE menu, there are 2 sets of menus related to degrees and radians: trigonometric modes, and complex displayed modes. They are essentially independent of each other. This separation is different from other calculators, and I hope that this is not too confusing.

The trigonometric modes (RAD, DEG) affect the computation of trigonometric functions. They determine the unit of the angles consumed or returned by trigonometric functions. Complex functions (with the sole exception of CANG, see above) are not affected by the trigonometric modes:

The complex display modes (RECT, PRAD, PDEG) control how complex numbers are rendered on the screen. These modes do not affect the behavior of any complex functions (with the sole exception of 2ND LINK, see above):

Complex Numbers in Storage Registers

Both the RPN stack registers and the storage registers have been upgraded to accept real or complex numbers transparently. For example, we can store 1+2i into R00, then add 2+3i into it, to get 3+5i:

1 2ND i 2
STO 00
2 2ND i 3
STO+ 00
RCL 00

Answer: 3 i 5

TI-OS Interaction

The RPN83P app interacts with the underlying TI-OS in the following ways.

The RPN83STK appVar holds the RPN stack registers (X, Y, Z, T, LastX).
The RPN83REG appVar holds the 25 storage registers (R00 to R24).
The RPN83SAV appVar preserves the internal state of the app upon exiting. When the app is restarted, the appVar is read back in, so that it can continue exactly where it had left off.
The X register of RPN83P is copied to the ANS variable in the TI-OS when the RPN83P app exits. This means that the most recent X register from RPN83P is available in the TI-OS calculator using 2ND ANS.
When the RPN83P app is started, it examines the content of the ANS variable. If it is a Real value (i.e. not complex, not a matrix, not a string, etc), then it is copied into the LastX register of the RPN83P. Since the LastX functionality is invoked in RPN83P as 2ND ANS, this means that the TI-OS ANS value becomes available in RPN83P as 2ND ANS.

The RPN83P app uses some of the same flags and global variables for its MODE configuration as the TI-OS version of MODE. Starting with v0.9, these configurations are now decoupled and kept independent. Changing the MODE settings in one app will not cause changes to the other. Some of these MODE settings include:

trigonometric mode: RAD or DEG
floating point number settings: FIX (named NORMAL in TI-OS), SCI, ENG

The TVM module in the RPN83P uses some of the same TI-OS floating point variables used by the Finance app (automatically provided by the TI-OS on the TI-84 Plus). Specifically, any values stored in the N, I%YR, PV, PMT, FV, and P/YR variables will reappear in the Finance app with slightly different names (N, I%, PV, PMT, FV, and P/Y respectively). The two variables that I could not synchronize between the 2 apps are:

BEG/END flag because I could not figure out where the Finance app stores this, and
C/Y (compoundings per year) is always set equal to P/YR in the RPN83P app

Future Enhancements

There seems to be almost an endless number of features that could go into a calculator app. I have grouped them as follows, since my time and energy is limited:

Near Future

datetime conversions
- date/time components to and from epoch seconds
GCD and LCM functions are slow
- Could be made significantly faster.
allow resize of storage registers using SIZE command
- The current default is fixed at 25.
- It should be relatively straightforward to allow this to be user-definable, up to a SIZE of 100.
decouple STAT registers from regular storage registers
- STAT registers use R11-R23 storage registers, following the convention used by the HP-42S
- there is no technical reason why RPN83P needs to follow this
- a better solution is to create a separate set of registers (e.g. an RPN83STA appVar) just for STAT so that they don't interfere with normal storage registers
add ROND menu function
- round real and complex numbers to the number of significant digits displayed on the screen
support complex numbers in various NUM functions
- IP, FP, FLR, CEIL, NEAR
- we could support complex numbers to % and %CH, but does that make sense? The HP-42S does not support it.
bigger RPN stack
- linking and unlinking a complex number to and from its 2 components effectively reduces the stack size by 1
- an option to increase the size to 5 or maybe 8 seems worthwhile
- should the stack size be user-configurable, say between 4 and 8?
- I am not convinced that an infinite stack like RPL or the NSTK mode of Free42 is worth the effort
add a ROOT > CLR > CLAL (Clear All) menu function
- becomes useful as more features and configuration options are added

Medium Future

custom button bindings
- a significant number of buttons on the TI-83/TI-84 keyboard are not used by RPN83P
- it would be useful to allow the user to customize some of those buttons for quick access
- among the currently unassigned keys, here are some notes on which may or may not be be available:
  - reserved for probable future use: 2ND INS, 2ND LIST, 2ND TEST, 2ND MATRIX 2ND CATALOG, 2ND MEM, APPS, PRGM, VARS
  - reserved for potential future use: 2ND DISTR, 2ND {, 2ND }, 2ND [, 2ND ]
  - potentially available: all ALPHA keys, except probably A-F, (space), " (double quote), : (colon)
  - probably available: 2ND u, 2ND v, 2ND w, XTTn
  - definitely available:2ND L1 to 2ND L6 (no obvious purpose in RPN83P)
user-defined alphanumeric variables
- The HP-42S shows user-defined variables through the menu system.
- Nice feature, but would require substantial refactoring of the current menu system code.
custom menu items
- The HP-42S supports up to 18 (3 rows of 6 menus) to be customized through the ASSIGN and CUSTOM menus.
- This seems like a useful feature, but would require substantial refactoring of the current menu system code, like user-defined variables.
polynomial solvers
- Quadratic, cubic, and quartic equations have analytical solutions so should be relatively straightforward... Except that they need complex number support. And we need to work around numerical cancellation or roundoff errors.
UNIT conversions for imperial (not just US) units
- several places assume US customary units (e.g. US gallons) instead of British or Canadian imperial units
- it'd be nice to support both types, if we can make the menu labels self-documenting and distinctive
TVM (time value of money)
- Improve TVM Solver for I%YR.
- The initial guesses could be better.
- The terminating tolerance could be selectable or more intelligent.
- Maybe change the root solving algorithm from Secant method to Newton's method for faster convergence.
support insertion cursor using LEFT and RIGHT arrow keys
- currently the cursor always appears at the end of the input buffer
- it may be useful to support moving the cursor into the interior of the input string using the LEFT and RIGHT arrow keys
- the DEL key would probably continue to delete to the left
- any other input would probably insert at the cursor position

Far Future

I'm not sure these features are worth the effort, but I may do them for curiosity and the technical challenge:

keystroke programming
- Although I think it is technically possible for the RPN83P app to support keystroke programming, like the HP-42S, I am not sure that the calculator world needs yet another calculator programming language.
- Is it sufficient that the user can drop into TI-BASIC programming if that is required?
automated testing infrastructure
- assembly language programming is not amenable to unit testing because it is difficult if not almost impossible to isolate a piece of code to be tested in isolation of its neighboring code and the operating system environment (i.e. TI-OS)
- unfortunately, the RPN83P code base has grown large enough that it is becoming painful to add additional features without automated testing
- two possible solutions:
  - testing through a TI calculator emulator hosted on a desktop/laptop
  - integration testing through keystroke programming within the RPN83P app itself
  - I'm not sure which solution would be easier and more maintainable
indirect STO and RCL operators
- STO IND nn, STO+ IND nn, STO- IND nn, STO* IND nn, STO/ IND nn
- RCL IND nn, RCL+ IND nn, RCL- IND nn, RCL* IND nn, RCL/ IND nn
- These are mainly used in keystroke programs, so I would probably want to implement programming before spending time to implement these indirect operators.
STO and RCL for RPN stack registers
- STO ST X, STO ST Y, STO ST Z, STO ST T
- RCL ST X, RCL ST Y, RCL ST Z, RCL ST T
- Similar to indirect STO and RCL operators, I think these are mainly useful for keystroke programming, so let's implement keystroke programming before this.
matrix and vectors
- I don't know how much matrix functionality is provided by TI-OS SDK.
- Creating a reasonable user-interface in the RPN83P could be a challenge.
- It is not clear that adding matrix functions into a calculator is worth the effort. For non-trivial calculations, it is probably easier to use a desktop computer and application (e.g. MATLAB, Octave, Mathematica).
root finder (i.e. SOLVE)
- one of the hallmarks of advanced HP calculators, but I think this feature would only be useful with keystroke programming
integration
- another feature of advanced HP calculators which also depends on keystroke programming
interaction with TI-BASIC
- it might be possible to define a data conduit (i.e. an API) between RPN83P and TI-BASIC, so that they can communicate with each other
- for example, the TI-BASIC predefined variables A to Z and Theta are not used by RPN83P. They could be made accessible within RPN83P using a new STO and RCL syntax, e.g. STO OS A and RCL OS B (maybe through the currently unused 2ND DISTR button, i.e. STO 2ND DISTR 2ND ALPHA A
- I think these would be different from the usual HP-42S alphabetic variables of STO "A" and RCL "B", which would be accessed through STO ALPHA A and RCL ALPHA B.
- also to consider: TI-OS List, Matrix, and String variables

Not Planned

graphing
- The TI-OS has extensive support for graphing equations.
- It does not make sense to duplicate that work in the RPN83P application.
computer algebra system (CAS)
- The TI-83 Plus and TI-84 Plus do not support CAS, so it is highly unlikely that the RPN83P will support CAS either.
rational numbers
- Not something that I have ever needed, so I probably will not want to spend my time implementing it.

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RPN83P User Guide

Table of Contents

Introduction

Why?

Short Answer

Long Answer

Installation

Obtaining the Program File

Uploading

Starting

Quitting

Supported Hardware

Basic Usage

Screen Areas

Input and Editing

RPN Stack

Menu System

Menu Hierarchy

Menu Buttons

Menu Indicator Arrows

Menu Shortcuts

Menu Shortcut Jump Back

Built In Help

Error Codes

Functions

Direct Functions

Menu Functions

Advanced Usage

Auto-start

Input Limits and Long Numbers

Floating Point Display Modes

SHOW Mode

Trigonometric Modes

Storage Registers

Prime Factors

BASE Functions

Base Modes

Shift and Rotate

Base Arithmetic

Carry Flag

Bit Operations

Base Word Size

Base Input Digit Limit

Base Number Retention

STAT Functions

TVM Functions

TVM Menu Buttons

TVM Payments Per Year

TVM BEG and END

TVM Solver Control

TVM Clear

TVM Variable Recall

TVM Examples

Complex Numbers

Complex Numbers and Screen Size

Complex Number Entry

Complex Display Modes

Complex Polar Mode Overflow

Complex SHOW

Complex FIX, SCI, ENG

Complex Functions

Complex Computation Modes

Complex Numbers and Trigonometric Modes

Complex Numbers in Storage Registers

TI-OS Interaction

Future Enhancements

Near Future

Medium Future

Far Future

Not Planned