1. About this User Manual

This document is work-in-progress.

It includes a brief introduction to Reverse Polish Notation aimed at new users.

Text is formatted after the following conventions:

XEQ

calculator keys are referenced as a black rectangle with text as printed on their top

GTO / EQN

shifted function calls are depicted by their color label as it appears on the calculator bezel; in an attempt to reduce visual noise, the preceding shift-key press is omitted

[Q]

letter keys (printed in white on the keypad bezel) are represented between square brackets;
depending on context, entering a letter may require pressing RCL beforehand

2 ENTER 3 +

step-by-step examples show key presses; numbers entered are set in plain text

CLVARS

sometimes functions are shown just by name
some function names differ from what is visible on the keypad

INVALID (i)

on a grey background are shown messages, annunciators, program lines or other elements as they appear on the LCD

/config.txt

paths, filenames, program listings and expressions are shown in monospace fonts

    

when necessary, the blue shift-key, also known as right-shift or RS, is referenced by a blue rectangle

    

when necessary, the orange shift-key, also known as left-shift or LS, is referenced by an orange rectangle

The legacy HP-32SII manual is available at https://literature.hpcalc.org/community/hp32sii-om-en.pdf

Be aware that, although similar, the DM32 and the HP-32SII have several significant differences. See [Behavior differences with legacy HP-32SII].

Example programs and equations in sections Mathematics programs, Statistics program and Miscellaneous programs and equations, and many more not included in this manual, have ready-to-use corresponding Statefiles available from the DM32 Examples page at https://technical.swissmicros.com/dm32/examples.

2. General information

2.1. Turning the calculator on and off

Turn the calculator on by pressing C.

To turn it off, press OFF (that is,      C). If left sitting idle, the calculator will automatically turn off after 10 minutes.

The DM32 retains its state when turned off. This means that it turns on in the same mode, or menu, or data entry situation it was in when turned off.

2.2. Overview of display

The calculator screen is divided in 3 areas arranged as in the illustration below.

display 1

The screen configuration is somewhat different when in DM32 Setup.

2.2.1. Operating system status bar

While in Calculator mode, the operating system (DMCP) black status bar has 3 sections:

display topbar

  • date and time,

  • name of active State,

  • power source icon:

    • power icon batt : the calculator is powered by the internal CR2032 3V battery and runs at 48MHz; the icon shows an approximation of the remaining capacity of the battery (to replace the battery, see chapter Battery),

    • power icon usb : the calculator draws power form the USB port and runs at 160MHz.

Due to battery cell chemistry, temperature, shelf life, and the widely varying qualities of construction, the capacity indicator may fluctuate slightly. When possible, use new and reputable brands of batteries.

2.2.2. Annunciators

These two rows consist of icons, or annunciators, which turn on or off to reflect various calculator states or to make the user aware of a certain condition.

display 2

  1. Accuracy indicators when fraction display is active. Also turn on when arrow keys and are available to browse a list.

  2. Either one of left- or right-shift annunciator turns on to indicate that either one of orange- or blue-shift key, respectively, was last pressed. Next key press executes the corresponding shifted function of the pressed key.

  3. Turns on when the calculator is in Program mode.

  4. Turns on when the calculator is in Equation list or other equation mode.

  5. These four annunciators reflect the status of user flags 0 to 3. When on, the corresponding flag is set. Useful for visual feedback, e.g. when conditional flags are used in programs.

  6. Current angular mode. When off, the calculator displays angles in degrees. Letters GRAD or RAD turn on to indicate that the calculator is in gradians or radians mode, respectively.

  7. Current base. When off, the calculator is in decimal (base-10) mode. The corresponding annunciator turns on to indicate that the calculator is either in hexadecimal (base-16), octal (base-8) or binary (base-2) mode.

  8. Left and right, long horizontal arrows indicate that the shown number is too long, and thus truncated because it overshoots the display to the left or right. Use SHOW to see the rest of a decimal number, or use scroll keys √x or Σ+ to see the rest of a binary number or equation.

  9. Alpha entry is active: next key press enters a letter.

  10. Attention! There is a special condition or an error. For a description of calculator messages, see Appendix C: Messages.

  11. When these down-pointing arrow symbols 🠷 are on, top row keys become soft keys and execute the corresponding displayed function in menus.

2.2.3. Main display area

This is the main number-crunching area. It is made up of four 12-character lines, one for each level of the RPN stack. Each line also has an extra space on the left to display a minus sign for negative numbers.

display 3

2.2.4. About DM32 modes

The DM32 can operate in 3 different modes. When this manual refers to one of the modes, the initial is capitalized as below.

  • Calculator mode is the main mode used to perform calculations. It expects digit input and calls to functions which take data from the stack to operate upon. In this mode, the display shows the 4 levels of the stack.

  • Program mode is used to review, write and modify programs. PRGM puts the calculator in Program mode, showing the contents of program memory. Annunciator PRGM turns on to indicate the mode is active. Pressing C or executing PRGM again exits Program mode and returns to Calculator mode.

  • Equation list is used to review, write and modify equations. EQN opens the Equation list. Annunciator EQN turns on to indicate the mode is active. Pressing C or executing EQN again closes the Equation list and returns to Calculator mode.

The calculator also allows to write an equation in Program mode.

2.2.5. Fonts

The calculator can use two fonts with variants, for a combined total of 5 font options. See section Stack Font from chapter DM32 Setup for a preview and details.

2.3. Overview of keypad

The keypad consists of a total 43 keys. There are 4 keypad areas, as described in the following table and illustration.

area keys function

top row

6

soft-keys, or F-Keys

main

34

input and function keys; every key has 3 or 4 functions

shift

2

call secondary functions of the main area and C keys

C

1

ON/OFF/CANCEL/EXIT functions

keypad areas

2.3.1. F-Keys

The row of blank keys at the top of the keypad, right under the LCD, are designated from left to right as F1 to F6.

fkeys
F-Key function

F1

open the Onboard help

F2

Debug view

F3

in Calculator mode: debug step-over (step-out when used with     )
while Onboard help opened: help file selection

F4

open Available States list

F5

equivalent to up arrow ; debug step-back

F6

equivalent to down arrow ; debug step-into

When the calculator is displaying a file selection dialog, like in the File menu, the Available States list or the help file selection dialog:

  • F5 toggles file size display between bytes and kilobytes (when file is above 1023 bytes),

  • F6 toggles between 1- and 2-column file listing.

2.3.2. Main area and shift keys

main keys

In addition to entering numbers and executing functions as they are labelled in white, each of these keys has 2, sometimes 3 additional functions. They can switch the calculator to Equation or Programming mode, summon menus (from which further functions can be invoked), execute math operations or add program instructions, perform conversions, act as a letter input keypad, and more. The labels to these extra functions are printed on the bezel, around each key, in orange, blue and white.

key zoom 1

The keypad has two color keys,      and     , just above the C key. To execute a function printed in orange or blue, press the corresponding color once before pressing the key. For example, number π can be entered by using key SIN. To do so, press and release the blue shift key      and the blue shift annunciator appears at the top left corner of the display:

display shift 1

Press SIN and number π appears in the x-register:

display shift 2

The annunciator automatically disappears and the next key press is unshifted. To clear the annunciator if shift has been pressed by mistake, press the same shift key again. In this manual, shifted function calls are depicted by their color label as it appears on the calculator bezel (the shift key press is omitted), for instance π or ASIN.

Keying in a letter is done by pressing the corresponding key when appropriate, to store or recall variables, execute a program, or when writing an equation. In this manual letter-key presses are depicted by the letter between square brackets, for instance [A] or [F].

2.3.3. C key

c key

Clear or Cancel key. When the calculator is off, pressing C turns the calculator on. When the calculator is on, it clears the x-register, exits menus and cancels input; orange-shifted, it opens DM32 Setup, controlling general calculator settings, OS and hardware functions; blue-shifted, it turns the calculator off.

Also useful to exit menus or cancel actions. DMCP, the calculator’s operating system, sometimes refers to this key as the “EXIT” key.

Note that the calculator retains the state it was in when turned off, i.e. it will turn on in the same state and mode it was turned off in.

2.3.4. Clearing keys

Depending on the situation and what needs to be achieved, the appropriate way to clear or backspace is different. There is also a CLEAR menu with functions usable as program instructions. See appendix Clearing functions for a complete reference.

2.4. Navigation keys summary

The DM32 frequently presents the user with lists or menus that can be navigated by moving a cursor or scrolling the display up and down. There are two general contexts where this happens: system and calculator operation. Each context uses its own set of keys for vertical motion.

system (DMCP OS) calculator operation

active navigation keys

  • / + : up/down

  • ÷ / × : page up/page down

  • / : up/down

  • F5 / F6 : up/down

context

2.5. Onboard help

The DM32 contains an onboard help document. It has a table of contents and contains many links which help navigate it. Here is how to use the onboard help:

key action

F1

open help file

2 / 8 or + /

next/previous line

3 / 9 or × / ÷

next/previous page

6 / 4

select next/previous link

5 / ENTER

follow link

jump to previously followed link

7

back to top

F1 or C

close help file

F3

open help file selection dialog

When pressing F1, the DM32 looks for file \HELP\dm32help.html. If no such file is present, a warning message appears with instructions on where to retrieve the file from or select another file from the internal disk.
Although the help file is in HTML format, the onboard browser has limited capability. Unless the HTML syntax is specifically tailored for the DM32, help file display will yield unpredictable results.

2.6. Screenshots

The calculator can save screenshots of the display as 1-bit BMP file to internal disk, in folder /SCREENS. To take a screenshot, hold down      while pressing E. Two beeps confirm the file has been saved.

2.7. CPU speed switch

The calculator CPU automatically switches speeds depending on the power source used (see “power source icon” in Operating system status bar). To avoid current draw problems associated with speed switching, it is recommended to always turn the calculator OFF before plugging or unplugging the USB cable.

3. RPN and the stack

3.1. What is RPN?

RPN stands for Reverse Polish Notation. It is commonly opposed to algebraic notation, found on the vast majority of calculators. It is an efficient way of writing and performing calculations, which makes parentheses useless, and uses a different order for numbers (operands) and operators.

There are actually three positions where the operator can be placed when writing an expression. Adding 3 and 4 could be expressed as:

  • + 3 4

  • 3 + 4

  • 3 4 +

These notations are called, from top to bottom, prefix, infix and postfix. The majority of users know infix. RPN is postfix, which means the operator is written after the operand(s).

Let’s use an example infix expression:

( 12 + ( ( 6 × 4 ) – 4 ) ) ÷ 8

While it works well to represent the expression on paper, it actually has not much to do with the actual sequence used to evaluate the expression. Indeed, the practical course of action is to evaluate the innermost parenthesis first, and then proceed outwards with intermediate results, like so :

  1. 6 × 4 = 24( 12 + ( 24 – 4 ) ) ÷ 8

  2. 24 – 4 = 20( 12 + 20 ) ÷ 8

  3. 12 + 20 = 3232 ÷ 8

  4. 32 ÷ 8 → answer is 4

Now, written using RPN, our expression translates to :

6 ↑ 4 × 4 – 12 + 8 ÷

This puzzling sequence has a simple explanation. RPN takes operands (numbers) first, then the operator. Usually, operands come in as a pair, and one operator follows, which acts upon the pair. In other words, instead of looking at “six times four”, the operator is moved to the end, making it “take six, take four and multiply them”. Symbol is used to explicitly represent numbers 6 and 4 as separate (“6 and 4”, and not “64”). There is no equal sign either to operate the calculator: invoking the operator implicitly “processes” the operands and returns the result.

Considering this, see below how RPN breaks down evaluation in chunks very similar to the natural, 4-step sequence of evaluation described above, with an intermediate result from each step picked as an operand in the next step:

  1. 6 4 × (6 times 4)24

  2. 24 4 - (24 minus 4)20

  3. 12 20 + (12 plus 20)32

  4. 32 8 ÷ (32 divided by 8)4

Of course, some operators only require one operand. For instance, writing the square root of 9 in RPN is:

9 √

So RPN is merely another way of writing expressions, as the word “notation” in its name implies. But the value of it becomes more apparent when used for chain calculations, in conjunction with the stack system.

3.2. Stack basics

The stack is intimately related to the way the calculator uses RPN to perform calculations. To properly use the DM32, it is essential to have a good understanding of how it works. It acts as a scratch pad and retains intermediate results so as to make using RPN effective.

The following demonstration explains how values move about in the stack.

3.2.1. The stack is 4 memory registers

The stack is a memory space made up of 4 registers. These registers are visible at all times as the 4 lines on display while in Calculator mode. Numbers used for calculations are invariably inserted in stack registers before performing operations. These registers are volatile in the sense that every new value introduced destroys the oldest value, as explained below. The 4 registers of the stack are named x, y, z and t. In the rest of this manual, registers are sometimes designated implicitly, i.e. simply with an italic x, y, z or t instead of the more complete “x-register”, “y-register”, “z-register” or “t-register”.

There is a “fifth” register called LASTx, which isn’t normally shown on display.

3.2.2. Chain calculation with the stack

Here is an example chain of operations to illustrate how the stack works. First, initialize the calculator with CLEAR ALL Y (warning: this will delete contents of the calculator). Also make sure the display mode is set with DISP FX 1. This limits the display to one decimal place so numbers are easier to read for the example.

The stack is now empty (or filled with value zero), and the display shows:

stack empty

When a new number is keyed in, it is placed on the “bottom of the stack” in the x-register. Let’s key in 2, the stack now looks like this:

stack 2

The underscore character on the right of value 2 means that digit-entry is still active. To terminate entry and key in a new number, press ENTER. The following happens:

stack 2lift

The value is now on registers x and y because two things actually happen at the same time when ENTER is executed: the entered value is immediately pushed up to y-register (this is called stack lift) and a copy is placed in the x-register. This is useful to perform an operation using two identical numbers. Since it isn’t our goal here, let’s key in number 1 2 3 4 5. The following changes happen:

stack 1.2345

Note how this new value replaces the copy placed in x-register. This is because key ENTER disables stack lift, which means that any key press following ENTER won’t lift the stack.

Pressing x⇄y swaps values between the x- and y-registers. Press it and the stack changes like this:

stack swap

This simple swap operation is very often useful when working with the stack. It also terminates digit-entry. (Note that number 1.2345 is truncated to 1.2, or 1 decimal place; that’s because of the active display setting that has just been set with DISP FX 1. Internally the number is stored complete, as 1.2345.)

To proceed with our example, let’s insert values 5 and 0.5 like so:

5 ENTER 5

Now all four registers are filled:

stack 0.5

Press ENTER one more time and the stack is modified so:

stack enter2

The value 1.2345 in the t-register has been pushed out of the stack and lost. The stack has 4 registers; every time the stack lifts, the value in the t-register is pushed out and permanently lost.

Key R↓ “rolls” the stack downwards, which means that the value in t goes to z, the value in z goes to y, the value in y goes to x, and the value in x wraps around to t. Press it and the stack changes like this:

stack rdown

A function opposite to R↓ exists to “roll up” the stack. Press R↑ and the stack rolls up. In this case it simply returns to its previous state:

stack rup

The stack as it now stands can be used for the upcoming example.

3.3. RPN in conjunction with the stack

Until now, we have only been moving numbers around within the memory space of the stack. Let’s start making calculations with it.

3.3.1. Stack drop, t-register duplication

Operators use values (or operands) in the x- and y-registers. Press + and the stack transforms like this:

stack plus

The following has happened:

  • the calculator took the operands in registers x and y to apply the addition operator,

  • the result was placed in the x-register; no need to press an “equal” key,

  • since two numbers (in the x- and y-registers) have been replaced by just one (in the x-register), the stack has dropped: z goes to y and t goes to z; in other words, like a pile subjected to gravity, when an element at the bottom is removed, every one on top shifts down one spot,

  • a copy of whatever the t-register contained was placed back in the t-register, which is why the two top numbers in the stack are now the same.

Now press . The following happens:

stack minus

The value in the x-register has been subtracted from the value in the y-register and the result placed in the x-register. The stack drops again. Note how, because the t-register retains a copy of its value every time the stack drops, all registers except x now have the same value.

Now press ×. The following happens:

stack mult

The value in the x-register has been multiplied by the value in the y-register and the result placed in the x-register. The stack drops again, although this didn’t produce any visible change, since the value in the t-register gets duplicated upon stack drop.

Now press ÷. The following happens:

stack divide

The value in the y-register has been divided by the the value in the x-register and the result placed in the x-register. The stack drops again. The displayed value 0.3 is internally stored as 0.25, but it is shown rounded with only one decimal place because of the current display setting. To view the entire number in the x-register, change the display mode with key sequence DISP FX 2 :

stack fix4

3.3.2. Using a constant in the stack

The duplicating effect of the t-register on stack drop can be used to make calculations with a constant. Since all stack levels (except the x-register) are filled with value 2, it’s easy to repeatedly multiply the value in x-register by 2. Press ×:

stack x21

Press × again:

stack x22

Press × one more time:

stack x23

Since a new copy of value 2 is inserted at the top of the stack after every two-number operation, the constant calculation can go on indefinitely (or at least until OVERFLOW is met — see Appendix C: Messages).

3.3.3. Example chain calculation

To proceed, clear memory with CLEAR ALL Y.

stack calc1

Here’s an example expression:

( 2 × ( 27 ÷ 2.5 ) - ( 2 + 4 ) ) × π

Start from the inner parenthesis that has a division and key in 2 7 ENTER 2 5 ÷. The result is:

stack calc2

Then multiply this with 2 ×. The display now shows:

stack calc3

Calculate the value of terms between the other parentheses with 2 ENTER 4 +. The display changes to:

stack calc4

Subtract x from y with and the display changes to:

stack calc5

Put π on the stack and multiply with ×:

stack calc6

The result is ≅ 49.0088 (and shows as 49.01 because of current FIX 2 display format).

Parentheses are not used when writing and evaluating expressions with RPN. The stack holds intermediate results and allows for chain calculations following a natural course.

To recap, here is the expression written in algebraic form (as it would be keyed in, without the final press on “equal” key):

( 2 × ( 27 ÷ 2.5 ) - ( 2 + 4 ) ) × π

And here it is in RPN, as it was entered in the calculator (character representing ENTER keypresses) :

27 ↑ 2.5 ÷ 2 × 4 ↑ 2 + - π ×

which saves 5 key presses compared to algebraic entry.

3.3.4. About stack lift

Most of the time, when a number is keyed in, the stack is lifted: values are pushed up the stack (x goes to y, y to z, z to t and t is pushed out and lost). Whether an action lifts the stack or not depends on the stack lift status at the moment the function is executed. Stack lift is usually enabled, but certain operations disable it. When stack lift is disabled, the next number keyed in overwrites the one present in the x-register without pushing numbers up the stack beforehand. Calculator functions have either one of 3 effects on stack lift status, they either:

  • disable stack lift,

  • enable stack lift,

  • or are neutral and don’t change the current stack lift status.

Disabling functions

  • ENTER

  • Σ+

  • Σ-

  • CLx

Function INPUT, which prompts for a value in a program, disables stack lift so user-entered value overwrites the x-register, but enables it again when program resumes.

Neutral functions

  • modes, display and base functions: DEG, RAD, GRAD, RADIX., RADIX,, FIX, SCI, ENG, ALL, DEC, HEX, OCT, BIN

  • clear functions: CLVARS, CLΣ, C,

  • , , R/S, STOP, OFF

  • EQN, FDISP, PRGM and program entry, GTO . ., GTO label nn

  • PSE, SHOW

  • errors, switching between binary windows, digit-entry

3.4. The LASTx register

The stack has a “fifth” register, a kind of extension, not normally shown on screen. The LASTx register retains whichever number was in the x-register before the last function was executed. To recall contents of the LASTx register to the x-register, press LASTx.

This can be put to use in two ways:

  1. to correct calculation errors,

  2. to reuse a number during calculations.

Functions which copy the x-register to LASTx are indicated in Appendix D: Functions index.

3.4.1. Correcting errors with LASTx

Error with one-number function

If the intended calculation is 1.2345 LOG but 1.2345 LN was used instead by mistake, there’s no need to start over. Just press LASTx LOG.

Error with two-number function

LASTx can be used to correct two-number functions by using LASTx and the inverse of the erroneous function: + or , × or ÷, or √x.

  1. Press LASTx to reclaim the second number (which sat in the x-register just before using the function),

  2. execute the inverse function, which will return the original first number of the two-number function; from here:

    • If the entered function was erroneous, press LASTx again to reclaim the original contents of the x- and y-registers. Now, execute the correct function.

    • If the second entered number was erroneous, key in the correct number and execute the function.

If the first entered number was erroneous, key in the correct first number, press LASTx to reclaim the second number, and execute the function. Press C to remove the incorrect result from the stack first.

Examples of LASTx use
Let’s consider the following calculation:

\$32 ÷ 4 = 8\$

Here are the three types of possible errors, and how to use LASTx to correct them:

wrong calculation type of error correction

32 ENTER 4 +

wrong function

LASTx LASTx ÷

31 ENTER 4 ÷

wrong first number

32 LASTx ÷

32 ENTER 5 ÷

wrong second number

LASTx × 4 ÷

3.4.2. Reusing numbers with LASTx

LASTx can be used to reclaim a number in a calculation, like a constant.

Let’s assume European astronauts Garrett and Neil need spacesuits that fit them. To make the suits, their size in feet is required. There are 3.28084 feet in a meter.

Garrett is 1.76 meter tall.
Neil is 1.85 meter tall.

keystrokes x-register description

1.

1.76 ENTER

1.7600

Garrett’s size in meters

2.

3.28084

3.28084_

the number of feet in a meter

3.

×

5.7743

Garrett’s size in feet

4.

1.85

1.85_

Neil’s size in meters

5.

LASTx

3.28084

the number of feet in a meter

6.

×

6.0696

Neil’s size in feet

4. DM32 menus

Most of the functions labeled on the keys and bezel of the calculator execute immediately upon key press. Some of them, on the other hand, are selected from menus. The DM32 has 14 menus allowing further access to math or programming functions or additional calculator configuration.

The DM32 Setup menu, controlling general calculator settings, OS and hardware functions, works differently and is not covered here.

The image below shows bezel labels corresponding to menus.

menu keys

4.1. Soft-keys

When displaying a menu, the top-keys labeled √x, , LN, , 1/x, Σ+ become soft-keys to select one out of a maximum six options from the menu. The available functions are displayed immediately above the keypad, at the bottom of the LCD, with annunciator arrows 🠷 pointing down to the corresponding keys. Pressing a soft-key executes the corresponding function.

menu display

The menu illustrated above is x?0 (called using keys      ÷). To invoke the (not equal) comparator, soft-key √x is pressed.

F-Keys can be used interchangeably with the soft-keys underneath when displayin a menu.

4.2. DM32 menus list

Here is a list of all menus and a succinct description of the functions they offer.

4.2.1. Parts menu

PARTS parts of number, see Parts of numbers; returns the number part on the x-register

IP

integer part

FP

fractional part

ABS

absolute value

4.2.2. Probability menu

PROB probability functions, see Probability; puts the calculated number on the x-register

Cn,r

combinations

Pn,r

permutations

SD

pseudo-random number seed

R

pseudo-random number

4.2.3. Linear regression menu

L.R. linear regression, see Statistics; puts the calculated number on the x-register

̂x

predict x for a given value of y

̂y

predict y for a given value of x

r

correlation coefficient

m

fit line slope

b

y-intercept

4.2.4. Mean menu

x̄,ȳ arithmetic and weighted means, see Statistics; puts the calculated number on the x-register

mean of x series of data

mean of y series of data

x̄w

weighted mean of x series of data

4.2.5. Deviation menu

S,σ sample and population standard deviation, see Statistics; puts the calculated number on the x-register

sx

sample standard deviation of x series of data

sy

sample standard deviation of y series of data

σx

population standard deviation of x series of data

σy

population standard deviation of y series of data

4.2.6. Summation menu

SUMS statistical data summations, see Statistics; puts the sum on the x-register

n

total number of statistical datapoints

x

sum of values in series x

y

sum of values in series y

x2

sum of squared values in series x

y2

sum of squared values in series y

xy

sum of products of x and y values

4.2.7. Memory menu

MEM calculator memory information, see Appendix B: Memory

nnnn

remaining available memory in kilobytes, including memory used by Available States in the Available States list

VAR

catalog of stored variables

PGM

catalog of stored programs (program labels)

4.2.8. Modes menu

MODES angular mode and radix (dot or comma decimal separator)

DG

angular mode: degrees (full turn = 360°)

RD

angular mode: radians (full turn = 2π radians)

GR

angular mode: gradians (full turn = 400 gradians)

.

decimal separator: dot

,

decimal separator: comma

4.2.9. Display menu

DISP number display format, see Display format

FX

fix notation

SC

scientific notation

EN

engineering notation

ALL

display 12 digits

4.2.10. Clear menu

CLEAR memory clearing functions, see Clearing functions

x

clear x-register

VARS

clear all variables

ALL

clear all of memory

PGM

clear all program memory (replaces ALL when in Program mode)

EQN

clears program line with equation (replaces PGM when in Program mode)

Σ

clear all statistical data

See Clearing functions for more detail.

4.2.11. x?y comparison menu menu

x?y programming: x VS y comparison tests; see Conditional instructions; return true if:

x is not equal to y

x is smaller than or equal to y

<

x is smaller than y

>

x is greater than y

x is greater than or equal to y

=

x is equal to y

4.2.12. x?0 comparison menu menu

x?0 programming: x VS zero comparison tests; see Conditional instructions; return true if:

x is not equal to zero

x is smaller than or equal to zero

<

x is smaller than zero

>

x is greater than zero

x is greater than or equal to zero

=

x is equal to zero

4.2.13. Flags menu

FLAGS set, clear and test flags, see Flags

SF

set flag

CF

clear flag

FS?

test flag, return true if flag set

4.2.14. Bases menu

BASE change number base used to enter and display numbers, see Number bases

DEC

decimal; base-10

HX

hexadecimal; base-16

OC

octal; base-8

BN

binary; base-2

5. Entering and displaying numbers

5.1. How digit-entry works

When keying in a number, an underscore cursor _ appears to the right of the line. This is where the next keyed-in digit appears and indicates that number is not complete. There are two ways to terminate entry:

  • If using a one-number function, the function is immediately executed using the number, the answer replaces it in the x-register and digit-entry is terminated (no underscore cursor _ on the line). Example: key in 9
    digit entry 1
    Press √x:
    digit entry 2

  • If using a two-number function, the first number must be indicated as complete by pressing ENTER. The second number is then keyed in and the two-number function executed (without using ENTER a second time). In other words, ENTER serves as a way to separate the operands of a two-number function. Example: key in 6 ENTER 8
    digit entry 3
    The two operands are on the stack (entry of the second one is not terminated yet). Press ×:
    digit entry 4

A number being keyed in can be corrected while digit-entry is active (underscore cursor _ on the line):

  • deletes the rightmost digit,

  • C resets the x-register to zero, terminates digit-entry and disables stack lift, which means the correct number can be entered directly.

To illustrate this, key in number 1 2 3 4 5:

digit entry 5

Press and the rightmost digit is removed:

digit entry 6

Press C and the x-register is reset to zero:

digit entry 7

See Clearing functions for more information.

5.1.1. Maximum input length and largest number

Numbers up to 34 digits long can be manually entered, plus a 4 digit exponent up to ±6144. If more digits are entered, nothing happens, except a warning annunciator briefly turning on.

The calculator can represent numbers with exponents between –1×106145 and 1×106145.

5.2. Making numbers negative

Press +/– to toggle the number in the x-register positive/negative. Note that numbers must be put on the stack prior to making them negative.

Example: put π on the stack:

plusminus 1

Putting this constant on the stack automatically terminates entry (no trailing _). Now press +/–:

plusminus 2

The number is now negative. Key in another number, like 2:

plusminus 3

digit-entry is active (line ends with _). Now press +/–:

plusminus 4

The number is now negative. Note how +/– doesn’t terminate entry.

5.3. Decimal display

5.3.1. Exponents of ten

Numbers with an exponent of ten are displayed with an E preceding the exponent. For instance, number 3.2×10-6 displays as

exponents 1

Any number too large or too small for the current display format is automatically displayed in exponential form. For instance, if the calculator is in FIX 3 mode, keying in 0 0 0 7 8 ENTER displays the rounded number on the stack (full precision is preserved internally):

exponents 2

But keying in 0 0 0 4 4 ENTER gives:

exponents 3

because otherwise, no significant digit would be visible.

5.3.2. Display format

Functions from the DISP menu are used to control the way the calculator displays numbers in decimal formats. There are 4 formats to select from:

  1. FX Fixed-decimal; displays the specified fixed number of decimal places after the integer part.

  2. SC Scientific; displays numbers as exponents of ten. The number of decimal places must be specified, and the integer part is always less than ten.

  3. EN Engineering; similar to SC, except the exponent is a multiple of 3. User specifies number of digits to display after the first significant digit.

  4. ALL All; uses the full 12-digit display width of the calculator display. Trailing zeros of the fractional part are omitted.

Numbers are always stored internally with full 34-digit precision, but the display only ever shows a rounded version of this internal number.

5.3.3. Fixed-decimal format example

Here are a few examples. Make sure the calculator is in the correct mode by using DISP FX 4. Let’s put π in the stack:

fix 4

The calculator shows 4 decimal places. To change this to 6 decimal places, use DISP FX 6. The displayed number changes to:

fix 6

5.3.4. Scientific and Engineering formats example

Make sure the calculator is in the correct mode by using DISP FX 4. Let’s put a number smaller than 1 on the stack with π 1/x:

fix 7

Switch to scientific format with 3 decimal places by using DISP SCI 3:

fix 9

Now switch to engineering format with 2 digits after the most significant digit with DISP EN 2:

fix 8

Revert to fix-decimal FIX 4 with DISP FX 4:

fix 7

Most of the time, the calculator can’t display the entire number as it is stored internally. To show the complete number, press and hold SHOW. See Function SHOW to display long numbers and Rounding for more information.

5.4. Fraction display

The DM32 allows for entering and displaying numbers as fractions. To enter a number as a fraction, use twice:

  • once to separate the integer part of the number from its fractional part,

  • a second time to separate the fraction numerator from the denominator.

To enter 34/7, press 3 4 7. The x-register shows:

frac 1

Enter another fractional number 67/9 with keys ENTER 6 7 9:

frac 2

Now press +:

frac 3

Although numbers are entered as fractions, the calculator still displays results in the current decimal format (either FIX, SCI, ENG or ALL), unless fraction display mode is active. Activate it with FDISP. The displayed result changes to:

frac 4

If results differ, the way fractions are displayed may have been accidentally changed. See Fraction format.

Now key in 1 7 5 ENTER. The calculator shows:

frac 5

Press FDISP and the number displays as decimal:

frac 6

Press FDISP again and the number reverts to fraction.

Numbers can be keyed in either as fractions (using twice) or as decimal, no matter what mode the calculator is in. All functions work the same in both display modes (except for RND).

Numbers are always stored internally in full-precision, decimal format. Fraction display mode merely represents the internal decimal number according to current Fraction format setting.

5.4.1. Long Fractions

If a fraction is so long that it won’t fit in the display, the integer part is shoved off screen to the left and the display is focused on the fractional part. A …​ to the left indicates this. Long fractions can’t be scrolled, but the integer part can be shown using SHOW.

Example: enable fraction display with FDISP and calculate e15 with 1 5 :

frac 7

The …​ on the left shows that the integer part is only partly visible. The fractional part is always entirely shown. Now press SHOW to show the number in full precision (see Function SHOW to display long numbers for details); the integer part is visible:

frac 8

5.4.2. Accuracy indicator

To indicate how the displayed fraction compares to the internal decimal number, annunciator or can turn on. If no annunciator is lit, it means that the displayed fraction represents the internal number exactly. If is lit, it means that the internal decimal number is slightly greater than the displayed fraction. More precisely, it means that the exact numerator is 0.5 or less above the displayed numerator. Annunciator means the same thing but the other way around, that is, the internal decimal number is slightly less than displayed fraction.

frac roundoff

5.4.3. Rules

A set of rules, called Fraction format, determines how the calculator handles fractions. These rules are determined by the status of flags 7, 8 and 9 plus the setting of maximum denominator. Depending on how the rules are defined, a fraction might be automatically changed when entry is terminated. In the default fraction format (flag 8 and 9 clear), the following rules apply:

  • the number has an integer part and, if necessary, a proper fraction (where the numerator is less than the denominator);

  • the denominator is a maximum 4095;

  • the fraction is reduced as far as possible.

The following table shows a few numbers: how they are entered as fractions, the internal stored value, and how the calculator displays them. The meaning of annunciators or is explained above.

entered fraction internal value displayed fraction

1 3/4

1.75

1 3/4

102/24

4.25

4 1/4

19/8255

0.002301635372501514…​

▲ 0 2/869

5.4.4. Setting maximum denominator

Fractions are represented as \$a\$  \$b//c\$, where \$//c\$ is the value of the denominator. Function /c is used to set the maximum denominator, which can be any integer between 0 and 4095. Enter the value and press /c to use it as the maximum denominator value. Function /c uses the absolute value of the integer part of the number in the x-register and doesn’t change the value of the LASTx register.

n /c

sets the maximum denominator to n; also turns on fraction mode (like FDISP)

1 /c

recalls current value of /c to the x-register

0 /c

sets the maximum denominator to default 4095; also turns on fraction mode (like FDISP)

4095 /c

sets the maximum denominator to default 4095; also turns on fraction mode (like FDISP)

8500 /c

sets the maximum denominator to default 4095; also turns on fraction mode (like FDISP)

5.4.5. Fraction format

There are three possible formats fractions can be displayed in:

  • Most precise fraction
    Fractions have any denominator up to the /c value, and they’re reduced as much as possible.

  • Factors of denominator Only factors of the /c value are allowed for the denominator, and fractions are reduced as much as possible. For instance, if the value of /c is 12, possible denominators are 2, 3, 4, 6, and 12.

  • Fixed denominator Fractions may only use the /c value as denominator, therefore they’re not reduced. For example, make /c = 60 to work with time measurements (as in 60 minutes).

Fraction display configuration is controlled by flags 7, 8 and 9. Flags 8 and 9 are used to configure fraction format.

configuration flag 7 flag 8 flag 9

fraction display off

clear

-

-

most precise fraction

set

clear

-

factors of denominator

set

set

clear

fixed denominator

set

set

set

Flag 7 toggles between decimal and fraction display and is identical to pressing FDISP. Flag-based configuration makes it possible to test for and control fraction display programmatically.

Here is how value 4.89 is displayed with different fraction formats and /c values:

configuration /c = 4095 /c = 16

most precise fraction

4 89/100

▲ 4 8/9

factors of denominator

▼ 4 81/91

▲ 4 7/8

fixed denominator

▼ 4 3645/4095

▲ 4 14/16

To further illustrate how fraction configuration influences number display, here is how different numbers are represented for a /c value of 16:

configuration 8 8.5 8 2/3 8.999 8 22/30

most precise fraction

8

8 1/2

▲ 8 2/3

▼ 9

▼ 8 11/15

factors of denominator

8

8 1/2

▼ 8 11/16

▼ 9

▼ 8 3/4

fixed denominator

8 0/16

8 8/16

▼ 8 11/16

▼ 9 0/16

▼ 8 12/16

Some results could be displayed differently than on the HP-32SII due to bugs in that machine (later corrected on the HP-33S and HP-35S). See Behavior differences with HP-32SII for details.

5.4.6. Rounding fractions

If fraction display is active, function RND rounds the internally stored number to the closest decimal representation of the fraction. The rounding is done according to maximum denominator and fraction format configuration.

In equations and programs, RND function does fractional rounding if fraction display is active.

5.4.7. Fractions in equations and programs

Fractions which are keyed into equations or programs are held in fraction form internally, although they always display as decimal numbers. The recorded fraction can be viewed by pressing SHOW with the relevant equation selected in the Equation list, or with the cursor at the relevant program line in Program mode.

For instance, here is the display while entering fraction 12/3 as a program line:

fraction show1

Once digit-entry is terminated, the fraction is expressed as decimal number 1.6666…​:

fraction show2

Pressing SHOW produces 1.2.3, which is exactly how the fraction has been keyed in:

fraction show3

Note that when the calculator prompts for values, these can be entered as fractions. A running program shows values as fractions if fraction display is active.

Programs can control fraction display and configuration by setting or clearing fraction flags.

5.5. Function SHOW to display long numbers

Each of the four lines on the display has a maximum 12-character capacity. Whenever the length of the number in the x-register exceeds this limit, press SHOW to bring up the SHOW box. The number is displayed in full precision, in a box appearing on top of the current display, using a smaller version of the current font. This works in all number bases. While in decimal mode, if Fraction display is active, a fractional number is shown in decimal.

Function SHOW has 3 modes of operation:

  1. peek — press and immediately release SHOW to display the SHOW box for about 2 seconds;

  2. momentary — press and hold SHOW to display the SHOW box as long as held down;

  3. hold — press SHOW twice to keep the SHOW box on display indefinitely (see SHOW hold).

Here is an example illustrating how the SHOW box works:

  1. Clear the calculator with CLEAR ALL Y.

  2. Set decimal mode with DISP FX 4.

  3. Press π. The x-register shows the approximation of pi:

    show off

  4. Now press      and then press and hold SHOW ( ENTER ). The SHOW box appears and remains on display until SHOW is released.

    show on

SHOW also works to view long numbers from the VAR catalog, to view long equations, and for both long number and equations in Program mode.

5.5.1. SHOW hold

The SHOW box can be held on display indefinitely. To do it, press      and press SHOW ( ENTER ) twice. The SHOW box remains on display until either C or is pressed. Pressing any other key clears the SHOW box as well, but also executes that key’s function.

5.6. Changing how period and comma are used (radix mark)

The decimal point (radix mark) and digit separator use . and , by default. This can be swapped:

  1. Press MODES to display the MODES menu.

  2. Specify the desired format for decimal point (radix mark) by pressing . or ,.
    For example, number ten million looks like:

    • 10,000,000.0000 if radix mark set to ., or

    • 10.000.000,0000 if radix mark set to ,.

6. Variables

The DM32 can store numbers, programs and equations. Numbers are stored in memory registers called variables. Each variable has a 1-letter name from A to Z.

In addition to these directly available registers, the DM32 has two sets of exclusively indirectly addressable registers. Instructions on how to use them can be found in chapter Indirect addressing.

When appropriate, annunciator A..Z turns on; pressing a letter-key in this context inputs the corresponding letter.

Stack registers x, y, z and t are different from variables with the same name. The RPN stack has its own, independent 4-register memory space.

This chapter uses one continuous example, starting with the next section.

6.1. Storing and recalling numbers

Numbers are stored with function STO, and recalled with function RCL.

Start with a fresh calculator by pressing CLEAR ALL Y. Put number 5 on the x-register:

vars new 1

To store it into variable A, first invoke function STO and the calculator prompts for a variable name to view (annunciator A..Z turns on to confirm this):

vars new 2

Press the key for letter A, which is √x:

vars new 3

Value 5 has been copied into variable A. Store number 60 in variable B with 60 STO [B].

Recall variable A with RCL [A]:

vars new 4

The number is recalled to the x-register.

Storing a number into a variable already holding a value triggers no warning; the variable is overwritten without notice.

Let’s store a few more variables for the sake of the coming examples:

  • 123 STO [C]

  • 3.14 STO [P]

  • 1.41 STO [X]

Display now looks like this:

vars new 5

6.2. Viewing a variable (without recalling it)

Function VIEW shows the contents of a variable without putting it on the x-register. Press VIEW and the calculator prompts for a variable name to store the number into (annunciator A..Z turns on to confirm this):

vars new 6

Press letter-key [B]. The contents of variable B is displayed, with a label to identify it:

vars new 7

Press C or to cancel VIEW and the display reverts to the x-register.

6.3. Reviewing variables in the VAR catalog

To access the catalog of variables, press MEM VAR. This opens a list of all stored variables (including statistics registers), showing the name and value of each.

vars new 8

The arrow on the left points to the currently selected variable. Navigate to variable X using four presses on :

vars new 9

Note how the list starts scrolling up when the arrow reaches the bottom of the display. Variable X is now selected (arrow on the left). Note that annunciator ▼▲ indicates that the list can be browsed with nagivation keys. Long numbers are shown complete with SHOW (see Function SHOW to display long numbers for details).

Variable X is the last in the catalog; since the list wraps around when one end is reached, it would also have been possible to select variable X by pressing once.

From this catalog display, the selected variable can be copied to the x-register. Press ENTER to copy the value of the selected variable (variable X) to the x-register. This also exits the catalog and return to normal Calculator mode, with the stack display.

vars new 10
Variable X and the x-register are separate and unrelated. Although both are memory registers technically, the latter is a stack level and the former a variable.

6.4. STO and RCL arithmetic

This technique allows one to perform calculations directly using the x-register and a variable as operands, without the need to recall a variable.

6.4.1. Store arithmetic

STO arithmetic uses STO +, STO , STO ×, STO ÷, writes the result of the operation to the designated variable and leaves the x-register untouched.

Press STO +, and the calculator prompts for a variable name to store to:

vars new 11

Press [A]. The value in the x-register (1.41 if the example has been followed from the beginning) has been added to the number in variable A (value 5), and the result written there. Press RCL [A] to check. The value of variable A, now 6.41, is copied to the x-register:

vars new 12
operation effect

STO + variable

adds value in variable and x-register, overwrites variable with result

STO variable

subtracts x-register from value in variable, overwrites variable with result

STO × variable

multiplies value in variable by x-register, overwrites variable with result

STO ÷ variable

divides value in variable by x-register, overwrites variable with result

6.4.2. Recall arithmetic

RCL arithmetic uses RCL +, RCL , RCL ×, RCL ÷, writes the result of the operation to the x-register and leaves the designated variable untouched.

Press RCL +, and the calculator prompts for a variable name to recall from:

vars new 13

Press [B]. The value in variable B (value 60 if the example has been followed from the beginning) has been added to the number in the x-register, and the result written there. The x-register is now 66.41:

vars new 14
operation effect

RCL + variable

adds value in variable and x-register, overwrites x-register with result

RCL variable

subtracts value in variable from x-register, overwrites x-register with result

RCL × variable

multiplies value in variable by x-register, overwrites x-register with result

RCL ÷ variable

divides x-register by value in variable, overwrites x-register with result

6.5. Clearing variables

Single variable

Storing value zero in a variable clears it. Enter 0 STO [A]. Now open the variables catalog with MEM VAR. Variable A has been cleared and removed from the catalog:

vars new 15
Selected variable

It is possible to select the variable to delete from the variables catalog. Select the variable and press CLEAR. With the variables catalog still open (use MEM VAR if it has been closed), select variable P using navigation key . Press CLEAR. Variable P is deleted immediately.

vars new 16

This cannot be undone. Exit the catalog using C.

All variables

Press CLEAR VARS. All variables are deleted immediately. This cannot be undone. Check that the variables have been deleted with MEM VAR. The catalog is closed. Attention annunciator and message ALL VARS=0 appear:

vars new 17

Clear the message with C.

6.6. Exchanging any variable with x

Pressing x⇄ allows to exchange the contents of any variable with that of the x-register. Other stack registers y, z and t are not modifed.

Create variable F by pressing 5 STO [F]. Enter another value in the x-register, say 10:

vars new 18

Press x⇄ and the calculator prompts for a variable:

vars new 19

Press [F]. Values in the x-register and variable F are swapped:

vars new 20

Check this by pressing RCL [F]. Value in variable F is brought to the x-register:

vars new 21

6.7. Variable “i”

Variable i can store numbers just like any other variable. It is special only in the sense that function (i) uses value the of i when it is invoked. Function (i) allows for Indirect addressing of variables, described in the Programming techniques section.

7. Overview of math functions

Numbers must be on the stack before executing a function. Every function uses either one (x-register) or two (x- and y-registers) operands (except for some complex operations, which require all 4 stack registers). In the indications below, numbers are sometimes simply referred to as the register they are in, x or y.

7.1. Function preview/internal name

Keeping a key pressed displays the internal name of the function (the internal name is the one appearing in program listings or equations, and it isn’t necessarily the same as the labels printed on the keypad). For instance, keeping key √x pressed shows SQRT. Releasing the key executes the function. To prevent execution, hold the key, and after around about 2.5 seconds, the function name is replaced by NULL. Releasing the key now produces no effect.

7.2. One- VS two-number functions

7.2.1. One-number functions

Functions like +/—, √x, LN, ➞°F or 10ˣ use x as the operand. Enter the number and press the function key immediately. There’s no need to press ENTER beforehand.

For example, keystrokes to get the reciprocal of 8 are 8 1/x.

7.2.2. Two-number functions

Functions like ÷, ˣ√y, , y,x or ➞Θ,r use numbers from both x- and y-registers. Key in the first number, press ENTER, key in the second number and then press the function key.

For example, keystrokes to get the cube root of 27 are 27 ENTER 3 ˣ√y.

7.2.3. Order of numbers

For two-number operations, order must be observed in non-commutative functions. When using , the number in x is subtracted from the number in y. When using ÷, the number in y is divided by the number in x. Other functions, like , explicitly identify which number is where, on the stack (in this case, the number in y is elevated to the power of the number in x). If two numbers have been entered the wrong way around, they can be swapped before execution of the function with x⇄y.

7.3. Exponential and logarithmic

These are one-number functions. Key in the number and press the function key without using ENTER. The answer replaces the contents of the x-register.

LN

natural logarithmic (base-e)

LOG

common logarithmic (base-10)

natural exponential

10ˣ

common exponential

7.4. Power

x2

square x

√x

square root of x

elevate y to the power of x

ˣ√y

x-th root of y

7.5. Trigonometry

π

put π on the x-register
enables stack lift and terminates entry, i.e. no need to press ENTER to key in next number

MODES option

menu to set angular mode
360 degrees DG = 2π radians RD = 400 gradians GR
annunciators RAD and GRAD appear on the display in radians and gradians mode, respectively

SIN

sine of x

COS

cosine of x

TAN

tangent of x

ASIN

arc sine of x

ACOS

arc cosine of x

ATAN

arc tangent of x

7.6. Hyperbolic

These are one-number functions. Key in the number and press the function key without using ENTER. The answer replaces the contents of the x-register.

HYP SIN

hyperbolic sine of x

HYP COS

hyperbolic cosine of x

HYP TAN

hyperbolic tangent of x

HYP ASIN

hyperbolic arc sine of x

HYP ACOS

hyperbolic arc cosine of x

HYP ATAN

hyperbolic arc tangent of x

7.7. Percentage

Calculations are made using values in the x- and y-registers. The answer replaces the contents of the x-register, the y-register remains untouched.

y ENTER x %

x% of y

y ENTER x %CHG

percentage change from y to x

7.8. Conversions

7.8.1. Coordinates conversion

Calculations are made using values in the x- and y-registers.

➞Θ,r

from rectangular to polar

➞y,x

from polar to rectangular

Coordinates are measured as shown in the illustration below.

coords

When the coordinate is in rectangular format, the x-register contains the x-axis value and the y-register, the y-axis value. When the coordinate is in polar format, the x-register contains radius (r) and the y-register, the angle (Θ).

Angle Θ uses units set by the current angular mode. Results for angle Θ are between:

  • -180° and 180° degrees

  • -π and π radians

  • -200 and 200 gradians

Example
Considering the triangle below:

coords triangle 1

To find angle Θ and radius r in the above example, first make sure the unit is set to degrees mode with MODES DG. Then key in 3 ENTER 4:

polar 1

Then press ➞Θ,r:

polar 2

Angle Θ is placed in the y-register and radius r in the x-register.

7.8.2. Time conversion

These are one-number functions. Key in the number and press the function key without using ENTER. The answer replaces the contents of the x-register.

➞HR

from time or angle to decimal-fraction time (H.h) or angle (D.d)

➞HMS

from decimal-fraction time or angle to time (H.MMSSss) or angle (D.MMSSss)

The conversion works for time and clock angles from and to either of two number formats:

  • decimal: H.r, where the fractional part is a decimal fraction of an hour,

  • sexagesimal: H.MMSSss, where H represents hours, MM minutes, SS seconds and ss hundredths of seconds.

Here are some example calculations. To get the sexagesimal format of 3 1/3 hours, key in the fraction 3 1 3:

time 1

Now press ➞HMS and the calculator returns:

time 2

which is 3 hours, 20 minutes and zero second.

Practical example
If a constant power engine has a fuel consumption of 1.23 gallons per hour, and runs for 5 hours, 43 minutes and 21 seconds, the total fuel consumption can be calculated as follows. Key in 5 4 3 2 1 as in 5h 43m 21s:

time 3

Execute ➞HR to convert time value to decimal format:

time 4

Multiply by 1.23 gallons with 1 2 3 ×:

time 5

The engine run consumes about 7 gallons.

7.8.3. Angular conversion

These are one-number functions. Key in the number and press the function key without using ENTER. The answer replaces the contents of the x-register.

➞DEG

from radians to degrees

➞RAD

from degrees to radians

7.8.4. Unit conversions

These are one-number functions. Key in the number and press the function key without using ENTER. The answer replaces the contents of the x-register.

key press converts with operation

➞kg

from pounds to kilograms

×0.45359237

➞lb

from kilograms to pounds

×2.20462262…​

➞°C

from degrees Farenheit to degrees Celsius

×1.8 +32

➞°F

from degrees Celsius to degrees Farenheit

-32 ÷1.8

➞cm

from inches to centimeters

×2.54

➞in

from centimeters to inches

×0.39370079…​

➞l

from U.S. gallons to liters

×3.785411784

➞gal

from liters to U.S. gallons

×0.26417205…​

7.9. Probability

7.9.1. Factorial

Pressing x! calculates the factorial of number in the x-register and replaces it with the answer. The number in x must be a positive integer from 0 to 2123.

7.9.2. Gamma

To calculate the gamma function of a noninteger x, \$Γ(x)\$, key in (x-1) and press x!. The value for x cannot be a negative integer.

7.9.3. Probability menu

This menu is opened with PROB and provides with functions to calculate combinations and permutations. It also includes a RANDOM function which yields a sequence of pseudo-random numbers based on a seed, which can also be manually set. Here is a description of all four options from the menu:

menu label description

Cn,r

Combinations. Calculates the number of possible sets of n items taken r at a time. No item occurs more than once in a set, and sets with the same items but in different orders all count as 1. Enter n, then r and press PROB Cn,r.

Pn,r

Permutations. Calculates the number of possible arrangements of n items taken r at a time. No item occurs more than once in an arrangement, and arrangements with the same items but in different orders count separately. Enter n, then r and press PROB Pn,r.

SD

Seed. Stores number in the x-register as a new seed for the pseudo-random number sequence. See About pseudo-random number sequences below.

R

Random number. Puts the next pseudo-random number on the x-register. The number generated is in the range 0 ≤ x ≤ 1. See About pseudo-random number sequences below.

Combinations example
To win the Swiss national lottery, one must have ticked 7 winning numbers out of the available 50. A same number cannot be picked twice. To calculate the probability of picking the right combination, put the two operands on the stack with 5 0 ENTER 7:

prob 1

Select the Combinations option from the Probability menu with PROB Cn,r and the total number of combinations displays:

prob 2

Which means the chance to win the jackpot is a little over one in a hundred million.

Permutations example
A racing team with 4 drivers must set up a 3-driver strategy to take part in an edurance race. To calculate how many different parties and orders of driving are possible, put the two operands on the stack with 4 ENTER 3:

prob 3

Select the Permutations option from the Probability menu with PROB Pn,r and the total number of strategies displays:

prob 4

7.9.4. About pseudo-random number sequences

Function RANDOM, invoked using PROB R, uses a seed to generate a random number. This number becomes the seed for the next random number. Therefore, any sequence of random numbers can be reproduced that start with the same seed. A seed can be input manually by keying it in and using PROB SD.

7.10. Parts of numbers

This group of functions allows for retrieving the integer part, fractional part or absolute value of the number in the x-register. The answer replaces the x-register. These functions are sometimes useful when programming. The menu is opened with PARTS and shows three options:

menu label description

IP

Integer part. Returns the part of the number before the decimal separator.

FP

Fractional part. Returns the part of the number after the decimal separator.

ABS

Absolute. Returns the absolute value of number.

7.11. Rounding

Rounding function RND is called using RND. It truncates the internally stored number to the length set by the current Display format (see DISP menu).

Make sure the calculator is in FIX 4: press DISP FX 4. Put π on the stack, then press and hold SHOW:

round 1

Number π is stored internally in full 34-digit precision. Press RND and then, again, press and hold SHOW:

round 2

The internally stored number has been truncated to the number of digits set by function FIX. Change the display setting to a lower number, say DISP FX 2, and then execute RND and SHOW again to see the result.

Function RND is sensitive to fraction display and fraction display configuration. See Rounding fractions for details.

8. Complex numbers

The DM32 can use complex numbers in the rectangular form x + iy. For two complex numbers z1 and z2, the calculator can perform complex arithmetic:

  • z1 + z2

  • z1z2

  • z1 × z2

  • z1 ÷ z2

Complex trigonometry:

  • sin(z1)

  • cos(z1)

  • tan(z1))

As well as return negative, reciprocal, natural logarithm and natural exponential:

  • z1

  • 1/z1

  • ln z1

  • ez1

To enter a complex number:

  1. key in the imaginary part,

  2. press ENTER,

  3. key in the real part.

Complex numbers are handled by storing the real and imaginary parts separately on two stack registers. Thus, to enter two complex numbers, the four parts must be entered on stack registers x, y, z and t. To execute a complex operation, press CMPLX before the operator.

For example, to calculate (1 + i2) + (3 + i4) as z1 + z2, enter z1 by pressing 2 ENTER 1:

cmpx 1

Then enter z2 with ENTER 4 ENTER 3:

cmpx 2

Then press CMPLX to indicate that the next operation is complex:

cmpx 3

Then press the operator, +. The result is (4 + i6). The two parts of the answer are placed in the x- and y-registers :

cmpx 4
Remember to always enter the imaginary part first. The x- and z-registers contains the real parts, and the y- and t-registers the imaginary ones.

8.1. Complex operations

Complex operations are used just like real operations, only the operator must be preceded by CMPLX.

8.1.1. One-number complex operations

  1. Enter complex number z in two parts x + iy by keying in y ENTER x.

  2. Select one of the complex operators:

operation notation keystrokes

sign reversal

z

CMPLX +/–

reciprocal

1/z

CMPLX 1/x

natural logarithm

log z

CMPLX LN

natural exponent

ez

CMPLX

sine

sin(z)

CMPLX SIN

cosine

cos(z)

CMPLX COS

tangent

tan(z)

CMPLX TAN

8.1.2. Two-number complex operations

To perform two-number complex operations with numbers z1 and z2:

  1. Enter the first complex number z1 in two parts x1 + iy1 by keying in y1 ENTER x1 ENTER.

  2. Enter the second complex number z2 in two parts x2 + iy2 by keying in y2 ENTER x2.

  3. Select one of the complex operators:

operation notation keystrokes

addition

z1 + z2

CMPLX +

subtraction

z1z2

CMPLX

multiplication

z1 × z2

CMPLX ×

division

z1 ÷ z2

CMPLX ÷

power

z1 z2

CMPLX

8.2. Using complex numbers in polar notation

Applications which use real numbers in polar form use pairs of numbers — as do complex numbers — so it is possible to do arithmetic for those numbers using complex operations on the DM32. It must be remembered that, given how complex numbers work on the unit, the input must be converted to rectangular form prior to executing operations, and the output converted back to polar form.

[width=70%
\$a+ib=r(cos Theta + sin Theta) = re^(iTheta) = r angle Theta\$

Example: vector addition
Three loads add up to a single vector. Convert the polar coordinates to rectangular before calculations.

vectors cplx
keystrokes stack description

1.

MODES DG

sets degrees mode

2.

58 ENTER 103 y,x

t 0.0000
z 0.0000
y 87.3490
x 54.5817

enters L1 and converts it to rectangular form

3.

122 ENTER 194 y,x

t 87.3490
z 54.5817
y 164.5213
x –102.8043

enters L2 and converts it to rectangular form

4.

CMPLX +

t 87.3490
z 54.5817
y 251.8703
x –48.2227

adds L1 and L2

5.

253 ENTER 168 y,x

t 251.8703
z –48.2227
y –160.6592
x –49.1184

enters L3 and converts it to rectangular form

6.

CMPLX +

t 251.8703
z –48.2227
y 91.2111
x –97.3411

adds L3 to L1 and L2

7.

➞Θ,r

t 251.8703
z –48.2227
y 136.8621
x 133.3970

converts vector to polar coordinates
(only the x- and y-registers are affected)

9. Number bases

The BASE menu allows one to change the number base used to enter and display numbers.

menu label description

DEC

Decimal mode. No annunciator. Converts numbers to base-10. Numbers have an integer and a fractional part.

HX

Hexadecimal mode. Annunciator HEX turns on. Converts numbers to base-16. Uses integers only. Keys √x, , LN, , 1/x, Σ+ become digits A through F.

OC

Octal mode. Annunciator OCT turns on. Converts numbers to base-8. Uses integers only. Keys 8 and 9 are inactive.

BN

Binary mode. Annunciator BIN turns on. Converts numbers to base-2. Uses integers only. Keys other than 0 and 1 are inactive. If a number is longer than 12 digits, annunciators and/or turn on, and pressing keys √x or Σ+ allow for scrolling the display left or right, respectively.

Example conversions

Convert decimal number 12.34 to different bases:

keystrokes x-register description

1.

12.34 BASE HX

C

converts the integer part (12) and switched the display to base-16

2.

BASE OC

14

converts to base-8

3.

BASE BN

1100

converts to base-2

4.

BASE DEC

12.3400

converts back base-10; the fractional part has been preserved internally

Convert hexadecimal number 5A7F to different bases:

keystrokes x-register description

1.

BASE HX 5A7F

5A7F_

enters hexadecimal number 5A7F
(keys √x, , LN, , 1/x, Σ+ become digits A through F)

2.

BASE BN

101001111111

converts to base-2

3.

√x

101

scrolls the display left and shows the rest of the number

4.

Σ+

101001111111

scrolls the display right and returns to the first 12 digits of the number

5.

BASE DEC

23+167.0000

converts to base-10

9.1. Arithmetic in base-2, -8, and -16

Operations +, , ×, ÷ are available in any base. Functions √x, , LN, , 1/x, Σ+ are the only deactivated keys outside decimal mode. But it must be remembered that many operations might produce irrelevant results, since operations truncate the numbers to their integer part.

Conversion (switching from one base to another) only changes the display of the number. Its decimal version, with fractional part, is retained internally. But doing arithmetic when in any base other than decimal will truncate the numbers and lose their fractional part.

Arithmetic in bases 2, 8 and 16 is in 2’s complement form and uses integers only:

  • if a number has a fractional part, only the integer part is used for the calculation,

  • the result of an operation is always an integer (any fractional part is truncated).

If the result of an operation cannot be represented in 36 bits, message OVERFLOW is displayed, and the calculator shows the largest negative or positive number possible.

Examples of base-2, -8, -16 arithmetic

Calculate FF16 + 40016 :

keystrokes x-register description

1.

BASE HX FF ENTER

FF

sets base-16 and enters number FF16
(keys √x, , LN, , 1/x, Σ+ become digits A through F)

2.

400

400_

enters number 40016

3.

+

4FF

adds the two numbers and displays the result

Calculate 7128 – 568 :

keystrokes x-register description

1.

BASE OC

2377

enter a number convert it to, and set base-8

2.

712 ENTER

712

enter number 7128

3.

56

56_

enter number 568

4.

634

subtracts 568 from 7128 and displays the result

Calculate 3FD16 × 10112 :

keystrokes x-register description

1.

BASE HX 3FD

3FD_

sets base-16 and enters number 3FD16
(keys √x, , LN, , 1/x, Σ+ become digits A through F)

2.

BASE BN

1111111101

converts the displayed number to, and sets base-2; also terminates entry

3.

1011 ×

101111011111

enter number and multiply the two numbers to display the result; annunciator indicates number is longer that 12 digits

4.

√x

10

scrolls display to the left to see the rest of the number; annunciator turns on to indicate number isn’t complete as displayed

5.

Σ+

101111011111

scrolls display to the right, reverting to the previous view

6.

BASE HX

2BDF

switches display to base-16

7.

BASE DEC

11+231.000

switches display to decimal (base-10)

10. Statistics

One- or two-variable statistics data can be entered in the calculator This data set can then be analyzed in various ways by using functions in dedicated statistics menus.

10.1. Entering statistics data

Data is entered using key Σ+. The entered data is accumulated in 6 special statistics registers.

Before beginning a new set of data, always clear the statistics registers by pressing CLEAR Σ.

10.1.1. Entering one-variable data

  1. Key in the data point value and press Σ+,

  2. the calculator displays the value of n (register 28), which is the number of accumulated data points,

  3. repeat from 1. for each data point.

Note that the display of n replaces the contents of the x-register; to recall the just-entered value, use LASTx.

Σ+ actually always accumulates both x- and y-series of data; the y-series is simply ignored when subsequent statistical analysis is based on one-variable data points. It can still be reviewed but obviously has no meaning in such a context.

10.1.2. Entering two-variable data

When data consist of two variables, for each data point, x is the independent variable and y is the dependent variable. Because of how data lands on the stack, remember to enter an x,y pair in reverse order y,x, so that y ends up in the y-register and x in the x-register.

  1. Key in the y value first for the data point and press ENTER,

  2. then, key in the x value for the data point and press Σ+,

  3. the calculator displays the value of n (register 28), which is the number of accumulated two-variable data points,

  4. repeat from 1. for each two-variable data point.

10.1.3. Correcting data-entry errors

To correct an error, the wrong data point must be first deleted using key Σ–.

  1. Re-enter the data point to delete and press Σ–,

  2. enter the correct value(s) for the data point and press Σ+

The statistics registers are updated accordingly. For two-variable series of data, both the x- and y-values must be deleted and re-entered for the data point to correct.

If the wrong data point is the one just entered, simply press LASTx and Σ– (the incorrect y-value was still in the y-register and function LASTx recalls the x-value, which has been replaced by n, to the x-register).

10.2. Analyzing statistics data

The statistics menus in the DM32 provide functions to statistically analyze the accumulated set of one- or two-variable data:

10.2.1. Mean

The mean is the arithmetic average of a group of numbers. The available functions are:

  • x̄,ȳ returns the mean of the x-values,

  • x̄,ȳ returns the mean of the y-values,

  • x̄,ȳ x̄w returns the weighted mean of the x-values, using the y-values as weights. The weight value of each datapoint can also be an integer so as to use the y-value as the frequency of the associated x-value.

Example: mean
David intentionally drains various lithium cells to test for their capacity. 5 of them gave the following values in mAh (milliampere hour): 174, 182, 188, 194, 205.

Here is the way to find the average capacity of the tested units:

keystrokes x-register description

1.

CLEAR Σ

clear statistical data

2.

174 Σ+

1.0000

enters data and displays n

3.

182 Σ+

2.0000

4.

188 Σ+

3.0000

5.

194 Σ+

4.0000

6.

205 Σ+

5.0000

7.

x̄,ȳ

188.6000

mean capacity of the tested cells

Example: weighted mean
Michael purchases the same semiconductor component every year. After 5 years, he has accumulated the following data.

number of pieces price per piece [$]

500

6.15

1300

4.80

800

5.55

2200

4.50

1250

5.70

To find the average price for this component across the years, and taking into account the quantity for each purchase, proceed like so:

keystrokes x-register description

1.

CLEAR Σ

clear statistical data

2.

500 ENTER 6.15 Σ+

1.0000

enters data and displays n

3.

1300 ENTER 4.8 Σ+

2.0000

4.

800 ENTER 5.55 Σ+

3.0000

5.

2200 ENTER 4.5 Σ+

4.0000

6.

1250 ENTER 5.7 Σ+

5.0000

7.

x̄,ȳ x̄w

5.0876

mean price weighted for the quantity purchased

8.

SUMS y

6050.0000

total quantity of components purchased

10.2.2. Standard deviation

Standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean (“variability”). A low number means data are clustered about the mean, and high standard deviation indicates data are more spread out. More specifically, an empirical rule states that 68% of the collected data points fall around the mean plus or minus the standard deviation value. The calculator can compute standard deviation in two ways:

  • Population standard deviation assumes the data being analyzed is the complete set.

  • Sample standard deviation assumes the data being analyzed is a sample of a larger set. It uses a slightly different formula because it would otherwise give a consistently underestimated variability. By making the deviation value artificially larger, sample standard deviation, while not unbiased, gives a more accurate inference for the partial set.

Example
Using the lithium cell capacity test example above, here is how to calculate standard deviation:

keystrokes x-register description

1.

CLEAR Σ

clear statistical data

2.

174 Σ+

1.0000

enters data and displays n

3.

182 Σ+

2.0000

4.

188 Σ+

3.0000

5.

194 Σ+

4.0000

6.

205 Σ+

5.0000

7.

x̄,ȳ

188.6000

mean capacity of the tested cells

8.

S,σ σx

10.5376

population standard deviation

This indicates that 68% of the tested cells have a capacity equalling the mean, plus or minus the standard deviation, that is to say between approximately 178 and 199 mAh.

Pressing S,σ sx returns the sample standard deviation, estimating the spread for a hypothetical larger set:

s sdev

10.2.3. Linear regression

Linear regression is a statistical method to find a straight line that fits the points on a graph drawn using values from the x- and y-series of data. The available functions are:

  • L.R. ̂x predicts x for a given y-value (which is on the x-register of the stack),

  • L.R. ̂y predicts y for a given x-value (which is on the x-register of the stack),

  • L.R. r returns the correlation coefficient, which varies between –1 and +1 and measures how closely the calculated line fits the points on the graph,

  • L.R. m returns the slope of the calculated line,

  • L.R. b returns the y-intercept of the calulcated line, which is the value of y when x = 0.

Example
Bob has been going on the same hike for a few years and has accumulated hike time and ambient temperature data.

time [decimal format] ambient temp [°F]

3.45

59

3.79

69

3.82

85

4.01

89

4.30

100

Here is how to enter and analyze this dataset.

keystrokes x-register description

1.

CLEAR Σ

clear statistical data

2.

3.45 ENTER 59 Σ+

1.0000

enters data and displays n

3.

3.79 ENTER 69 Σ+

2.0000

4.

3.82 ENTER 85 Σ+

3.0000

5.

4.01 ENTER 89 Σ+

4.0000

6.

4.30 ENTER 100 Σ+

5.0000

7.

L.R. r

0.9465

correlation coefficient; here the data approximate a straight line

8.

L.R. m

0.0181

slope of the line

9.

L.R. b

2.4198

y-intercept (value of y when x = 0)

lr

To estimate how long the hike would take if ambient temprature was 110°F based on the accumulated data, key in 1 1 0 and then invoke the y-estimation function L.R. ̂y. The calculator returns the estimated y-value:

lr 1

Convert the result to sexagesimal format with ➞HMS. The answer is a little over 4 hours and 24 minutes:

lr 2

About the correlation coefficient
As explained above, L.R. r returns the correlation coefficient, which is a value between –1 and 1. Here is what this number means in more detail.

correlation coefficient meaning

1

perfect positive correlation; when variable x increases, variable y increases too, in a linear fashion

0

no correlation, or zero correlation; there is no apparent relationship between the x and y values

–1

perfect negative correlation; when variable x increases, variable y decreases, in a linear fashion

coefficient

10.3. Summation values and statistics registers

The statistics registers are special memory locations which store the accumulated statistics data and associated products. Values in these registers are automatically updated when accumulating statistical data using the Σ+ key.

sum register number description

n

28

number of accumulated data points

Σx

29

sum of x-series of data

Σy

30

sum of y-series of data

Σx2

31

sum of the squares of x-series of data

Σy2

32

sum of the squares of y-series of data

Σxy

33

sum of the products of x- and y-series of data

There are three ways to recall values from these registers:

  • Invoking the SUMS menu.

  • Invoking the variable catalog of the MEM menu with MEM VAR. Pressing ENTER puts the selected register’s stored value on the stack’s x-register.

  • Using indirect addressing: store the desired register number in variable i (for instance, for Σx2, press 3 1 STO [i]) and then recall it by using RCL [(i)].

11. Equations

The DM32 allows for writing, storing and editing stored equations. A stored equation can then be either:

  • evaluated

  • solved for an unknown variable

  • integrated as a function

This chapter explains how equations work in detail. For a recap and/or general description of how to work with equations on the DM32, see Equations in a nutshell.

11.1. About backing up and restoring equations

To backup and restore equations to and from external media, use States. Read chapter Calculator State where it is shown how the Equation list can be stored on the internal USB disk as part of an ASCII text file with extension *.d32.

11.2. Practical example of equation evaluation

Before getting into the nuts and bolts of equations as exposed in this chapter, let’s have a general look at how an equation can be put to use on the DM32. Suppose it is frequently needed to determine the volume of a sphere cap.

sphere cap
\$V = π × H^2 × ( R - H / 3 )\$

Note that this equation is of the assignment-type. In the equation, \$R\$ is the radius of the sphere and \$H\$ and \$V\$ are the height and volume of the cap, respectively. The calculation could very well be keyed in manually over and over. For instance, for the cap of height 2.75 meters from a sphere of radius 17.3 meters:

  π 2.75 x² × 17.3 ENTER 2.75 ENTER 3 ÷ ×

Instead, the relationship between sphere radius and cap height and cap volume can be stored in an equation and queried as many times as necessary. Here is a step-by-step description of how to enter and evaluate this example equation:

keystrokes x-register description

1.

EQN

EQN LIST TOP

summon Equation list; annunciator EQN turns on

2.

RCL [V]

V█

start new equation and enter letter V

3.

=

V=█

insert equal sign

4.

π × x²

V=π×SQ(█

x² is SQ(x) in algebraic

5.

RCL [H] )

V=π×SQ(H)█

enter letter H and close parenthesis

6.

× ( RCL [R]

=π×SQ(H)×(R█

equation exceeds display width and starts scrolling; annunciator turns on

7.

RCL [H] ÷ 3 )

(H)×(R–H÷3)█

finish equation; H÷3 is evaluated before subtraction from R

8.

ENTER

V=π×SQ(H)×(R

terminate entry; annunciators 🠷 and turn on to show that equation can be scrolled with √x and Σ+

The equation is now part of the Equation list. To immediately evaluate it:

keystrokes x-register description

1.

ENTER

H?value

prompt for cap height (variable H could be non-zero depending on previous calculator use)

2.

2.75

H? 2.75_

enter value for cap height

3.

R/S

R?value

store H; prompt for sphere radius (variable R could be non-zero depending on previous calculator use)

4.

17.3

R? 17.3_

enter value for sphere radius

5.

R/S

V=389.2401

store R; calculate volume V in cubic meters and store value in variable V

The process can be easily repeated for other cap height and sphere volume values: since, when summoned, the Equation list opens where it was last used, it only takes EQN ENTER to restart evaluation of the same equation.

11.3. Types of equations

There are three types of equations:

Equality

Contains symbol “=” and the left side of the equation contains more than one variable. Example: \$A + B^2 = C^3\$

Assignment

Contains symbol “=” and the left side of the equation contains only one variable. Example: \$A = W*L\$

Expression

Contains no “=” symbol. Example: \$sqrt(N) + 4\$

Equations evaluate differently according to their type, but it can be typically said that solving for an unknown variable requires equality- or assignment-type equations, whereas integration uses expression-type equations.

11.4. Viewing and selecting equations

The Equation list contains the equations entered. There, it is possible to review equations and select one to work with.

11.4.1. To display and select an equation

  1. Press EQN to summon the Equation list.

  2. Press or to move up or down the Equation list. The cursor on the left shows the currently selected equation. (The image below assumes several equations have been entered in the calculator.)

    eqn list select

EQN LIST TOP represents the top of equation memory. Scrolling down past the last equation in the list rolls back to EQN LIST TOP. Conversely, scrolling up past this line wraps around to the last equation in the list.

If the Equation list is empty, only line EQN LIST TOP displays. See Writing equations to add an equation to the list.

11.4.2. To view a long equation by scrolling

  1. Select the equation in the Equation list (see above). The display can only show the first 12 characters from an equation. When the equation is longer, annunciator turns on. Annunciator 🠷 also turns on, meaning that Σ+ can be used to scroll the equation.

  2. Press Σ+ to scroll the equation and show the next character to the right. Annunciator turns on too, meaning there are characters off-screen to the left. Scroll the opposite direction to the left with √x. Annunciator or turns off to point out that the beginning or end of the equation has been reached.

Equation scrolling can be deactivated with SCRL. The equation is scrolled back to its beginning and annunciator 🠷 is turned off. Top row keys √x LN 1/x Σ+ now perform their normal, non-shifted function. Scrolling must be turned off this way to enter a new equation starting with one of these functions, like LN, for instance.

Example: scrolling an equation
To view the equation entered in the above Practical example of equation evaluation:

keystrokes x-register description

1.

EQN

V=π×SQ(H)×(R

summon the Equation list;
annunciator EQN turns on

2.

/ or F5 / F6

may be used to browse the Equation list;
if the currently selected equation is too long for the display, annunciators 🠷 and turn on

3.

Σ+ Σ+

π×SQ(H)×(R–H

scroll two characters to the right;
annunciators 🠷 and turn on

4.

√x

=π×SQ(H)×(R–

scroll one character to the left

5.

C

close the Equation list

The “scroll state” of an equation in the list remains the same as is as long as the equation is selected.

11.4.3. To view a long equation using SHOW

A long equation can also be displayed by holding down SHOW while viewed in the Equation list (for details on function SHOW, see Function SHOW to display long numbers).

The image below demonstrates the SHOW box used on the TVM equation, described later in this manual.

show eqn

11.5. Evaluating equations

Equations can be evaluated, that is, return a numeric result. If the equation contains an equal “=” sign, its basic value is the difference between the values of the two sides. The equal “=” is treated as a minus “–”, and the result of this subtraction is a measure of how well the equation balances.

The DM32 uses two keys to evaluate an equation: XEQ and ENTER. Their function differs only when evaluating an assignment-type equation:

  • XEQ returns the value of the equation, regardless of its type;

  • ENTER does the same thing, except for an assignment-type equation. In this case:

    • only the value of the right side is returned, and

    • that value is stored into the variable of the left side (just like STO variable).

type of equation example result for ENTER result for XEQ

equality

\$x^2 + y^2 = r^2\$

\$x^2 + y^2 - r^2\$ (same as XEQ)

\$x^2 + y^2 - r^2\$ (same as ENTER)

assignement

\$A = π*r^2\$

\$π*r^2\$

\$A - π*r^2\$

expression

\$π*2*r\$

\$π*2*r\$ (same as XEQ)

\$π*2*r\$ (same as ENTER)

Also stores the result in the variable on the left of the equal “=” sign (A in this example).

To evaluate an equation:

  1. Select the desired equation (see Viewing and selecting equations above).

  2. Press ENTER or XEQ. The equation prompts for the value of each variable. Base is automatically returned to base-10.

  3. For each prompt, there are two possible actions (see How equation prompts work for more detail):

    • if the displayed value is correct, press R/S,

    • if another value is to be entered either:

      • enter the new value directly and press R/S, or

      • make a calculation to get the new value, for instance 6 ENTER 7 ÷ and then press R/S.

Evaluation of an equation makes no use of numbers currently on the stack. It only uses values from the equation itself and from variables. The value of the equation is returned to the x-register. Register LASTx is unaffected.

When the equation is part of a program, it is evaluated using the XEQ function as described above.

11.5.1. Evaluation using ENTER

With the Equation list open, the currently selected equation can be evaluated by pressing ENTER. (While writing an equation, key ENTER terminates entry and saves the equation, it doesn’t evaluate it.)

  • For an assignment-type equation, the value of the left-hand variable is found. Here is what happens:

    • only the right-hand side is evaluated,

    • the result is returned to the x-register,

    • the result is stored into the left-hand variable,

    • the left-hand variable is displayed automatically using function VIEW (which doesn’t affect the stack).

  • For equality- or expression-type equations, the entire equation is evaluated (just like when using XEQ). The result is returned to the x-register.

See Practical example of equation evaluation for a demonstration.

11.5.2. Evaluation using XEQ

With the Equation list open, the currently selected equation can be evaluated by pressing XEQ. The entire equation is evaluated, regardless of the type of equation. The value of the equation is returned to the x-register.

11.5.3. How equation prompts work

When equations are evaluated, a prompt appears for each needed variable. The prompt shows the variable name and its currently stored value, for instance X?3.1416. From here, there are several options.

  • Leave this number unchanged and proceed with the calculation
    Press R/S.

  • Change the number
    Key in the new number and press R/S. This new number overwrites the x-register. A number can be entered as a fraction if required.

  • Calculate a new number
    Use the keypad as in a normal calculation, then press R/S. For instance, 8 ENTER 7 ÷ R/S.

  • Calculate using the displayed number
    Press ENTER before entering another number (because a new number entered here overwrites the x-register, and thus the former number is lost).

  • Cancel the prompt
    Press C. The current value of the variable is left on the x-register. If pressed during digit-entry (underline cursor _ on), C resets the number to zero. Pressing C again cancels the prompt.

  • Display digits hidden by the prompt
    Press SHOW.

11.6. Writing equations

To write an equation, the calculator must be out of any special mode (i.e. have the stack displayed).

  1. Press EQN to summon the Equation list (annunciator EQN turns on).

  2. Start writing the equation.

  3. The new equation is inserted in the list, on the line immediately following the position of the cursor at that moment. The other lines are greyed out.

    eqn list edit
  4. Errors can be corrected by pressing .

  5. Equation entry is terminated by pressing ENTER. Block cursor disappears. If the equation is longer than the display, the equation is scrolled back to its beginning.

  6. This new equation is immediately saved into the Equation list.

Note that pressing C saves the equation into the list but also leaves equation entry.

Equations may contain variables, numbers, functions and parentheses. To enter a letter, press RCL before using the desired letter-key. To insert a space, use [SPACE] (i.e. key R/S without pressing RCL beforehand).

If the equation being entered becomes longer than what the display can show, the equation moves out of view towards the left and annunciator appears to indicate that the display has started scrolling. The length of an equation is limited only by available memory.

See Practical example of equation evaluation for a step-by-step demonstration of equation entry.

Since equations aren’t evaluated when added to the Equation list, they can contain any sequence of characters. This can be put to use to create custom messages to display in a program.

11.6.1. Variables in equations

Any of the 28 calculator variables — from A through Z, plus i and (i) — can be entered into an equation, as many times as necessary. (See Indirect addressing for information about i and (i)). To enter a variable, press RCL variable or STO variable. When RCL or STO is pressed, annunciator A..Z is lit to indicate that the next key press will invoke a letter (printed in white on the keypad bezel).

11.6.2. Numbers in equations

Any base-10 number can be entered in an equation. Numbers in equations are always shown in ALL display format.

Numbers are entered like in normal operation with usual number keys and , E and +/–. To enter a negative number, key in at least the first digit of the number before pressing +/–.

When number entry starts, block cursor changes to _, indicating active number entry. It returns to when the next non-number key is pressed.

11.6.3. Functions in equations

Many of the DM32’s functions can be used in an equation. See the complete list of available functions below, or the Appendix D: Functions index, which gives this information as well.

Functions in equations are used much like they would in an algebraic equation. But each function uses either one of the two possible notations:

  • Infix, where the function is written between its arguments, like “+” or “÷”. These are typed in natural algebraic order.

  • Prefix, where one or more arguments are written after the function name, like “COS” or “LN”. These must be entered where they are needed in the equation, and an opening parenthesis is automatically added to the right, after which its argument(s) can be typed.

    For functions with more than one argument, separate them using [SPACE] (R/S). If the function is followed by other operations and/or arguments, close the parenthesis with ).

When viewing the Equation list, if the currently selected equation is too long to display entirely, annunciators 🠷 and are turned on. In this condition, top row keys √x Σ+ are functional for scrolling the equations, and other top row keys LN 1/x are deactivated. If a new equation starting with one of these functions (like LN, for instance) is to be added to the Equation list, these function keys must be reactivated and annunciators turned off with SCRL.

11.6.4. Parentheses in equations

Parentheses in equations can be used to control the order of operations when normal operator precedence isn’t adequate.

Use ( and ) to enter parentheses.

Expression \$A(B(C+1))\$, requires parentheses to evaluate correctly. Here is how to enter it:

keystrokes selected line description

1.

EQN

EQN LIST TOP
or current equation

summon the Equation list

2.

RCL [A] ×

A×█

begin writing equation; note that multiplication is not implicit, operator × must be used

3.

( RCL [B] × (

A×(B×(█

enter opening parentheses

4.

RCL [C] + 1

A×(B×(C+1█

finish equation

5.

) )

A×(B×(C+1))█

close parentheses (optional)

6.

ENTER

A×(B×(C+1))

terminate and save equation

Trailing, closing parentheses are optional. In the above example, entering the equation as A×(B×(C+1 is valid syntax.

11.7. Equations syntax

Valid syntax of equations on the DM32 is determined by a set of conventions defining:

  • how operators interact,

  • validity of a function when used in an equation,

  • how equations are checked for syntax errors.

11.7.1. Operator precedence

Operators are processed in a definite order. This makes for a logical and predictable evaluation.

order operator example

1.

functions and parentheses

COS(X+1), (X+1)

2.

unary minus (+/–)

–R

3.

power ()

A^3

4.

multiply and divide

X×Y, P÷R

5.

add and subtract

A+B, S–T

6.

equality

Y=Z

The syntax check doesn’t validate implied multiplication. For instance, expression \$R(3–S)\$ must be written as R×(3–S), with the explicit × operator before the parenthesis.

11.7.2. Equation functions

All the functions listed below are valid in equations. The same information can be found in the Appendix D: Functions index.

LN

LOG

EXP

ALOG

SQ

SQRT

INV

IP

FP

RND

ABS

x!

SIN

COS

TAN

ASIN

ACOS

ATAN

SINH

COSH

TANH

ASINH

ACOSH

ATANH

→DEG

→RAD

→HR

→HMS

%CHG

XROOT

Cn,r

Pn,r

→KG

→LB

→°C

→°F

→CM

→IN

→L

→GAL

RANDOM

π

+

×

÷

^

sx

sy

σx

σy

w

̂x

̂y

r

m

b

n

Σx

Σy

Σx2

Σx2y2

Σxy

For convenience, prefix-type functions (which require one or two arguments), automatically add the left parenthesis when invoked.

11.7.3. Two-argument functions in equations

The prefix functions that require two arguments are

  • %CHG

  • XROOT

  • Cn,r

  • Pn,r

The two arguments must be separated with a space (invoked with key R/S).

Function XROOT takes arguments in the reverse order compared to normal RPN usage. For example, RPN’s 5 ENTER 3 ˣ√y is equivalent to XROOT(3 5) in an equation.

The other two-argument functions take arguments in the same Y, X order as with RPN. For example, RPN’s 50 ENTER 7 Cn,r is equivalent to Cn,r(50 7) in an equation.

Pay special attention if the second argument is negative: it must not start with “subtraction” ().

  • For a number, use +/–.

  • For a variable, use parentheses and .

As is illustrated in these two valid equations:

  • %CHG(–X 2)

  • %CHG(X (–Y))

11.7.4. Differing function names in equations

Six of the equation functions have names that differ from their equivalent RPN operations:

RPN operation equation name

x2

SQ

ex

EXP

10x

ALOG

1/x

INV

ˣ√y

XROOT

^

11.8. Editing equations

Saved equations can be edited.

  1. Select an equation from the Equation list.

  2. Press . Block cursor appears at the end of the equation. The other lines are greyed out. (The display is scrolled to the right end of the equation if longer than 12 characters).

  3. Use to backspace until the desired part of the equation is reached.

  4. Rewrite from there. When typing a number, block cursor changes to number entry cursor _ and deletes the number digit by digit. When the number is entirely deleted, number entry cursor _ is changed back to block cursor .

  5. Press ENTER to save the equation (C also saves the equation but additionally closes the Equation list).

11.9. Deleting equations

Entire equations can be deleted.

  1. Select an equation from the Equation list.

  2. Press CLEAR.

  3. The equation is deleted immediately. This cannot be undone.

12. Solving equations

In the above example, Practical example of equation evaluation, is shown how ENTER may be used to find the value of the left-hand variable in an assignment-type equation. Function SOLVE can be used to find the value of any of the variables in any type of equation.

For instance, in the formula:

\$(V/R)=0.75\$

if value of V is known, then SOLVE can solve for R. Conversely, if R is known, SOLVE can solve for V. Some equation terms can be replaced by words to make them easier to understand:

\$"volts" ÷ "resistance" = "current"\$

Knowing any two of these variables makes it possible for function SOLVE to find the unknown third.

12.1. Basic principle of SOLVE

When the equation has only one variable, or when known values are supplied for all variables except one, then to solve for x is to find a root of the equation. Considering the various equation-types, a root of an equation occurs:

  • where an equality- or assignment-type equation balances exactly, or

  • where an expression-type equation equals zero.

This is equivalent to the value of the equation being zero.

The SOLVE algorithm’s behavior is always determined by user-fed initial guesses. While these initial guesses may be ignored, different guesses can lead to different SOLVE results.

12.2. Solving an equation

To solve for an unknown variable in an equation:

  1. Press EQN and select the desired equation, or write the equation.

  2. Press SOLVE and then the letter-key of the unknown variable. Function then prompts for every other variable in the equation.

  3. For each prompt, there are two possible actions (see How equation prompts work for more detail):

    • if the displayed value is correct, press R/S,

    • if another value is to be entered either:

      • enter the new value directly and press R/S, or

      • make a calculation to get the new value, for instance 6 ENTER 7 ÷ and then press R/S.

  4. When the last known variable value has been entered, SOLVE immediately starts searching for a root after pressing R/S.

The running SOLVE can be interrupted with C or R/S.

When the root is found, it is stored in the unknown variable, and the variable value is automatically displayed with function VIEW. In addition, the stack registers contain SOLVE-related values:

x-register

root

y-register

previous estimate (see Understanding and controlling SOLVE)

z-register

value of the equation at the root, which should be zero

It can happen, under complicated mathematical conditions, that a definitive solution cannot be found. When so, the calculator displays NO ROOT FND. See Verifying the result later in this chapter.

For certain equations it helps to provide one or two initial guesses for the unknown variable before solving the equation. This can speed up the calculation, direct the answer toward a realistic solution, and find more than one solution, if appropriate. See Choosing initial guesses for SOLVE later in this chapter.

Example: equation of linear motion
The equation describing motion of a free-falling object is

\$d = v_0 t + 1/2 g t^2\$

where \$d\$ is the distance, \$v_0\$ is the initial velocity, \$t\$ is the time and \$g\$ is the acceleration imposed by gravity.

Here is how to type in the equation (on how to type letters see Writing equations):

keystrokes selected line description

1.

CLEAR ALL Y

clear the calculator

2.

EQN

open the Equation list

3.

RCL [D] = RCL [V] × RCL [T] +

D=V×T+█

4.

.5 × RCL [G] × RCL [T] 2

T+0.5×G×T^ 2_

5.

ENTER

D=V×T+0.5×G×T

terminate and save equation

\$g\$ is written as a variable so it is possible to express the acceleration of gravity in different units (for instance, 9.8 m/s2 or 32.2 ft/s2).

How many meters will an object fall in 4 seconds, starting from rest? With the equation selected in the list, solve for variable D:

keystrokes selected line or x-register description

1.

SOLVE

SOLVE _

prompt for unknown variable

2.

[D]

V?0.0000

select D; prompt for V

3.

0 R/S

T?0.0000

store 0 in V; prompt for T

4.

4 R/S

G?0.0000

store 4 in T; prompt for G

5.

9.8 R/S

SOLVING

store 9.8 in G; solve for D

6.

D=78.4000

answer is 78.4 meters

Use the same equation to answer a different question: how long does it take for an object to fall 450 meters from rest?

keystrokes selected line or x-register description

1.

EQN

D=V×T+0.5×G×T

open Equation list

2.

SOLVE [T]

D?78.4000

solve for T; prompt for D

3.

450 R/S

V?0.0000

store 450 in D; prompt for V

4.

R/S

G?9.8000

keep 0 in V; prompt for G

5.

R/S

SOLVING

keep 9.8 in G; solve for T

6.

T=9.5831

answer is 9.5831 seconds

Example: equation of the ideal gas law
The equation characterizes the relationship between pressure, volume, temperature, and the amount (moles) of an ideal gas.

\$P × V = N × R × T\$

where \$P\$ is pressure (in atmospheres or N/m2), \$V\$ is volume (in liters), \$N\$ is the number of moles of gas, \$R\$ is the universal gas contant (0.0821 liter-atm/mole-K or 8.314 J/mole-K) and \$T\$ is temperature (in Kelvins, where K = °C + 273.1).

Here is how to type in the equation (on how to type letters see Writing equations):

keystrokes selected line description

1.

EQN RCL [P] ×

P×█

open Equation list and begin new equation

2.

RCL [V] = RCL [N] ×

P×V=N×█

3.

RCL [R] × RCL [T]

P×V=N×R×T█

4.

ENTER

P×V=N×R×T

terminate and save equation to the list

A 2-liter bottle contains 0.005 moles of carbon dioxide at 24 °C. Assuming it behaves like an ideal gas, calculate its pressure. With the equation in display, solve for variable P:

keystrokes x-register description

1.

SOLVE [P]

V?value

solve for P; prompt for V

2.

2 R/S

N?value

store 2 in V; prompt for N

3.

.005 R/S

R?value

store 0.005 in N; prompt for R

4.

.0821 R/S

T?value

store 0.0821 in R; prompt for T

5.

24 ENTER 271.3 +

T?295.3000

calculate T (Kelvins)

6.

R/S

SOLVING

store 297.1 in T; solve for P

7.

P=0.0606

answer is 0.0606 atmospheres

A 5-liter vessel contains nitrogen gas at a pressure of 0.5 atmospheres when the tempreature is 18 °C. To calculate the density of the gas (i.e. \$N × 28 ÷ V\$, where 28 is the molecular weight of nitrogen):

keystrokes selected line or x-register description

1.

EQN

P×V=N×R×T

open Equation list

2.

SOLVE [N]

P?0.0606

solve for N; prompt for P

3.

. 5 R/S

V?2.0000

store 0.5 in P; prompt for V

4.

5 R/S

R?0.0821

store 5 in V; prompt for R

5.

R/S

T?295.3000

keep 0.0821 in R; prompt for T

6.

18 ENTER 271.3 +

T?289.3000

calculate T (Kelvins)

7.

R/S

SOLVING

store 289.3 in T; solve for N

8.

N=0.1053

answer is 0.1053 moles

9.

28 ×

2.9472

calculate mass in grams (\$N × 28\$)

10.

RCL [V] ÷

0.5894

calculate density in grams per liter

12.3. Understanding and controlling SOLVE

SOLVE uses an iterative procedure to solve for the unknown variable. It starts by evaluating the equation using two initial guesses for the unknown variable. Using the results based on those two guesses, SOLVE generates another, better guess. Through successive iterations, SOLVE finds a value for the unknown that makes the value of the equation equal to zero. When SOLVE evaluates an equation, it does it the same way XEQ does — any equal sign “=” in the equation is treated as a minus “–”. For example, the Ideal Gas Law equation is evaluated as \$P × V – (N × R × T)\$. This ensures that an equality- or assignment-type equation balances at the root, and that an expression-type equation equals zero at the root (see Types of equations).

Some equations are more difficult to solve than others. In some cases, initial guesses are needed in order to find a solution (see Choosing initial guesses for SOLVE below). When SOLVE can’t find a solution, the calculator displays NO ROOT FND.

12.3.1. Verifying the result

When function SOLVE ends, values are left for review in the x-, y- and z-register to verify that the answer is indeed a solution. To consult the registers, first press C to clear the variable shown by automatically invoked function VIEW.

  • The x-register contains the solution (root) for the unknown. It’s the value which makes evaluation of the equation equal to zero.

  • The y-register contains the previous estimate for the root. This should be the same number as the value in the x-register. If not, then the root found is only an approximation, and the actual solution is somewhere between values in the x- and y-registers. They should be close together.

  • The z-register contains the value of the equation at the root. This number is zero for an exact root. If it is not, then the root found is only an approximation. It should be close to zero.

If SOLVE ends with message NO ROOT FND, the calculator could not converge on a root. The final estimate of the root is in the x-register, just press C to clear the message. Values in the x- and y-registers bracket the interval that was last searched to find the root. The z-register contains the value of the equation at the final estimate.

These numbers are interpreted so:

  • If the x- and y-register values aren’t close together, or the z-register value isn’t close to zero, the estimate from the x-register probably isn’t a root.

  • If the x- and y-register values are close together, and the z-register value is close to zero, the estimate from the x-register may be an approximation to a root.

12.3.2. Interrupting function SOLVE

A SOLVE calculation can be interrupted at any time using C or R/S. The current estimate of the root is stored in the unknown variable. Use VIEW to display its contents without touching the stack.

12.3.3. Choosing initial guesses for SOLVE

The calculator always uses these numbers as initial guesses:

  • value currently stored in the unknown variable,

  • value in the x-register.

If only one guess is entered and stored in the unknown variable just before the call to SOLVE, then both guesses are the same, since the value stored in the unknown variable is also left in the x-register.

Entering meaningful guesses has the following advantages:

  • By narrowing down the range of values to search, calculation time can be reduced.

  • If there is more than one mathematical solution, guesses can direct the solution algorithm to the desired answer. For instance, the equation of linear motion
    \$d = v_0 t + 1/2 g t^2\$
    can have two solutions for \$t\$. With appropriate guesses, the answer can be directed towards the only meaningful one, which is greater than zero.
    The example using this equation earlier in this chapter didn’t require entering guesses before solving for T because a realistic value for T had been entered when solving for D, so that could be used as a valid guess.

  • If an equation does not allow certain values for the unknown, guesses can prevent these values from occurring. For example
    \$y = t + log x\$
    produces an error if \$x <= 0\$, either LOG(0) or LOG(NEG).

The set of initial guesses determines the SOLVE algorithm’s domain of convergence. Those initial guesses are required and used, even when ignored. Ignoring the initial guesses and using whatever values are left in the x-register and unknown variable may lead to apparently random behavior on the part of the SOLVE algorithm.
The DM32 SOLVE algorithm is deterministic: for a given equation or expression, the same initial guesses will yield the same results.

The equation in the following example can have more than one root. Guesses help find the desired root.

Example: using guesses to find roots
Using a rectangular piece of sheet metal 60 × 50 cm, form an open-top box having a volume of 7500 cm3. The unknown value is the height of the box — in other words, the width of the flaps to fold up along each of the four sides.

eqn solve box

Given height \$H\$, the length of the box is \$(60-2H)\$ and the width is \$(50-2H)\$. The volume is then:

\$V = (60-2H) × (50-2H) × H\$

which may be simplified as

\$V = (30-H) × (25-H) × 4 × H\$

Here is how to type in the equation (on how to type letters see Writing equations):

keystrokes selected line description

1.

EQN RCL [V] =

V=█

open Equation list and begin new equation

2.

( 30 RCL [H] )

V=(30-H)█

3.

× ( 25 RCL [H] )

0-H)×(25-H)█

4.

× 4 × RCL [H]

×(25-H)×4×H█

5.

ENTER

V=(30-H)×(25

terminate and save equation to the list

For the same volume, two different shapes are possible for the box to be formed: either tall and narrow, or short and flat. To get the height of the taller box, large initial guesses should be used. It is however clear that the height cannot exceed 25 cm, since the sheet is only 50 cm wide. Therefore, 15 an 25 are appropriate initial guesses.

keystrokes selected line or x-register description

1.

C

close Equation list

2.

15 STO [H] 25

25_

store lower estimate in unknown variable and put higher estimate on x-register

3.

EQN

V=(30-H)×(25

open Equation list

4.

SOLVE [H]

V?value

solve for H; prompt for V

5.

7500 R/S

SOLVING

store 7500 in V; solve for H

6.

16.5739

answer is 16.5739 cm3

Solving algorithm is probably too fast for message SOLVING to show and possibly only the answer is visible.

Use the information stored in the stack registers to verify the accuracy of this solution.

keystrokes x-register description

1.

R↓

16.5739

shows value left by SOLVE in the y-register, which is the estimate found by the algorithm just before the final result; since this is the same as the solution left in the x-register after calculation, this solution is an exact root

2.

R↓

0.0000

shows value left by SOLVE in the z-register, which shows the value of the equation at the root; a result of zero confirms the accuracy of the found root

The height of the flatter version of the box can be found by entering lower guesses, like 0 and 15 cm, which converge to 3.2127 cm. If estimates are higher, for instance 40 and 50 cm, then the solution is a physically meaningless height of 35.2134 cm.

If appropriate guesses can’t be determined, a graph can be plotted to understand the behavior of the equation. For each point on the graph, display the equation and press XEQ. At the prompt, enter the x-coordinate and the calculator will return the corresponding value of the equation as the y-coordinate. For the problem at hand, the value for V is constant, \$V=7500\$, and only value H varies, to produce different values for the equation, and thus different points on the graph to plot the equation. It must be remembered that, for this equation, the value is the difference between the left and right sides of the equation.

eqn solve box plot
\$f(x) = 7500 - (30-H) × (25-H) × 4 × H\$

13. Integrating equations

Many problems in mathematics, science, and engineering require calculating the definite integral of a function. In the following mathematical expression of an integral, the function is denoted as \$f(x)\$ and the interval of integration is \$a\$ to \$b\$:

eqn intg plot
\$Q = int_a^b f(x)dx\$

Quantity Q can be interpreted geometrically as the area of a region enclosed by the plot of function \$f(x)\$ and the x-axis, and the limits \$x=a\$ and \$x=b\$ (provided that \$f(x)\$ is non-negative throughout the interval of integration). Calculator function ∫FN (key ) integrates the current equation with respect to a specified variable (∫FN d _). The function may have more than one variable.

∫FN works only with real numbers.

13.1. To integrate equations with ∫FN

To integrate an equation:

  1. If not already present in the Equation list, write the equation defining the integrand’s function. For this application, the equation is usually of the expression-type. When done, close the Equation list.

  2. Define the limits of integration:

    • key in the lower limit and then press ENTER

    • key in the upper limit.

  3. Open the Equation list with EQN and bring the desired equation into view. If necessary, use to scroll the list.

  4. Select the variable of integration with variable. Calculation of integration starts immediately.

The running ∫FN can be interrupted with C or R/S, but no information about the integration is available unless the calculation finishes normally.

The current display format affects the level of accuracy assumed for the function and used for the result. Integration is more accurate but takes longer when display is in ALL or higher settings of FX SC and EN. The uncertainty of the result is placed in the y-register, pushing the limits of integration up into the z- and t-registers. See Accuracy of integration below for more information.

To use the same limits for a subsequent integration calculation, press R↓ R↓ to place the values back into the x- and y-registers before proceeding with point 3 above.

Example: Bessel function
The Bessel function of the first kind of order 0 can be expressed as

\$J_0 (x) = 1/pi int_0^pi cos(x sin(t))dt\$

To find the Bessel function for \$x\$-values of 2 and 3, start by keying in the integrand’s function:

keystrokes selected line or x-register description

1.

CLEAR ALL Y

clear memory

2.

EQN

EQN LIST TOP
or current equation

open Equation list

3.

COS RCL [X]

COS(X█

beginning equation entry

4.

× SIN RCL [T]

COS(X×SIN(T█

5.

) )

S(X×SIN(T))█

close parentheses (optional)

6.

ENTER

COS(X×SIN(T)

terminate and save equation to the list

7.

C

close Equation list

Now, to integrate this function with respect to \$t\$ from zero to π; \$x=2\$:

keystrokes selected line or x-register description

1.

MODES RD

switch to radians mode; annunciator RAD turns on

2.

0 ENTER π

3.1416

enter limits of integration (lower limit first)

3.

EQN

COS(X×SIN(T)

open Equation list

4.

∫FN d _

prompt for variable of integration

5.

[T]

X?value

select T; prompt for X

6.

2 R/S

INTEGRATING

store 2 in X; start calculation

7.

∫=0.7034

result for \$int_0^pi f(t)\$

8.

π ÷

0.2239

result for \$J_0(2)\$

Example: Sine integral
Certain problems in communications theory (for example, pulse transmission through idealized networks) require calculating an integral (sometimes called the sine integral) of the form

\$Si(t) = int_0^t (sin(x)/x)dx\$

Here’s how to find \$Si(2)\$.

The expression to enter, which defines the integrand’s function, is:

\$sin(x)/x\$
In the event that the calculator tries to calculate this function when \$x=0\$, which is the lower limit of integration, it would encounter an error DIVIDE BY 0. Nevertheless, the integration algorithm typically avoids evaluating functions at the limits of integration unless the interval’s endpoints are extremely close together or there is an exceptionally large number of sample points.
keystrokes selected line or x-register description

1.

EQN

EQN LIST TOP
or current equation

open Equation list

2.

SIN RCL [X]

SIN(X█

beginning equation entry

3.

)

SIN(X)█

close parenthesis

4.

÷ RCL [X]

SIN(X)÷X█

5.

ENTER

SIN(X)÷X

terminate and save equation to the list

6.

C

close Equation list

Now, to integrate this function with respect to \$x\$ (that is, variable X) from zero to 2; \$t=2\$:

keystrokes selected line or x-register description

1.

MODES RD

switch to radians mode; annunciator RAD turns on

2.

0 ENTER 2

2_

enter limits of integration (lower limit first)

3.

EQN

SIN(X)÷X

open Equation list

4.

∫FN d _

prompt for variable of integration

5.

[X]

INTEGRATING

start calculation

6.

∫=1.6054

result for \$Si(2)\$

13.2. Accuracy of integration

The calculator only ever approximates the exact value of an integral. The accuracy of this approximation depends on the accuracy of the integrand’s function as calculated by the selected equation, which is affected by round-off error in the calculator and the accuracy of the empirical constants. Functions with certain characteristics such as spikes or very rapid oscillations might result in inaccurate integration, but the occurrence is unlikely.

13.2.1. Controlling accuracy

The level of precision in the integration calculation is determined by the chosen display format (FIX, SCI, ENG, or ALL). When more digits are displayed, the calculated integral becomes more precise (but takes longer to calculate). On the other hand, fewer displayed digits result in a faster calculation, but the calculator assumes that the function is accurate only up to the number of digits specified in the display format.

To control the level of accuracy in the integration, adjust the display format to show only the number of digits that are deemed accurate for the integrand’s values. This chosen level of accuracy will also be reflected in the calculated integral result.

When fraction display is active (flag 7 set), the accuracy is determined based on the previous display format.

13.2.2. Interpreting accuracy

Once the integral is calculated, the estimated uncertainty of the integral’s result is stored in the y-register. To view the value of the uncertainty, press xy.

In the previous Sine integral example, if calculation of integral \$Si(2)\$ returns 0.0001 to the y-register when finished, then the calculated result of 1.6054 is accurate to ±0.0001.

Example: specifying accuracy
Calculate the integral in the expression for \$Si(2)\$ from the previous example with display format set to SCI 2.

keystrokes selected line or x-register description

1.

DISP SC 2

1.61E0

switch to scientific notation with two decimal places; this specifies that the function is accurate to two decimal places

2.

R↓ R↓

2.00E0

roll the stack to reclaim values for limits of integration

3.

EQN

SIN(X)÷X

open Equation list; select equation

4.

[X]

INTEGRATING

calculation runnning

5.

∫=1.61E0

integral approximated to two decimal places

6.

xy

1.00E-3

uncertainty of the approximation

The integral is 1.61±0.00100. Given that the uncertainty only affects the third decimal place, all the displayed digits in this approximation can be considered to be accurate.

If the uncertainty exceeds limits set by the particular context, increase the number of digits in the display format and perform the integration again (assuming that \$f(x)\$ is still calculated accurately based on the displayed digits). Generally, each additional digit specified in the display format results in a tenfold decrease in the uncertainty of the integration calculation.

Example: changing accuracy
Continuing with the same example and using the same integral of \$Si(2)\$, specify an accuracy of four decimal places instead of two.

keystrokes selected line or x-register description

1.

DISP SC 4

1.0000E-3

specify accuracy to four decimal places; uncertainty from previous calculation still in x-register

2.

R↓ R↓

2.0000E0

roll the stack to reclaim values for limits of integration

3.

EQN

SIN(X)÷X

open Equation list; select equation

4.

[X]

INTEGRATING

calculation runnning

5.

∫=1.6054E0

integral approximated to four decimal places

6.

xy

1.0000E-5

uncertainty is about 100 times smaller as with previous SCI 2 setting

7.

DISP FIX 4

1.0000E-5

return calculator to default FIX 4 display format

8.

MODES DEG

1.0000E-5

return calculator to default degrees mode

Although uncertainty suggests that the result may be accurate only up to four decimal places, this calculated result is actually accurate to seven decimal places when compared to the true value of the integral. It’s important to note that, in most cases, the calculator’s approximation is often more accurate than its reported uncertainty because the uncertainty is calculated conservatively.

13.3. Equations in a nutshell

Here is a recap/standard course of action to deal with equations on the DM32:

Open Equation list to view the stored equations

Press EQN. The Equation list is browsed by using or . The list wraps around when either end is reached. If no equation is presently stored, only the EQN LIST TOP message shows. Only the first 12 characters of an equation are shown. If an equation is too long to be displayed in its entirety, special annunciators appear at the bottom of the display, enabling the use of keys √x and Σ+ to move the equation to the left and right, respectively.
See Viewing and selecting equations for more detail.

Write an equation

With the Equation list open, simply start keying in numbers, letters and operators. To enter a letter, press RCL before using the letter-key. When the equation is entirely keyed in, press ENTER and it is stored in the list immediately.
See Writing equations for more detail.

Edit an existing equation

Find the equation in the Equation list and press . This puts the calculator in equation entry mode and turns on block cursor at the right end of the equation. If the equation is longer than what the display can show, the display will be moved to the end of the equation. From here, parts of the equation can be added or deleted. The cursor can only act from the end of the equation, i.e. it’s not possible to move it to the middle of the equation to insert or delete elements from there.
See Editing equations for more detail.

Evaluate an equation

Find the equation in the Equation list and press ENTER. Note that XEQ can also be used to evaluate an equation, although it will behave somewhat differently depending on the type of the equation being either an equality, an assignment or an expression.
See Evaluating equations for more detail.

Solve an equation

Find the equation in the Equation list and press SOLVE. The prompt asks for the unknown variable to be solved for. Press the corresponding letter key (no need to press RCL beforehand). The display automatically proceeds and prompts for the values of each known variable in the equation. For each known variable, key in the desired value and proceed to the next known variable by pressing R/S. Solving starts automatically after the last known has been entered. If the solution takes enough time, the display shows message SOLVING. When a root has been found, the value and name of the variable being solved for will be shown.
See Solving equations for more detail.

Integrate an equation

First enter the limits of integration. In Calculator mode, key in the lower limit, press ENTER, then key in the upper limit. Enter equation mode by pressing EQN and select the desired equation. Select the variable of integration with variable.
See Integrating equations for more detail.

Delete an equation

Find the equation from the list and press CLEAR. The equation is immediately deleted. This cannot be undone.

Equations can also be written as a program line and be evaluated, solved or integrated within the program. An equation written as a program line does not appear in the Equation list.

14. Basic programming

Almost any sequence of operations imaginable on the calculator can be stored in a program and executed at a later time. Writing a program is as simple as recording a sequence of keypresses. Programs can also be momentarily paused for the user to input values for subsequent calculations, as is shown later in this chapter.

Here are a few fundamental things to remember about how programs are stored and executed on the DM32.

  • Program memory is a dedicated space made of instruction lines (of which the first at the top is permanent and called PRGM TOP). The number of lines stored in program memory is only limited by available memory.

  • LBL (“label” = beginning) and RTN (“return” = end) are special instruction lines that allow for splitting this continuous column into discrete programs.

  • It is then possible to execute only the program lines found between a specific LBL and the next RTN instruction using function XEQ label. It could be said that individual programs exist as label-delimited ranges of lines from program memory, rather than as self-contained objects. The word label is therefore used, by extension, to designate the program this label delimits. Another way of thinking is to consider program memory as one large program in which labels define sub-routines, or modules, made to work together in the larger or parent program. The latter can jump directly to such labels using instruction GTO label.

  • Labels are always 1-letter, uppercase (A through Z), which means there is a maximum of 26 labels, or programs, possibly existing at any one time in program memory (although this limitation can be overcome by using Multi-State and Remote XEQ). Note that, although variables are also named using this convention, labels and variables names have nothing to do with one another; calculator memory can contain program A and variable A without any conflict.

14.1. About backing up and restoring programs

To backup and restore programs to and from external media, use States. Read chapter Calculator State where it is shown how program memory can be stored on the internal USB disk as part of an ASCII text file with the extension *.d32.

14.2. Entering and executing a simple program

14.2.1. Writing the program

The circumference of a circle can be calculated with formula \$C = r*2π\$. To find the circumference of a circle of radius 10, the RPN sequence of keypresses is therefore

1 0 ENTER 2 × π ×

If this formula is used to calculate the circumference of many different circles, the user has to repeat a large portion of the keypresses (except the value of the radii). To avoid this repetition, the keys used repeatedly can be stored in a program:

001 2
002 ×
003 π
004 ×
005 RTN

This 5-line program assumes that the value for the radius is in the x-register before execution.

To write this program, start by clearing the calculator with CLEAR ALL Y. Enter Program mode with PRGM. Annunciator PRGM turns on and the display shows the topmost line of program memory:

prg list 1

Now key in the formula. Start with 2:

prg list 2

The 3 digits on the left show the program line number. Go on with ×:

prg list 3

Observe how line 2 of the program now contains instruction "multiply". On the next line, put π:

prg list 4

Now key in the second ×:

prg list 5

Always terminate a program with a "return" RTN instruction. The RTN instruction returns the program pointer to the top of program memory PRGM TOP and halts execution. For this, use RTN:

prg list 6

Exit Program mode with PRGM. The display returns to Calculator mode.

14.2.2. Executing the program

To execute the program, first move the program pointer (or "read-head") to the top of program memory PRGM TOP with GTO . The stack display remains the same after that, which is normal. Enter the radius in the x-register with 1 0 and execute the stored program with R/S. The program runs and the result in visible in the x-register:

pgm1 stp7

Now enter a different radius, say 3 3, and execute the program with R/S:

pgm1 stp8

When the program pointer executes the RTN instruction, it is immediately sent back to the topmost line and the program halted, which is why there was no need to manually place the pointer at the top with GTO like it was required to do the first time.

14.3. About the program pointer

The program pointer designates the next program instruction to be executed (either when program is running or when user invokes single-step execution in Calculator mode with ).

Program mode (summoned with PRGM) opens the program listing at the current pointer position. If program memory is empty, the pointer sits at the only and topmost line PRGM TOP, which cannot be deleted.

See How the program pointer moves for more about the pointer.

14.4. Entering a labeled program

The following example assumes the previous circle circumference example program has been entered from an empty memory. It adds a second program to calculate the area of a circle and shows how to execute one or the other separately using function XEQ.

The equation to find the area of a circle is \$A = π*r^2\$. Assuming the radius value is in the x-register before executing the program, the RPN for this is:

x² π ×

Start by moving the program pointer to the top of program memory PRGM TOP with GTO . Enter Program mode with PRGM.

prg list 10

Give the already stored program a label by pressing LBL [C].

prg list 11

Note how the line number now shows the program label this line belongs to with prefix C01. This means it is the first line of program C.

Any instruction entered in a program inserts a new line after the one at the program pointer.

To enter the new program above the first one, move up one line with :

prg list 12

The program pointer is again at the top of program memory PRGM TOP. Enter the new program label "A" for "area" with LBL [A]:

prg list 13

Enter the program instructions x2 π ×. The display shows:

prg list 14

Finish program with RTN.

prg list 15

At this point, programs A and C are in memory. The listing of program memory looks like this (navigation keys can be used to check correct entry against this listing):

PRGM TOP
A01 LBL A
A02 x²
A03 π
A04 ×
A05 RTN
C01 LBL C
C02 2
C03 ×
C04 π
C05 ×
C06 RTN

14.5. Executing a labeled program

The calculator can execute program lines associated with a label. To do this, press XEQ and the letter key corresponding to the desired label.

Example
The following demonstration uses the example program from previous section Entering a labeled program.

If calculator is still in Program mode, revert to Calculator mode with C. Put radius 5 on the x-register and execute the area program by pressing XEQ [A]. The result is the area of a circle with radius 5:

pgm2 stp7

Put the same radius on the stack and calculate the circumference with program C, using XEQ [C]. The radius for the circle is returned to the x-register:

pgm2 stp8

Function XEQ label moves the program pointer directly to the designated label and starts running the program. When the program pointer meets the RTN instruction, it is moved back to the top of program memory PRGM TOP and the program is halted. The calculator is ready for the next XEQ call. This is how the combination of LBL and RTN instructions allows for dividing the program memory into discrete programs or modules.

Press XEQ [J]. Because label J has not been created, the warning annunciator turns on and the calculator throws an error message:

pgm2 stp9

To clear the message, press C.

14.6. Executing a remote label

Taking advantage of the Multi-State functionality, the calculator can remotely execute a program from any of the States in the Available States list. To do this, press XEQ XEQ.

Example
Let’s assume there are two Available States squares and circles. State circles holds example program from above section Entering a labeled program, which has labels A and C to calculate the area or circumference of a given circle, respectively. The goal is to use programs from Available State circles without exiting State squares. Here is how.

In Calculator mode, with State squares activated, enter radius 3.

remote xeq man 1

Press XEQ as for a normal XEQ. Press XEQ again to make the XEQ remote. The list of Available States appears:

remote xeq man 2

With State circles highlighted (use navigation keys to highlight it if necessary), press ENTER. The display now shows the XEQ instruction prompting for a label letter from State circles:

remote xeq man 3

Press [A] to execute label A from State circles, which calculates the area of a circle, using value in the x-register as the radius. Result is returned to the x-register. Note that squares is still the active State:

remote xeq man 4
Although possibly called manually like shown above, remote XEQ is intended to be primarily used as a program instruction, to build larger programs with dependent States.

14.7. Using equations in programs

The above examples use RPN operations, one per program line. It is also possible to use an equation in the program to achieve the same result.

advantages of RPN operations advantages of equations

use less memory

easier to write and read

execute a bit faster

can automatically prompt for values

When the program pointer ecounters an equation, the equation is evaluated like XEQ evaluates an equation from the Equation list. When evaluated as part of a program, a “=” in an equation is treated as a “–”.

There is no programmable equivalent to ENTER, which stores the answer into the assignment variable when evaluated from the Equation list. This behavior must be explicitly programmed using STO to store the value in the variable.

14.8. Entering a program: recap

  1. Enter Program mode by pressing PRGM.

  2. Move to the top of program memory with GTO .

  3. Give the program a meaningful single-letter label. Press LBL [LETTER].

  4. Write the program by pressing keys as would be done to calculate manually in RPN. See below how to enter an equation.

  5. End program with a RTN instruction.

  6. Exit Program mode with C.

14.9. Entering an equation as a program line

While in Program mode (PRGM annunciator on):

  1. Activate equation mode with EQN. Annunciator EQN turns on and a block cursor appears at the beginning of the line.

  2. Enter the equation normally as seen in chapter Equations. backspaces. See Clearing in Program mode for more detail.

  3. ENTER terminates equation entry. The display shows the left end of the equation. The equation is not added to the Equation list, it is only part of that program it has been entered in.

When the equation length exceeds display width, annunciators 🠷 and appear and keys √x and Σ+ scroll the display. To insert one of these functions (SQRT or Σ+) as a program line from here, deactivate scrolling with SCRL. Annunciators 🠷 and disappear and the keys now work normally.

14.10. Editing a program

Programs in memory can be modified by first moving the program pointer to the appropriate position and then inserting and/or deleting program lines. Only program lines with an equation can be modified without deleting the entire program line.

14.10.1. Moving to a specific program line with navigation keys

Put the calculator in Program mode with PRGM and use navigation keys to position the pointer to the required line in the program.

14.10.2. Moving to a specific program line with GTO

In larger programs, function GTO is useful to locate the line where modification is necessary. GTO can be used in Calculator or Program mode. It comes in two flavors:

  • standard: invoked with GTO, quickly locates labeled program lines numbered between 1 and 99;

  • extended: invoked with GTO XEQ, can locate any program line in memory, labeled or unlabeled, but requires a few extra key presses.

Below is a description of both.

14.10.3. Standard GTO

Press GTO. The GTO prompt appears:

gto std 1

Two options are available:

  • go to first line of label: press the letter key for the required program label. The program pointer is moved to the first line of the specified label, except when the calculator is in Program mode: in this context, a GTO label instruction is inserted as a program line (see Branching (GTO)).

  • go to specific line of label: press ; the GTO prompt changes to:
    gto std 2
    The prompt expects label nn (with nn ≥1 and ≤99), for instance [A] 0 6 for line A006. The program pointer is moved to the required position. If the specified line number exceeds the last line number for that label, the pointer is placed at the last line for that label.

Use C or to cancel the GTO prompt. If the specified label doesn’t exist, the calculator throws error message NONEXISTENT.

14.10.4. Extended GTO

Press GTO XEQ. The GTO dialog appears:
gto ext 1
The dialog expects label line number. There are two options:

  • To point to a labeled line, press the letter key for the required program label followed by any line number (for instance, [P] 1 2 3 4 for line P1234).
    gto ext 2

  • To point to an unlabeled line, press followed by any line number (for instance, 2 0 2 4 for line 2024).

The line number can be any positive integer. Press R/S and the program pointer is moved to the required position.

There can be 3 alternative scenarios:

  • Specified line number exceeds the last line number for that label: the pointer is placed at the last line for that label (or the last of unlabeled lines if was used).

  • Line number is omitted before confirming with R/S: the pointer is moved to the first line of the specified label (if was used instead of a label letter, then pointer is moved to PRGM TOP).

  • R/S is pressed without entering any argument: the pointer is moved to PRGM TOP.

Use to correct entry. Use C to cancel the GTO dialog and return to Calculator mode. If the specified label doesn’t exist, the calculator throws error message NONEXISTENT.

14.10.5. Executing GTO in Calculator mode

GTO moves the program pointer also when the unit in Calculator mode, even though the effect is not visible. This can be useful to position the pointer at a specific line before running the program with R/S.

For a complete description of how to move the program pointer, see How the program pointer moves.

14.10.6. Modifying the program

With the unit in Program mode and the program pointer positioned where modification is needed, the following actions are possible.

  • To delete a program line
    Delete the line using . If the line contains an equation, use CLEAR EQN (otherwise enters equation entry mode).
    The program pointer moves to the preceding line. This means that, to delete a group of lines, place the program pointer at the last line of the group before pressing (or CLEAR EQN for an equation).

  • To insert a program line
    Key in a new instruction. The new instruction is inserted after the program pointer. In other words, to insert an instruction between lines C09 and C10, the program pointer must be positioned at line C09. The newly inserted instruction bears line number C10, and the remaining lines of the program are moved down one line and renumbered accordingly.

  • To edit an equation as program line
    Select the program line containing the equations and press . This turns on equation editing and block cursor appears at the end of the line. Every subsequent press on deletes the rightmost character from the equation. Proceed until the desired location is reached and enter the correct characters.
    Press ENTER to validate modifications and leave equation entry.

There is no way to place the cursor mid-equation; it is only possible to edit an equation from its right end.

14.11. Function SHOW in Program mode

Function SHOW in Program mode displays the current program line, complete with label and line number, also when it contains an equation.

Move the program pointer on the relevant program line and use SHOW. See Function SHOW to display long numbers for details about function SHOW.

14.12. Input and output

Programs can take data:

  • using instruction INPUT, which halts execution and prompts for user input,

  • from values on the stack,

  • from already stored variables,

  • using equations auto-prompting (flag 11 must be set).

Programs can only write data to variables (STO) and stack registers, but they have several means to display data:

  • on the stack, which is visible at the end of execution,

  • using instruction VIEW, which halts execution and shows the name and value of a variable,

  • using instruction PSE, which pauses execution for approximately 1 second to show the contents of the x-register,

  • as an "equation" (which is not an equation in the mathematical sense, but rather a custom message created using equation mode).

14.12.1. Using INPUT instruction

This instruction is called using INPUT. The program calculating the area of a circle with an INPUT instruction looks like this:

PRGM TOP
A01 LBL A
A02 INPUT R
A03 x²
A04 π
A05 ×
A06 RTN

When the program pointer encounters the INPUT instruction, execution is halted and a prompt for user input appears:

input

The "?" question mark signals the prompt. 0.000 is the current value stored in variable R.

See Responding to INPUT prompts below for details.

Instruction INPUT can be invoked in the middle of a program, but it makes most sense in longer programs, where all needed variables are stored up front, before the calculations happen. To write such a program,

  • start by deciding which variables the program will use and assign a meaningful name to each of them,

  • at the very beginning of the program, insert an INPUT instruction for each of the variables. That way, all necessary variables are available for calculation later in the program. When needed in the program, use instruction RCL variable to put these variables on the stack.

14.12.2. Responding to INPUT prompts

When the program pointer encounters an INPUT instruction, execution halts until the next R/S press. In the meantime, either one of the following is possible:

  • Use the number as it stands. Press R/S and program execution resumes.

  • Change the number. Key in the new number and press R/S to resume execution.

  • Do calculations. While the program is halted and the prompt is on (? character on the prompt line), math functions can be used to calculate a number. Press R/S when done to resume execution.
    To make calculations using the present value of the variable, press ENTER beforehand, because newly keyed-in digits replace the contents of the x-register.

  • Cancel INPUT prompt by pressing C. The value of the variable remains in the x-register. Pressing R/S resumes program execution but repeats the cancelled INPUT prompt.

  • Press SHOW to view a number too long to display.

Remember that when using INPUT, a program shouldn’t rely on the contents of the stack, because the user may scramble the stack when doing calculations at INPUT. Rather the program should recall (RCL) needed variables when appropriate.

14.12.3. Using VIEW to display data

When executed as a program line, instruction VIEW halts execution and displays the name and contents of a variable:

output

It is only a display feature, i.e. it does not replace contents of the x-register. If fraction mode is active, the number is displayed as a fraction. While the variable is displayed with VIEW:

  • Press ENTER to copy the value to the x-register.

  • Press SHOW to display a number larger than 10 digits; scroll keys √x and Σ+ can be used to view a large binary number.

  • Press C or to erase the VIEW display and reveal the x-register.

  • Press CLEAR to clear the variable contents (set the variable value to zero).

  • Press R/S to resume program execution.

It is possible to have the program still run "in the background" while VIEW instruction displays a variable. See below.

14.12.4. Using equations to display messages

The syntax of an equation isn’t checked until it is evaluated. This means that the contents of an equation can be virtually any string of characters. On any program line, press EQN to enter equation mode. Enter the characters as needed (letters are invoked using RCL [LETTER]). See Entering an equation as a program line for more detail.

For the program to display equations instead of evaluating them, flag 10 must be set. When the program displays such a message, execution is halted. Press R/S to resume execution. If the message is longer than 12 characters, annunciators 🠷 and appear and √x and Σ+ can be pressed to scroll the message. It is also possible to press SHOW to display the message in a SHOW box (see Function SHOW to display long numbers for details about function SHOW).

It is possible to have the program still run "in the background" while a message displays. See below.

14.12.5. Run in the background while displaying information

Instruction VIEW and the displaying of an equation (with flag 10 set) both halt program execution. Only R/S normally resumes the program. There is a way to keep the program running while a message displays. Insert a PSE instruction on the line immediately following the call to VIEW or the “message” equation. Program execution resumes after 1 second, without clearing the message. Annunciator PRGM blinks to show the program is running. Scrolling the displayed message isn’t possible in this context. Such VIEW-PSE or VIEW-equation line pairs in a program are treated as a single operation when using step-by-step execution (with or F6 navigation keys).

14.13. Stopping or interrupting a program

14.13.1. Programmatically stopping with STOP or PSE

  • Pressing R/S during program entry inserts a STOP instruction. This will halt a running program until resumed by pressing R/S from the keypad. STOP can be used rather than RTN to end a program. The difference is STOP won’t return the program pointer to the top of memory.

  • Pressing PSE during program entry inserts a PSE (pause) instruction. This will briefly halt a running program and display the contents of the x-register and resume execution after about 1 second. An exception to this is if PSE immediately follows a VIEW instruction or an equation that’s displayed (flag 10 set): then, the variable or equation is displayed instead of the x-register, and the display remains after the 1-second pause. See Run in the background while displaying information above.

14.13.2. Manually halting a running program

A program can be interrupted at any time by pressing C or R/S. The program completes its current instruction before stopping. Press R/S to resume the program. If XEQ, GTO or RTN is pressed, the interrupted program cannot be resumed with R/S. It has to be reexecuted instead with XEQ label.

14.13.3. Errors

When a running program encounters an error, program execution halts and an error message is displayed. See the list of calculator errors in Appendix C: Messages. The program stops at the program instruction causing the error, so that pressing PRGM starts Program mode with the program pointer sitting at the line causing the error.

14.14. Clearing programming entries

Clearing keys have dedicated functions when the calculator is in Program mode. See appendix Clearing in Program mode.

14.15. Program memory

Program memory is a single memory space containing all program lines and labels. The special, topmost program line PRGM TOP always remains at the top of program memory and cannot be deleted. When instruction RTN is met during program execution, the program pointer returns to the PRGM TOP line (except after a call to XEQ, see Programming techniques).

14.15.1. Viewing program memory

Entering Program mode with PRGM essentially shows the contents of program memory. The memory space is viewed by scrolling it up and down, by moving the program pointer.

See How the program pointer moves for more detail.

14.15.2. Programs catalog

Press MEM PGM to invoke the programs catalog. The catalog lists all program labels and the memory used by the instruction lines associated with each of them. Use navigation keys to browse the list. From here, these actions can be performed:

key usage/description

and

Review used label names and how much memory each associated program or module consumes.

XEQ or R/S

Execute the program associated with the selected label.

PRGM

Enter Program mode with the program pointer at the selected label.

CLEAR

Clear the program associated with the selected label. Deletes immediately without confirmation. Cannot be undone.

Step back to VAR / PGM selection.

Press C to exit the programs catalog.

14.16. How the program pointer moves

There are several functions to move the program pointer about in program memory.

internal name key usage/description

— / STOP

R/S

When program is halted, makes the program run. When program is running, finishes current instruction and lets the pointer sitting at the next instruction line.
When R/S is pressed while writing a program, inserts instruction STOP. When a running program meets this instruction, execution is halted and the pointer is positioned at the following line.

PSE

PSE

Halts (PauSEs) the program for around 1 second and resumes running (except if it follows instruction VIEW ). Useful to show an intermediate result in the middle of a running program. Has no effect when the program isn’t running.

GTO

GTO

Standard
GTO label or GTO label nn: moves the pointer to either the first line of a label or a specific labeled line in the range 1 ≥ nn ≤ 99. Unlabeled lines are not reachable. Available in Calculator and Program modes, but please note that, in Program mode, GTO label inserts a GTO label program instruction. See Moving to a specific program line with GTO.
Extended
GTO XEQ label nn R/S or GTO XEQ nn R/S: moves the pointer to any line in program memory. Available in Calculator and Program modes. See Moving to a specific program line with GTO.
 
GTO doesn’t halt nor start program execution.

XEQ

XEQ

Standard XEQ (local)
XEQ label
Positions the pointer at label and immediately starts execution.
Remote XEQ
XEQ XEQ State label
Activates State, positions the pointer at label and immediately starts execution. Available in Calculator and Program modes. See Executing a remote label and Remote XEQ.

RTN

RTN

RTN
Halts execution and returns the pointer to top line PRGM TOP. If current program has been invoked as a subroutine with an XEQ program instruction, returns the pointer to the line immediately following that XEQ instruction and resumes execution from there.

n/a

Single-step execution when in Calculator mode
Useful for debugging. Executes the instruction at the current pointer position and moves the pointer one line down. Similar to function preview, holding the key shows the program line and executes the instruction upon releasing it. Holding it 2.5 seconds or more displays NULL, cancels execution of the instruction and leaves the program pointer where it was.
Moving the program pointer down, or fast-forward, when in Program mode
Useful for program editing. Moves the program pointer down to the next line. If held down, after 2.5 seconds, automatically “fast-forwards” to the following line at an approximate 3-line per second rate. Program instructions are not executed. When the bottom line of program memory is reached, wraps around to line PRGM TOP.
Note that any newly inserted instruction is placed after the currently displayed line.

n/a

Moving the program pointer up, or rewind, when in calculator and Program mode
Moves the program pointer one line up and displays it without executing the instruction. In Calculator mode, the line is shown as long as the key is held down. If kept held down, after 2.5 seconds, automatically “rewinds” to the previous line at an approximate 3-line per second rate. When the top line PRGM TOP is reached, wraps around to the last, bottom line of program memory.
Note that any newly inserted instruction is placed after the currently displayed line.

n/a

F3

Step-over
Works in Calculator mode as debugging function. Similar to , except when pointer meets an XEQ instruction. Then, XEQ is treated as a single instruction invoking the whole subroutine in one step.
See Debugging.

n/a

     F3

Step-out
Works in Calculator mode as debugging function. Runs current subroutine and stops after the return from the subroutine.
See Debugging.

14.17. Non-programmable functions

The following functions have no equivalent program instruction and therefore are not programmable:

CLEAR ALL

GTO

CLEAR PGM

GTO label nn

CLEAR EQN

MEM

SHOW

EQN

FDISP

PRGM

14.18. Programming with BASE

Instructions to change the base mode can be inserted in a program using BASE, just like when executed from the keypad. This makes it possible to write programs which accept numbers, do arithmetic, and display results in any of the four bases.

When writing a program designed to work in a base other than 10, set the base mode in both places: in Calculator mode and in the program as an instruction.

14.18.1. Setting a base mode in a program

Insert a BIN, OCT, or HEX instruction at the beginning of the program. It’s a good idea to include a DEC instruction at the end of the program to revert to base-10 when program execution is finished.

Such a program instruction determines how user input is interpreted and how the output looks during and after program execution, but it doesn’t affect how numbers are entered as program lines.

Equation evaluation, SOLVE and ∫FN automatically set base-10.

14.18.2. Entering numbers as program lines

Set the current base mode with BASE before activating Program mode with PRGM. The current base mode (watch for base mode annunciator) setting determines the base used for entering numbers as instruction lines while in Program mode.

15. Programming techniques

This chapter covers more advanced programming techniques.

  • Routines and subroutines, which break up a larger program into portions which perform specific tasks. A routine can be called manually or by a program XEQ instruction (subroutine). If the same task is to be executed several times in a program, it is then only necessary to write the adequate subroutine once, making for a shorter program.

  • [Branching], which moves the program pointer to a specific label.

  • Conditional instructions, which determine which instructions or subroutines to use depending on other factors or values.

  • Flags, information bits useful to keep track of various statuses.

  • Loops, to automatically repeat the desired program steps, a determined number of times.

  • Indirect addressing, giving the ability to access different variables using the same instruction RCL(i).

  • Debugging functions which help finding the causes of problems and errors in programs.

This chapter shows special flow diagrams using the larger calculator font for clarity, plus a few additional symbols and comments:

list graphics

Detailed example programs are provided in sections Mathematics programs, Statistics program and Miscellaneous programs and equations.

15.1. Routines and subroutines

A relatively complex program is traditionally broken up in smaller blocks called routines. Each routine is a functional unit designed to accomplish a specific task. This modular approach makes it easier to read, understand, write, and debug programs.

In the DM32, a routine starts with a label (LBL instruction) and ends with an instruction that changes or stops execution, like RTN, GTO or STOP, or maybe another label. Up to this point in this manual, what is here called a routine has effectively been called a program, which isn’t untrue, because a routine is a program, but for the fact that it is meant to be a part, a module of a larger, more complicated program.

A subroutine is a routine executed (XEQ) by a parent routine. The following paragraphs and examples demonstrate how they work together.

15.1.1. Calling subroutines: XEQ/RTN

A subroutine is a routine that is called from, or executed by, another routine, and returns the program pointer to that routine when the subroutine execution has been completed. The subroutine must start with a LBL, and end with a RTN (return) instruction. A subroutine is itself a routine, and it can execute other subroutines.

  • From the parent routine, instruction XEQ redirects the program pointer to a subroutine label (LBL).

  • When the program pointer reaches the RTN instruction in the subroutine, it returns to the line immediately following the XEQ instruction in the parent routine.

list subroutine

To insert a subroutine call in a program, while in Program mode, press XEQ and then the letter-key corresponding to the label of the desired routine.

15.1.2. Remote XEQ

XEQ can call a subroutine from any of the Available States. To make a remote routine call:

  1. Press XEQ as for a normal routine call.

  2. Before entering the target XEQ label, press XEQ again to make the routine call remote.

  3. In the list of Available States which appears, select the target State to call a routine from with system navigation keys.

  4. Press ENTER.

  5. The display is returned to Program mode and the calculator prompts for a routine label from the selected State.

  6. Press the letter key for the desired target label. The remote XEQ instruction is added to the program and shows the label and State name separated by a colon: XEQ label:State.

The instruction only shows the first two letters from the State name. Subsequent characters overshoot the display. Here is an example instruction line to remotely execute label G from State maxwell:

remote line

The complete instruction can be reviewed in a SHOW box by pressing SHOW:

remote show

SHOW in this context works like it does in Calculator mode, or to display long equations.

When the RTN instruction from the remote routine is met, execution resumes in the parent routine after the remote XEQ instruction.

If the specified label doesn’t exist in the target State, or if the targeted State doesn’t exist in the Available States list, error message NONEXISTENT appears and the calculator is left at the remote XEQ instruction line.

15.1.3. More about Remote XEQ

When executing a Remote XEQ, the calculator

  1. activates the State specified in the Remote XEQ instruction (working exactly like activating a State manually,

  2. executes the routine specified in the Remote XEQ instruction (working exactly like using XEQ locally).

This mechanism has the following implications:

  • A routine executed by a Remote XEQ call operates local to the State it belongs to; it only accesses the variables and labels from that State, and no other.

  • When an error halts program execution, the calculator is left in the State active when the error occurred, which is not the caller State.

  • The only parts of memory which are visible to all States are:

Trying to insert a Remote XEQ instruction targeting the Active State automatically turns the instruction into a local XEQ call.

15.1.4. Subroutine nesting

A subroutine can call another subroutine, and that subroutine can call yet another subroutine, and so on. This “nesting” of subroutines — the calling of a subroutine within another subroutine — is limited to 15 levels (not counting the topmost program level). The operation of nested subroutines can be represented as this diagram:

list nesting

Any nested call counts as one level of nesting, also for routines called from another State with Remote XEQ. Attempting to call a subroutine beyond the 15-level limit throws error message XEQ OVERFLOW.

Subroutine nesting example
The following routine, labeled S, calculates the value of the expression √(a² + b² + c² + d²) as part of a larger calculation in a larger program. The routine calls upon a subroutine (a nested subroutine), labeled Q, to do the repetitive squaring and addition. This saves memory by keeping the program shorter than it would be without the subroutine.

list nesting xmpl

15.2. Branching (GTO)

While running, the program executes line-by-line. Branching refers to the practice of skipping directly to a specific position in the program. Instruction GTO (go to) does just that. It is invoked with GTO label. GTO points to the first line of a specified label. It doesn’t start nor stop a program.

Instruction GTO can also be invoked manually from Calculator mode. In such a context, GTO is useful to place the program pointer at a desired line to aid while editing a program.

Example of programmed GTO instruction

The program below calculates the side of a square whose area matches that of either a circle or a rectangle of arbitrary dimensions. Here is the logic flow:

  1. Routine C prompts for radius R and calculates the area of that circle.

  2. Routine R prompts for height H and width W and calculates the area of the corresponding rectangle.

  3. Both these routines transfer execution to routine S (with instruction GTO S), which calculates the side of a square with equal area.

  4. The user starts the program with XEQ [C] for a circle and XEQ [R] for a rectangle.

list gto xmpl

Using GTO from the keypad

GTO can move the program pointer to a specified label or line number without starting execution in various ways:

  • To PRGM TOP (top of program memory): GTO .

  • To a label: GTO label. For example, GTO A. If used while in Program mode, enters a GTO program instruction.

  • To a line number: GTO label nn For example, GTO A 05.

15.3. Conditional instructions

The sequence of execution of a program can be altered by a conditional true/false test. Program execution follows the "do-if-true" rule. A conditional instruction compares two numbers and,

  • if the test returns true, executes the following instruction,

  • if the test returns false, skips the following instruction.

For instance, a conditional instruction x=0? (which means "is x equal to 0?") compares the contents of the x-register with zero. If the x-register indeed contains value zero, the test returns true and proceeds to the next line ("do-if-true" rule). If the value in the x-register is anything but zero, the test result is false and the program skips the next line.

list conditional

The example above illustrates a typical use of conditional instructions. The line immediately following the test instruction (which is only executed if the test returns true) branches to another label. This useful technique provides a means to redirect program execution (GTO different routine) depending on a test result.

Three categories of conditional tests are available to the programmer:

  • Comparison tests
    Compares two numbers: either value of x-register to zero or values of x- to y-register.

  • Flag tests
    These check the status of a specified flag (set or clear).

  • Loop counters
    Used to run the program in a ISG),loop a specified number of times.

15.3.1. Comparison tests

There are 12 comparison instructions. They are accessible in 2 menus:

  • press x?y for instructions comparing values from in the x- and y-registers,

  • press x?0 for instructions comparing value in the x-register against zero.

Select the desired menu and press the soft-key corresponding to the instruction needed.

x?y x?0

xy

x ≠ 0

xy

x ≤ 0

<

x < y

<

x < 0

>

x > y

>

x > 0

xy

x ≥ 0

=

x = y

=

x = 0

Executing a comparison instruction manually, from the keypad, returns either message YES for true and NO for false. The message displays in the x-register but doesn’t modify the stack. Press C to clear the message.

15.4. Flags

A flag indicates a status. It can be either set (true) or clear (false).

15.4.1. Meaning of flags

The DM32 has 12 flags numbered 0 to 11. Every one of them can be set, cleared and tested either from the keypad or by a program instruction. By default, they are all clear. Clearing function CLEAR ALL Y doesn’t affect the status of the flags. Below is a list of flags and their meaning.

flag number(s) meaning

0, 1, 2, 3, 4

These five user flags have no predetermined meaning. They can serve any purpose defined by the user in a particular program. Test status of a flag with FLAGS FS? (see Using flags).

5

When set, halts the program at the line immediately following the instruction causing an overflow condition. Message OVERFLOW is displayed. Overflow happens when a calculation returns a number larger than the calculator can handle.
When clear, an overflow doesn’t halt the program, but briefly displays message OVERFLOW when execution ends.

6

Is automatically set when an overflow condition is met. Manually setting this flag produces no effect. By testing for this flag, program execution can be modified in relation to overflow.

7, 8, 9

Control if and how fractions are displayed. See Fraction format for details.

10

Controls how equations are handled in programs.
When clear, equations in programs are evaluated and the result put on the stack.
When set, equations are treated as text to display messages, making them behave like a VIEW instruction. The program halts at the next line and the calculator displays the equation as a message without affecting the stack. Press C or to clear the message. If the next line contains a PSE instruction, execution resumes after a 1-second pause. Otherwise, press R/S to manually resume execution.
Flag 10 can only be controlled by instructions CF and SF, invoked either manually or as a program line.

11

Controls prompting when executing equations in a running program (does not affect prompting when executing equations manually from the Equation list).
When clear, evaluating, solving (SOLVE) and integrating (∫FN) a program equation does not prompt for values of variables. Instead, the calculator uses the current variable values at the time of execution. Prompting from instruction INPUT is unaffected.
When set, the program prompts for the value of each variable in the same order as they appear in the equation. Each variable value is prompted for only once, even if it appears twice or more in the equation. When solving, there is no prompt for the unknown; when integrating, there is no prompt for the variable of integration. Prompts halt execution. Pressing R/S resumes execution with the displayed value. To change the value for the variable, key in the value before pressing R/S.
Flag 11 is automatically cleared after evaluating, solving (SOLVE) or integrating (∫FN) is done. Flag 11 can also be controlled by instructions CF and SF, invoked either manually or as a program line.

15.4.2. Flag annunciators

Flags 0, 1, 2 and 3 have their status shown as annunciators at the top of the display. When set, a corresponding digit appears there. These annunciators serve as a user-defined visual feedback before, during or after program execution. There is no annunciator for flags 4 to 11. To determine the status of those flags, use function FS? from the keypad with FLAGS FS? nn.

15.4.3. Using flags

Flags functions are selected from the flags menu, itself called with FLAGS.

function effect

SF

To set a flag.

CF

To clear a flag.

FS?

To test a flag.

Once the desired function is selected, the calculator prompts for a flag number. For instance, to set flag 3, use FLAGS SF 3. To act upon flags 10 and 11, use : for instance, to clear flag 11, use FLAGS CF 1.

Testing a flag with FS? manually, from the keypad, returns either message YES for set and NO for clear. The message displays in the x-register but doesn’t modify the stack. Press C to clear the message.

A flag test is another kind of conditional test similar to the comparison tests described above, and it follows the same "do-if-true" rule: if the tested flag is set, equivalent to true, the program executes the instruction on the next line; if the tested flag is clear, equivalent to false, the program skips the next line.

Because flags can be set or cleared by previously run programs, and because their status isn’t directly visible on the display, it is recommended to check them and change their status as needed prior to executing a program. Programs can also have flag instruction lines at their beginning to ensure the required flags are in the correct status to work with.

15.4.4. Example fraction display control program

The following program shows how flags 7, 8 and 9 control fraction display on the DM32. It also serves as an example of how to use equations as messages by setting flag 10. It requires two inputs from the user:

  • a non-integer number to interpret as a fraction,

  • an integer number to use as denominator.

Messages in this example are entered as equations:

  1. on the relevant program line, activate equation entry mode with EQN (annunciator EQN turns on),

  2. to enter letters, press RCL [letter-key], to enter a space, press R/S,

  3. press ENTER to terminate entry.

F01 LBL F           beginning of fraction program
F02 CF 7            clear fraction display flags
F03 CF 8
F04 CF 9
F05 SF 10           display (equations as) messages
F06 DEC             decimal base mode
F07 INPUT V         prompt for a number
F08 INPUT D         prompt for the denominator (2-4095)
F09 RCL V
F10 DECIMAL         display the message
F11 PSE             PSE cancels message after 1 second
F12 STOP            number on stack is now visible
F13 RCL D           recall value for denominator
F14 /c              set /c value and sets flag 7
F15 MOST PRECISE    display the message
F16 PSE             PSE cancels message after 1 second
F17 STOP            fraction on stack is now visible
F18 SF 8            set flag 8
F19 FACTOR DENOM    display the message
F20 PSE             PSE cancels message after 1 second
F21 STOP            fraction on stack is now visible
F22 SF 9            set flag 9
F23 FIXED DENOM     display the message
F24 PSE             PSE cancels message after 1 second
F25 STOP            fraction on stack is now visible
F26 GTO F           go to beginning of program

15.5. Loops

Branching backwards (that is, to a label on a previous line) makes it possible to execute the same portion of a program multiple times. This is called looping.

list loop

The above routine is an example of an infinite loop. It is used to collect the initial data prior to executing other routines. After entering the three values, it is up to the user to manually interrupt this loop by executing (XEQ) the desired routine.

15.5.1. Conditional loops (GTO)

It can be useful to repeatedly execute a portion of a program until a condition is met, not knowing in advance how many times the loop needs to repeat. To do this, a loop can be created with a conditional test and a GTO instruction.

The following program uses a loop to decrease value A by constant B until the resulting A is less than or equal to B.

list conditional loop

15.5.2. Loops with counters (DSE, ISG)

To execute a loop a specific number of times, use conditional instructions ISG (increment; skip if greater than) and DSE (decrement; skip if less or equal to). Each time one of these functions is executed, a loop-control number stored in a variable is increased or decreased. It compares the current counter value to a final counter value, and either restarts or exit the loop depending on the result.

Use DSE variable for a count-down loop.

Use ISG variable for a count-up loop.

Used together with instruction GTO, these functions accomplish the same thing as a for loop in a computer programming language:

for (variable = start value; test variable against final value; increment or decrement variable) {
  instructions in the loop;
}

Loop-control number
The specified variable should contain a loop-control number with format ±ccccccc.fffii:

  • ±ccccccc is the current counter value (1 to 12 digits). This value changes with loop execution.

  • fff is the final counter value (must be three digits). This value does not change as the loop runs.

  • ii is the interval for incrementing and decrementing (must be two digits or unspecified). This value does not change. An unspecified value for ii is assumed to be 01 (increment/decrement by 1).

Given loop-control number ccccccc.fffii, instruction DSE does the following:

  • decrement ccccccc to cccccccii,

  • compare new ccccccc with fff,

  • if cccccccfff, make program skip the next program line.

list dse

Given loop-control number ccccccc.fffii, instruction ISG does the following:

  • increment ccccccc to ccccccc + ii,

  • compare new ccccccc with fff,

  • if ccccccc > fff, make program skip the next program line.

list isg

For example, with loop-control number 0.020 when using instruction ISG means:

  • start counting at zero,

  • increase number by 1 each loop (implied when ii is omitted),

  • count up to 20,

  • when at 20, exit loop.

The following program uses ISG to loop 20 times. The loop counter (0000001.02000) is stored in variable C. Leading and trailing zeros can be left out.

list cond loop 2

Checking the loop-control number with VIEW [C] shows:

inc loop result

15.6. Indirect addressing

Indirect addressing is a technique used in advanced programming to specify a variable or label without specifying beforehand exactly which one. Instead, the variable or label is determined when the program runs, so it depends on the intermediate results (or input) of the program. Indirect addressing uses two different, special letter-keys: i and (i) (invoked using keys and R/S, respectively). These keys are active for many functions that take A through Z as variables or labels.

  • i is a variable whose contents can refer to another variable or label. It holds a number just like any other variable (A through Z). It has nothing to do with variable I.

  • (i) is a programming function that directs, “Use the number in i to determine which variable or label to address.” This is an indirect address. A through Z (including I) are direct addresses.

Both i and (i) are used together to create an indirect address. (See the examples below.) By itself, i is just another variable. By itself, (i) is either undefined (no number in i) or uncontrolled (using whatever number happens to be left over in i).

15.6.1. Variable i

The contents of variable i can be manipulated just like with any other variable A to Z. It is even possible to solve for and integrate using i.

Below is the list of functions which can use i:

STO i

x<> i

INPUT i

RCL i

∫FN d i

VIEW i

STO +,–,×,÷ i

SOLVE i

DSE i

RCL +,–,×,÷ i

ISG i

15.6.2. Indirect address: (i)

Many functions that use A through Z (as variables or labels) can use function (i) to refer to A through Z indirectly. The function uses the absolute of value in variable i to determine which variable or label to address. This table shows how:

if i contains (i) addresses variable or label

±1

A

±2

B

±3

C

[…​]

[…​]

±24

X

±25

Y

±26

Z

Statistics registers can be addressed in the same fashion:

if i contains (i) addresses register type of data

±28

n

number of accumulated data points

±29

Σx

sum of x-series of data

±30

Σy

sum of y-series of data

±31

Σx2

sum of the squares of x-series of data

±32

Σy2

sum of the squares of y-series of data

±33

Σxy

sum of the products of x- and y-series of data

Values <–33 or >33 trigger error INVALID (i).

Values ≤–100 and ≥–999 or ≥100 and ≤999 are valid to address indirect-only registers. See below.

Below is the list of functions which can use (i) as an address. For GTO, XEQ, and FN=, (i) refers to a label; for all other functions it refers to a variable.

STO (i)

XEQ (i)

DSE (i)

RCL (i)

GTO (i)

ISG (i)

STO +,–,×,÷ (i)

INPUT (i)

SOLVE (i)

RCL +,–,×,÷ (i)

VIEW (i)

∫FN d (i)

x<> (i)

FN= (i)

15.6.3. Indirect-only registers

The DM32 has two sets of 900 registers which can be controlled only by indirect addressing:

  • Extended registers
    Index numbers 100 to 999 address Extended registers which are saved to/restored from Statefile.

  • Global registers
    Index numbers –100 to –999 address Global registers, used as common storage accessible from all Available States. This area is used as a scratch pad and to pass data back and forth between States; it cannot be saved and will be lost upon any RESET and also when updating the DM32 firmware; be sure to copy any Global registers you want to save to Extended registers in the State you wish to retain them in prior to any firmware update.

These registers differ also in the sense that they must — and only can — be addressed indirectly. As a reminder, the following indirect address

  • 3 STO [i] RCL [(i)]

recalls variable C. This is equivalent to the direct address

  • RCL [C].

Indirect-only registers have no such direct way to be addressed, but can be useful in building programs dealing with much more values than the directly addressable variables A to Z.

Indirect-only registers support functions STO, RCL, INPUT, VIEW, x<>, ISG and DSE, as well as STO and RCL arithmetic.

Example
Clear memory using CLEAR ALL Y. To store numbers in Extended and Global registers:

keystrokes x-register description

1.

255 STO [i]

255.0000

set indirect index to 255

2.

123456.789 STO [(i)]

123456.7890

store number 123456.789 in Extended register 255

3.

255 +/– STO [i]

–255.0000

set indirect index to –255

4.

1024 STO [(i)]

1024.0000

store number 1024 in Global register –255

5.

255 STO [i]

255.0000

set indirect index to 255

6.

RCL [(i)]

123456.7890

recall number stored in Extended register 255 on the stack

7.

255 +/– STO [i]

–255.0000

set indirect index to –255

8.

VIEW [(i)]

–255=1024.000

VIEW number in Global register –255

15.6.4. Program control with (i)

Since the contents of i can change each time a program runs — or even in different parts of the same program — a program instruction such as GTO(i) can branch to a different label at different times. This maintains flexibility by leaving open (until the program runs) exactly which variable or program label will be needed.

Indirect addressing is very useful for counting and controlling loops. The variable i serves as an index, holding the address of the variable that contains the loop-control number for the functions DSE and ISG.

15.6.5. Equations using (i)

Function (i) can be used in an equation to reference a variable indirectly.

The following program uses an equation on line F02 to find the sum of the squares of variables A through Z.

E01 LBL E           begin program
E02 CF 10           set execution of equation (and not display)
E03 CF 11           disable equation prompting
E04 1.026           sets loop-control number for 1 to 26
E05 STO i           stores loop-control number
E06 0               initialize sum
F01 LBL F           start summation loop
F02 (i)^2           written as an equation to evaluate the i-th square
F03 +               add i-th square to the sum
F04 ISG i           increase counter, test for loop exit
F05 GTO F           branches for next variable
F06 RTN             if loop exited, end program

15.7. Debugging

It is sometimes unclear where an error occurs in a program. The DM32 offers two basic tools for debugging:

  • single-step execution, with step into, step over, step out and step-back functions,

  • Debug view, which monitors a selection of variables (up to 12).

15.7.1. Single-step execution

These functions allow for executing a program one line at a time and observing the effect of each executed instruction on data. The returned data can be compared to expected values, so as to validate the instruction before moving to the next.

Step-into
Single-stepping is performed by pressing F6 or while in Calculator mode:

  1. Place the program pointer at the start of the desired program with GTO label (if the program to debug is the first or only program, use GTO ).

  2. Press and hold F6 or : this displays the current program line. Releasing the key executes the instruction. (Note that this is similar to function preview, in that holding the key 2.5 seconds or more displays NULL; from that point execution of the instruction is cancelled and the pointer doesn’t move.) The effects of the instruction can be seen directly on the stack.

  3. The program pointer moves to the next line in the program.

This is also known in computer programming as a “step-into” function because when executing an XEQ instruction to call a subroutine, the program pointer will step into that routine, and every instruction from the routine will be single-stepped until the RTN instruction is met — contrary to function step-over described below.

Step-over
Pressing F3 has the exact same behavior as described as Step into with F6 above, except when the pointer meets an XEQ instruction (call to a subroutine). Then, F3 treats XEQ as a single instruction invoking the whole subroutine in one step.

This is useful to “skip” routines and subroutines which are known to work, saving time while debugging.

Step-out
Stepping out is performed at any point by using      F3. This function automatically runs the subroutine and stops after the return from the subroutine. In other words, it steps out of the current routine or subroutine and returns to the line following the parent XEQ call.

Step-back
At any time, F5 or can be used to step to the previous line in the program. No execution occurs in this case.

15.7.2. Debug view

The Debug view is a special window for monitoring variables and/or program lines, activated by F2. Here is how to use Debug view:

  1. Press F2.

  2. In the Debug Variables dialog which appears, create a list by entering either:

    • variables by pressing the corresponding letter keys, or

    • symbol + to include a program line.

  3. When ready, press F2 again.

  4. Debug view appears on top of the stack.

  5. Press F2 again to close the window.

When active, long-pressing F2 momentarily hides Debug view to show the entire stack.

When the number of items to monitor is ≤ 3, Debug view opens with a larger font and 1-column presentation:

debug5

Press F2 again to switch to the smaller font and 2-column presentation :

debug6

Up to 12 items can be entered in the Debug Variables list. Debug view shows items in the order they have been entered in the Debug Variables list, from left to right and from top to bottom.

Variable letters and “+” symbols can be repeated. A “+” symbol on its own shows the current program line (the line at the program pointer). Every subsequent “+” symbol entered in the list shows the next program line in Debug view. For instance, if the Debug Variables list contains 3 “+” symbols, then the second occurrence in Debug view shows current program line + 1, and the third occurrence shows current program line + 2.

All calculator functions work normally while Debug view is active. It means that the only way to close Debug view is by pressing F2 (C or work normally).

For the following two examples, clear the calculator memory with CLEAR ALL Y. Then, download and load the Statefile from the Vector operations example in this manual (name VECTOP visible in the top bar). This program converts vector coordinates from rectangular to polar format (of course it is also possible to manually enter the program).

Example: configuring Debug view
1. Make sure the program pointer is at the top of the polar routine by pressing GTO [P]. 2. Press F2 to open the Debug Variables dialog.

+ image::debug1.png[width=70%] 3. Populate the list of Debug Variables with the following characters, in that same order: +, \$R\$, +, \$T\$, +, \$P\$.

+ image::debug2.png[width=70%] 4. Press F2 again to bring up Debug view, configured such that the left column shows the current program line plus the next two, and the right column shows variables \$R\$, \$T\$ and \$P\$.

+ image::debug3.png[width=70%] 5. Then pressing F6 single-steps through the Vector operations program while monitoring variable values and incoming program instructions.

Using Debug view for display purpose only
Debug view isn’t tied to single-step execution or debugging in general. It remains active as long as it isn’t explicitly deactivated with F2. This means that it can be used simply to display variables in a creative way. Using the same Vector operations program:

  1. Make sure the pointer is at the top of program memory by pressing GTO .

  2. If Debug view is still active, press F2 to close it and press F2 again to configure it.

  3. Populate the list of Debug Variables with variable letters \$X\$, \$R\$, \$Y\$, \$T\$, \$Z\$, and \$P\$, in that same order.

  4. Press F2 again to bring up the Debug view.

  5. Press R/S to execute the Vector operations program.

  6. For the sake of the example, enter value 1 at the X, Y and Z prompts, each time confirming with R/S.

  7. After value for variable Z has been confirmed, the program is written so that subsequent presses on R/S are required to read variables \$R\$, \$T\$, and \$P\$. But this is superfluous thanks to the Debug window and how it is configured; all six variables are visible in real time, showing both the rectangular and polar coordinates for the current vector.

    debug4
  8. To convert another vector from rectangular to polar, press GTO and then R/S.

Keep in mind that Debug view simply lets you watch the status of the variables that you select, at each stage of program execution. Some programs were designed to be run requiring the user to press R/S to calculate and display one result at a time (due to the limited 1-line display of the original HP-32SII) so be sure not to interpret results seen in Debug view’s window as final until full program execution has been completed.

16. Solving and integrating programs

16.1. Solving a program

Chapter Equations shows how to add an equation to the Equation list and solve it for any of its variables. It is also possible to write a program and solve it for any variable. This is useful for when the equation to solve changes depending on certain conditions or if it requires repeated calculations.

16.1.1. Solving a programmed function

  1. Enter a program that defines the function. (See Writing a SOLVE program below.)

  2. Select the program to solve: press FN= label. (This step may be skipped if the same program is being solved again.)

  3. Solve for the unknown variable: press SOLVE variable.

Note how FN= is required to solve a programmed function, but not when solving an equation from the Equation list.

To halt a calculation, press C or R/S. The current best estimate of the root is in the unknown variable; use VIEW to view it without disturbing the stack. To resume calculation, press R/S.

16.1.2. Writing a SOLVE program

The program can use equations and RPN operations in whatever combination is most convenient.

  1. Begin the program with a label. This label identifies the function to be evaluated by SOLVE (FN=label).

  2. Include an INPUT instruction for each variable, including the unknown. INPUT instructions enable solving for any variable in a multi-variable function. INPUT for the unknown is ignored by the calculator, so only one program needs to be written that contains a separate INPUT instruction for every variable (including the unknown).
    If no INPUT instructions is included, the program uses the values stored in the variables or entered at equation prompts.

  3. Enter the instructions to evaluate the function.

    • A function programmed as a multi-line RPN sequence must be in the form of an expression that goes to zero at the solution. If the equation is \$f(z) = g(z)\$, the program should calculate \$f(z) - g(z)\$. “\$=0\$” is implied.

    • A function programmed as an equation can be any type of equation (equality, assignment, or expression). The equation is evaluated by the program, and its value goes to zero at the solution. To make the equation automatically prompt for variable values instead of including INPUT instructions at the beginning of the program, make sure flag 11 is set.

  4. End the program with a RTN. Program execution should end with the value of the function in the x-register.

SOLVE works only with real numbers. However, if a complex-valued function can be written to isolate its real and imaginary parts, SOLVE can solve for the parts separately.

Example: program using RPN
The following example shows a SOLVE program using RPN operations. It solves for any variable in the “ideal gas law” equation. The equation is \$P × V = N × R × T\$, where

  • \$P\$ = Pressure (atmospheres or N/m2).

  • \$V\$ = Volume (liters).

  • \$N\$ = Number of moles of gas.

  • \$R\$ = The universal gas constant (8.314 J / mole-K).

  • \$T\$ = Temperature (kelvins; K = °C + 273.1).

To enter the program, activate Program mode with PRGM and, if necessary, return the program pointer to the top of program memory with GTO .

G01 LBL G           identify the programmed function
G02 INPUT P         store P
G03 INPUT V         store V
G04 INPUT N         store N
G05 INPUT R         store R
G06 INPUT T         store T
G07 RCL P           pressure
G08 RCL× V          pressure × volume
G09 RCL N           number of moles of gas
G10 RCL× R          moles × gas constant
G11 RCL× T          moles × gas constant × temp
G12 –               (P × V) – (N × R × T)
G13 RTN             end program

Exit Program mode with C. Here is a step-by-step procedure for using program “G” to solve for the pressure of 0.005 moles of carbon dioxide in a 2-liter bottle at 24 °C.

keystrokes x-register description

1.

FN= [G]

select G as the program SOLVE evaluates to find the value of the unknown variable

2.

SOLVE [P]

V?value

select P as the unknown; prompt for V

3.

2 R/S

N?value

store 2 in V; prompt for N

4.

.005 R/S

R?value

store .005 in N; prompt for R

5.

.0821 R/S

T?value

store .0821 in R; prompt for T

6.

24 ENTER 273.1 +

T?297.1000

calculate T

7.

R/S

SOLVING

store 297.1 in T; solve for P

8.

P=0.0610

pressure is 0.0610 atm

Example: program using an equation
The following example shows a SOLVE program using an equation for the same “ideal gas law”.

H01 LBL H           identify the programmed function
H02 SF 11           enable equation prompting
H03 P×V–N×R×T       evaluate the equation (automatically clears flag 11)
H04 RTN             end program

Here is a step-by-step procedure for using program “H” to calculate the change in pressure of the carbon dioxide if its temperature drops by 10 °C from the previous example.

keystrokes x-register description

1.

STO [L]

0.0610

store previous pressure

2.

FN= [H]

0.0610

select H as the program SOLVE

3.

SOLVE [P]

V?2.0000

select P as the unknown; prompt for V

4.

R/S

N?0.0050

retain 2 in V; prompt for N

5.

R/S

R?0.0821

retain .005 in N; prompt for R

6.

R/S

T?297.1000

retain .0821 in R; prompt for T

7.

ENTER 10

T?287.1000

calculate new T

8.

R/S

SOLVING

store 287.1 in T; solve for new P

9.

P=0.0589

new P

10.

RCL [L]

–0.0021

pressure change is -0.0021 (pressure drop)

16.2. Using SOLVE in a program

Operation SOLVE can be used as a program instruction.

If appropriate, include or prompt for initial guesses (into the unknown variable and into the X-register) before executing the SOLVE variable instruction. The two instructions for solving an equation for an unknown variable appear in a program as:

  • FN= label

  • SOLVE variable

The programmed SOLVE instruction does not produce a labeled display like

N=1.2345

This is because it is assumed that the output is intended as input for subsequent operations in the program. To display the result, a VIEW variable instruction must be added after the SOLVE instruction.

If no solution is found for the unknown variable, then the next program line is skipped (in accordance with the "do-if-true" rule). The program should then handle the case of not finding a root, such as by choosing new initial estimates or changing an input value.

Example: SOLVE as a program instruction
The following program solves the diameter-to-area function of a circle. It uses indirect addressing. Program “F” is a SOLVE program. To find the area, use XEQ [A], to find the diameter, use XEQ [D].

A01 LBL A           setup for A (area)
A02 1               index for A
A03 GTO L           branch to main routine

D01 LBL D           setup for D (diameter)
D02 4               index for D
D03 GTO L           branch to main routine

L01 LBL L           main routine
L02 STO i           stores index
L03 FN= F           select F as SOLVE program
L04 SOLVE(i)        solve (indirect) variable
L05 VIEW(i)         view (indirect) variable
L06 RTN             end program

F01 LBL F           SOLVE program
F02 INPUT D
F03 INPUT A         put area (A) on the stack
F04 RCL D           put diameter (D) on the stack
F05 2
F06 ÷               divide by 2 for radius
F07 x²              square the radius
F08 π
F09 ×               multiply by π
F10 –               subtract from A
F11 RTN             end SOLVE program

16.3. Integrating (∫FN d) a program

Chapter Equations shows how to add an equation, or expression, to the Equation list and integrate it with respect to any of its variables. It is also possible to write a program that calculates a function and integrate it with respect to any of its variables. This is useful for when the function to integrate changes depending on certain conditions or if it requires repeated calculations.

16.3.1. Integrating (∫FN d) a programmed function

  1. Enter a program that defines the integrand’s function. (See Writing a ∫FN program below.)

  2. Select the program that defines the function to integrate: press FN= label. (This step may be skipped if the same program is being integrated again.)

  3. Enter the limits of integration:

    • key in the lower limit, press ENTER,

    • key in the upper limit.

  4. Select the variable of integration: press variable. The calculation starts.

Note how defining the integration function with FN= is required to integrate a programmed function, but not when integrating an equation from the Equation list.

To halt the running integration, press C or R/S. No information is available before the integration finishes normally. Calculation can be resumed with R/S. Pressing XEQ while integration calculation is running cancels the ∫FN operation. If this happens, ∫FN must start again from the beginning.

16.3.2. Writing a ∫FN program

The program can use equations and RPN operations in whatever combination is most convenient.

  1. Begin the program with a label. This label identifies the function to integrate (FN=label).

  2. Include an INPUT instruction for each variable, including the variable of integration. INPUT instructions enable integrating with respect to any variable in a multi-variable function. INPUT for the variable of integration is ignored by the calculator, so only one program needs to be written that contains a separate INPUT instruction for every variable (including the variable of integration).
    If no INPUT instructions is included, the program uses the values stored in the variables or entered at equation prompts.

  3. Enter the instructions to evaluate the function.

    • A function programmed as a multi-line RPN sequence must calculate the function values to be integrated.

    • A function programmed as an equation holds an equation written as an expression, though it can be any type of equation. To make the equation automatically prompt for variable values instead of including INPUT instructions at the beginning of the program, make sure flag 11 is set.

  4. End the program with a RTN. Program execution should end with the value of the function in the x-register.

16.4. Using ∫FN in a program

Operation ∫FN can be used as a program instruction.

It must be remembered to include or prompt for the limits of integration, and that accuracy and execution time are affected by the display format at the time the program runs. If appropriate, include or prompt for initial guesses (into the unknown variable and into the X-register) before executing the SOLVE variable instruction. The two instructions for integration appear in a program as:

  • FN= label

  • ∫FN d variable

The programmed ∫FN instruction does not produce a labeled display like

∫=1.2345

This is because it is assumed that the output is intended as input for subsequent operations in the program. To display the result, a PSE or STOP instruction must be added after the ∫FN instruction.

If no solution is found for the unknown variable, then the next program line is skipped (in accordance with the "do-if-true" rule). The program should then handle the case of not finding a root, such as by choosing new initial estimates or changing an input value.

16.5. Restrictions on SOLVE and ∫FN

Instructions SOLVE variable and ∫FN d variable cannot call a routine that contains another SOVE or ∫FN instruction. Attempting recursive integration results in an ∫(∫FN) error message. Also, SOLVE and ∫FN cannot call a routine that contains an FN=label instruction; if attempted, the calculator throws error message SOLVE ACTIVE or ∫FN ACTIVE. Solve cannot call a routine that contains an ∫FN instruction (throws a SOLVE(∫FN) error), just like ∫FN cannot call a routine that contains a SOLVE instruction (throws a ∫(SOLVE) error). In a program, the SOLVE variable and ∫FN d variable instructions use one of the fifteen pending subroutine returns (see Subroutine nesting).

The SOLVE and ∫FN operations automatically set base mode to decimal (base-10).

17. Mathematics programs

This chapter has 3 example programs:

17.1. Vector operations

This program calculates fundamental vector operations: addition, subtraction, cross product, and dot (or scalar) product. It is designed for three-dimensional vectors and offers input and output options in both rectangular and polar formats. Additionally, it calculates angles between vectors.

prg vector

Calculations in this program are based on the following set of equations.

Coordinate conversion:

\$X = R sin(P) cos(T)\$
\$Y = R sin(P) sin(T)\$
\$Z = R cos(P)\$
\$R = sqrt(X^2+Y^2+Z^2)\$
\$T = arctan(Y/X)\$
\$P = arctan(Z/sqrt(X^2+Y^2))\$

Vector addition and subtraction:

\$bbv_1 + bbv_2 = (X+U)bbi + (Y+V)bbj + (Z+W)bbk\$
\$bbv_2 - bbv_1 = (U-X)bbi + (V-Y)bbj + (W-Z)bbk\$

Cross product:

\$bbv_1 × bbv_2 = (YW-ZV)bbi + (ZU-XW)bbj + (XV-YU)bbk\$

Dot product:

\$D=XU+YV+ZW\$

Angle between vectors (γ):

\$G = arccos(D/(R_1×R_2))\$

where

\$bbv_1 = Xbbi + Ybbj + Zbbk\$

and

\$bbv_2 = Ubbi + Vbbj + Wbbk\$

The vector displayed by the input routines (LBL P and LBL R) is \$V_1\$.

 

Program listing

program line description

R01 LBL R

Beginning of the rectangular input/display routine.

R02 INPUT X

Display or accept input of \$X\$.

R03 INPUT Y

Display or accept input of \$Y\$.

R04 INPUT Z

Display or accept input of \$Z\$.

 

Q01 LBL Q

Define beginning of rectangular-to-polar conversion process.

Q02 RCL Y

Q03 RCL X

Q04 y,x→θ,r

Calculate \$sqrt((X^2+Y^2)\$ and \$arctan(Y//X)\$.

Q05 x<>y

Q06 STO T

Store \$T=arctan(Y//X)\$.

Q07 R↓

Get \$sqrt((X^2+Y^2)\$ back to the x-register.

Q08 RCL Z

Q09 y,x→θ,r

Calculate \$sqrt((X^2+Y^2+Z^2)\$ and \$P\$.

Q10 STO R

Store \$R\$.

Q11 x<>y

Q12 STO P

Store \$P\$.

 

P01 LBL P

Beginning of the polar input/display routine.

P02 INPUT R

Display or accept input of \$R\$.

P03 INPUT T

Display or accept input of \$T\$.

P04 INPUT P

Display or accept input of \$P\$.

P05 RCL T

P06 RCL P

P07 RCL R

P08 θ,r→y,x

Calculate \$R cos(P)\$ and \$R sin(P)\$.

P09 STO Z

Store \$Z = R cos(P)\$.

P10 R↓

P11 θ,r→y,x

Calculate \$R sin(P) cos(T)\$ and \$R sin(P) sin(T)\$.

P12 STO X

Store \$X = R sin(P) cos(T)\$.

P13 x<>y

P14 STO Y

Store \$Y = R sin(P) sin(T)\$.

P15 GTO P

Loop back for another display of polar form.

 

E01 LBL E

Beginning of the vector-enter routine.

E02 RCL X

Copy values in \$X\$, \$Y\$ and \$Z\$ to \$U\$, \$V\$ and \$W\$ respectively.

E03 STO U

E04 RCL Y

E05 STO V

E06 RCL Z

E07 STO W

E08 GTO Q

Loop back for polar conversion and display/input.

 

X01 LBL X

Beginning of vector-exchange routine.

X02 RCL X

Exchange \$X\$, \$Y\$ and \$Z\$ with \$U\$, \$V\$ and \$W\$ respectively.

X03 x<> U

X04 STO X

X05 RCL Y

X06 x<> V

X07 STO Y

X08 RCL Z

X09 x<> W

X10 STO Z

X11 GTO Q

Loop back for polar conversion and display/input.

 

A01 LBL A

Beginning of vector-addition routine.

A02 RCL X

A03 RCL+ U

A04 STO X

Store \$X+U\$ in \$X\$.

A05 RCL V

A06 RCL+ Y

A07 STO Y

Store \$V+Y\$ in \$Y\$.

A08 RCL Z

A09 RCL+ W

A10 STO Z

Store \$Z+W\$ in \$Z\$.

A11 GTO Q

Loop back for polar conversion and display/input.

 

S01 LBL S

Beginning of the vector-subtraction routine.

S02 ⎻1

Change the sign of \$X\$, \$Y\$ and \$Z\$.

S03 STO× X

S04 STO× Y

S05 STO× Z

S06 GTO A

Go to the vector-addition routine.

 

C01 LBL C

Beginning of the cross-product routine.

C02 RCL Y

C03 RCL× W

C04 RCL Z

C05 RCL× V

C06 -

Calculate component \$X = (YW - ZV)\$.

C07 RCL Z

C08 RCL× U

C09 RCL X

C10 RCL× W

C11 -

Calculate component \$Y = (ZU - WX)\$.

C12 RCL X

C13 RCL× V

C14 RCL Y

C15 RCL× U

C16 -

Calculate component \$Z = (XV - YU)\$.

C17 STO Z

Store component \$Z\$.

C18 R↓

C19 STO Y

Store component \$Y\$.

C20 R↓

C21 STO X

Store component \$X\$.

C22 GTO Q

Loop back for polar conversion and display/input.

 

D01 LBL D

Beginning of dot-product and vector-angle routine.

D02 RCL X

D03 RCL× U

D04 RCL Y

D05 RCL× V

D06 +

D07 RCL Z

D08 RCL× W

D09 +

 

D10 STO D

Store the dot product of \$XU + YV + ZW\$.

D11 VIEW D

Display the dot product.

D12 RCL D

D13 RCL÷ R

Divide the dot product by the magnitude of the \$X\$-, \$Y\$-, \$Z\$-vector.

D14 RCL W

D15 RCL V

D16 RCL U

D17 y,x→θ,r

D18 x<>y

D19 R↓

D20 y,x→θ,r

Calculate the magnitude of the \$U\$-, \$V\$-, \$W\$-vector.

D21 x<>y

D22 R↓

D23 ÷

Divide previous result by the magnitude.

D24 ACOS

Calculate angle.

D25 STO G

D26 VIEW G

Display angle.

D27 GTO P

Loop back for polar and display/input.

 

Flags used

None.

 

Note

The terms “polar” and “rectangular,” which refer to two-dimensional systems, are used instead of the proper three-dimensional terms of “spherical” and “Cartesian.” This stretch of terminology allows the labels to be associated with their function without confusing conflicts. For instance, if LBL C had been associated with Cartesian coordinate input, it would not have been available for cross product.

 

Program usage

  1. If the vector is in rectangular form, press XEQ [R] and go to step 3. If the vector is in polar form, press XEQ [P] and continue with step 2.

  2. Key in \$R\$ and press R/S, key in \$T\$ and press R/S, then key in \$P\$ and press R/S. Continue at step 4.

  3. Key in \$X\$ and press R/S, key in \$Y\$ and press R/S, and key in \$Z\$ and press R/S.

  4. To key in a second vector, press XEQ [E] (as in “enter”), then go to step 1.

  5. Perform desired vector operation:

    1. Add vectors by pressing XEQ [A];

    2. Subtract vector one from vector two by pressing XEQ [S];

    3. Compute the cross product by pressing XEQ [C];

    4. Compute the dot product and angle between vectors by pressing XEQ [D].

  6. Optional: to review \$bbv_1\$ in polar form, press XEQ [P], then press R/S repeatedly to see the individual elements.

  7. Optional: to review \$bbv_1\$ in rectangular form, press XEQ [R], then press R/S repeatedly to see the individual elements.

  8. When adding, subtracting, or computing the cross product, \$bbv_1\$ is replaced by the result, while \$bbv_2\$ is not altered. To continue calculations based on the result, remember to press XEQ [E] before keying in a new vector.

  9. Start again at step 1 to continue vector calculations.

 

Variables

\$X\$, \$Y\$, \$Z\$

Rectangular components of \$bbv_1\$

\$U\$, \$V\$, \$W\$

Rectangular components of \$bbv_2\$

\$R\$, \$T\$, \$P\$

Radius, angle in the x-y plane (θ), and angle from the z-axis of \$bbv_1\$, (\$U\$).

\$D\$

Dot product.

\$G\$

The angle between vectors (γ).

 

Example: antenna and emitter

An optical receiver for wireless data transmission must be pointed at the emitting laser. The emitter sits 4.3 kilometers North, 2.7 kilometers East and 0.24 kilometers above. Use the rectangular to polar conversion capability to find the total distance and the direction to the emitter.

prg vector example
keystrokes x-register description

1.

MODES DG

set degrees angular mode

2.

XEQ [R]

X?value

start rectangular input and display routine

3.

2.7 R/S

Y?value

set \$X\$ to 2.7

4.

4.3 R/S

Z?value

set \$Y\$ to 4.3

5.

.24 R/S

5.0831

set \$Z\$ to 0.24 and returns \$R\$, the radius

6.

R/S

57.8750

calculate \$T\$, angle in the x-y plane

7.

R/S

87.2937

calculate \$P\$, angle from the z-axis

17.2. 2×2 or 3×3 Simultaneous Equations

Ready-to-use Statefile direct download: https://technical.swissmicros.com/dm32/examples/STATE/SIMEQ.d32

This program solves simultaneous linear equations in two or three unknowns. It does this through matrix inversion and matrix multiplication.

A system of three linear equations

\$AX+DY+GZ=J\$
\$BX+EY+HZ=K\$
\$CX+FY+IZ=L\$

can be represented by the matrix equation below.

\$[[A,D,G],[B,E,H],[C,F,I]] [[X],[Y],[Z]] = [[J],[K],[L]]\$

The matrix equation may be solved for \$X\$, \$Y\$, and \$Z\$ by multiplying the result matrix by the inverse of the coefficient matrix.

\$[[A',D',G'],[B',E',H'],[C',F',I']] [[J],[K],[L]] = [[X],[Y],[Z]]\$

Specifics regarding the inversion process are given in the comments for the inversion routine, I.

 

Program listing

program line description

A01 LBL A

Starting point for input of coefficients.

A02 1.012

Loop-control value: loop from 1 to 12, one at a time.

A03 STO i

Store control value in index variable.

 

L01 LBL L

Start the input loop.

L02 INPUT(i)

Prompt for and store the variable addressed by i.

L03 ISG i

Adds one to \$i\$.

L04 GTO L

If \$i\$ is less than 13, go back to LBL L and get the next value.

L05 GTO A

Return to LBL A to review values.

 

I01 LBL I

This routine inverts a 3×3 matrix.

I02 XEQ D

Calculate determinant and save value for the division loop, J.

I03 STO W

I04 RCL A

I05 RCL× I

I06 RCL C

I07 RCL× G

I08 -

I09 STO X

Calculate \$E'\$ × determinant = \$AI - CG\$.

I10 RCL C

I11 RCL× D

I12 RCL A

I13 RCL× F

I14 -

I15 STO Y

Calculate \$F'\$ × determinant = \$CD - AF\$.

I16 RCL B

I17 RCL× G

I18 RCL A

I19 RCL× H

I20 -

I21 STO Z

Calculate \$H'\$ × determinant = \$BG - AH\$.

I22 RCL A

I23 RCL× E

I24 RCL B

I25 RCL× D

I26 -

I27 STO i

Calculate \$I'\$ × determinant = \$AE - BD\$.

I28 RCL E

I29 RCL× I

I30 RCL F

I31 RCL× H

I32 -

I33 STO A

Calculate \$A'\$ × determinant = \$EI - FH\$.

I34 RCL C

I35 RCL× H

I36 RCL B

I37 RCL× I

I38 -

Calculate \$B'\$ × determinant = \$CH - BI\$.

I39 RCL B

I40 RCL× F

I41 RCL C

I42 RCL× E

I43 -

I44 STO C

Calculate \$C'\$ × determinant = \$BF - CE\$.

I45 R↓

I46 STO B

Store \$B'\$.

I47 RCL F

I48 RCL× G

I49 RCL D

I50 RCL× I

I51 -

Calculate \$D'\$ × determinant = \$FG - DI\$.

I52 RCL D

I53 RCL× H

I54 RCL E

I55 RCL× G

I56 -

I57 STO G

Calculate \$G'\$ × determinant = \$DH - EG\$.

I58 R↓

I59 STO D

Store \$D'\$.

I60 RCL i

I61 STO I

Store \$I'\$.

I62 RCL X

I63 STO E

Store \$E'\$.

I64 RCL Y

I65 STO F

Store \$F'\$.

I66 RCL Z

I67 STO H

Store \$H'\$.

I68 9

I69 STO i

Set index value to point to last element of matrix.

I70 RCL W

Recall value of determinant.

 

J01 LBL J

This routine completes inverse by dividing by determinant.

J02 STO÷(i)

Divide element.

J03 DSE i

Decrement index value so it points closer to \$A\$.

J04 GTO J

Loop for next value.

J05 RTN

Return to the calling program or to PRGM TOP.

 

M01 LBL M

This routine multiplies a column matrix and a 3×3 matrix.

M02 7

Set index value to point to last element in first row.

M03 XEQ N

M04 8

Set index value to point to last element in second row.

M05 XEQ N

M06 9

Set index value to point to last element in third row.

 

N01 LBL N

This routine calculates product of column vector and row pointed to by index value.

N02 STO i

Save index value in \$i\$.

N03 RCL J

Recall \$J\$ from column vector.

N04 RCL K

Recall \$K\$ from column vector.

N05 RCL L

Recall \$L\$ from column vector.

N06 RCL×(i)

Multiply by last element in row.

N07 XEQ P

Multiply by second element in row and add.

N08 XEQ P

Multiply by first element in row and add.

N09 23

Set index value to display \$X\$, \$Y\$, or \$Z\$ based on input row.

N10 STO+ i

N11 R↓

Get result back.

N12 STO(i)

Store result.

N13 VIEW(i)

Display result.

N14 RTN

Return to the calling program or to PRGM TOP.

 

P01 LBL P

This routine multiplies and adds values within a row.

P02 x<>y

Get next column value.

P03 DSE i

Set index value to point to next row value.

P04 DSE i

P05 DSE i

P06 RCL×(i)

Multiply column value by row value.

P07 +

Add product to previous sum.

P08 RTN

Return to calling program.

 

D01 LBL D

This routine calculates the determinant.

D02 RCL A

D03 RCL× E

D04 RCL× I

Calculate \$A×E×I\$.

D05 RCL D

D06 RCL× H

D07 RCL× C

D08 +

Calculate \$(A×E×I) + (D×H×C)\$.

D09 RCL G

D10 RCL× F

D11 RCL× B

D12 +

Calculate \$(A×E×I) + (D×H×C) + (G×F×B)\$.

D13 RCL G

D14 RCL× E

D15 RCL× C

D16 -

\$(A×E×I) + (D×H×C) + (G×F×B) - (G×E×C)\$.

D17 RCL A

D18 RCL× F

D19 RCL× H

D20 -

\$(A×E×I) + (D×H×C) + (G×F×B) - (G×E×C) - (A×F×H)\$.

D21 RCL D

D22 RCL× B

D23 RCL× I

D24 -

\$(A×E×I) + (D×H×C) + (G×F×B) - (G×E×C) - (A×F×H) - (D×B×I)\$.

D25 RTN

Return to the calling program or to PRGM TOP.

 

Flags used

None.

 

Program usage

  1. Press XEQ [A] to input coefficients of matrix and column vector.

  2. Key in coefficient or vector value (\$A\$ through \$L\$) at each prompt and press R/S.

  3. Optional: press XEQ [D] to compute determinant of 3×3 system.

  4. Press XEQ [I] to compute inverse of 3×3 matrix.

  5. Optional: press XEQ [A] and repeatedly press R/S to review the values of the inverted matrix.

  6. Press XEQ [M] to multiply the inverted matrix by the column vector and to see the value of \$X\$. Press R/S to see the value of \$Y\$, then press R/S again to see the value of \$Z\$.

  7. For a new case, go back to step 1.

 

Variables

\$A\$ through \$I\$

Coefficients of matrix.

\$J\$ through \$L\$

Column vector values.

\$W\$

Scratch variable used to store the determinant.

\$X\$ through \$Z\$

Output vector values; also used for scratch.

\$i\$

Loop-control value (index variable); also used for scratch.

 

Note

For 2×2 solutions use zero for coefficients \$C\$, \$F\$, \$H\$, \$G\$ and \$L\$. Use 1 for coefficient \$I\$.

Not all systems of equations have solutions.

 

Example

For the system below, compute the inverse and the system solution. Review the inverted matrix. Invert the matrix again and review the result to make sure that the original matrix is returned.

\$23X+15Y+17Z=31\$
\$8X+11Y+6Z=17\$
\$4X+15Y+12Z=14\$
keystrokes x-register description

1.

XEQ [A]

A?value

Start input routine.

2.

23 R/S

B?value

Set first coefficient, \$A\$, equal to 23.

3.

8 R/S

C?value

Set \$B\$ equal to 8.

4.

4 R/S

D?value

Set \$C\$ equal to 4.

5.

15 R/S

E?value

Set \$D\$ equal to 15.

6.

…​

…​

Continue entries for \$E\$ through \$L\$

7.

14 R/S

A?23.0000

Return to first coefficient entered.

8.

XEQ [I]

1780.0000

Calculate the inverse and display the determinant.

9.

XEQ [M]

X=110.2309

Multiply by column vector to compute \$X\$.

10.

R/S

Y=300.7470

Calculate and display \$Y\$.

11.

R/S

Z=⁻412.6774

Calculate and display \$Z\$.

12.

XEQ [A]

A?0.0357

Begin review of the inverted matrix.

13.

R/S

B?⁻0.0611

Display next value.

14.

R/S

C?0.0645

Display next value.

15.

R/S

D?0.0637

Display next value.

16.

R/S

E?0.1766

Display next value.

17.

R/S

F?⁻0.2419

Display next value.

18.

R/S

G?⁻0.0823

Display next value.

19.

R/S

H?⁻0.0017

Display next value.

20.

R/S

I?0.1129

Display next value.

21.

XEQ [I]

0.0008

Invert inverse to produce original matrix.

22.

XEQ [A]

A?23.0000

Begin review of inverted inverted matrix.

23.

R/S

B?8.0000

Display next value…​

24.

…​

…​

…​ and so on.

17.3. Polynomial root finder

This program is designed to identify the solutions of polynomials with real coefficients, ranging in order from 2 to 5. It provides computations for both real and complex solutions.

In this program, a standard polynomial is represented as

\$x^n + a_(n-1)x^(n-1) + ... + a_1x + a_0 = 0\$

where \$n\$ = 2, 3, 4 or 5. It is assumed that the coefficient of the highest-order term (\$a_n\$) is 1. If the leading coefficient is different from 1, it should be adjusted to be 1 by dividing all coefficients in the equation by the leading coefficient.

For third- and fifth-order polynomial cases, the routines use SOLVE to identify a single real root within the equation. This approach stems from the requirement that odd-order polynomials must inherently have at least one real root. Upon discovering a single root, synthetic division is carried out to simplify the original polynomial into either a second- or fourth-order expression. Resolving a fourth-order polynomial requires an initial solution to the associated resolvant cubic polynomial:

\$y^3 + b_2y^2 + b_1y + b_0 = 0\$

where

\$b_2 = -a_2\$

\$b_1 = a_3a_1 - 4a_0\$

\$b_0 = a_0(4a_2 - a_3^2) - a_1^2\$

Let \$y_0\$ represent the largest real root of the above cubic equation. Then, the fourth-order polynomial is then broken down into two quadratic polynomials:

\$x^2 + (J+L)x + (K+M) = 0\$
\$x^2 + (J-L)x + (K-M) = 0\$

where

\$J = a_3/2\$

\$K = y_0/2\$

\$L = sqrt(J^2 - a_2 + y_0) ×\$ the sign of \$JK-a_1/2\$

\$M = sqrt(K^2 - a_0\$

The solutions for the fourth-degree polynomial’s roots are obtained through the resolution of these two quadratic polynomials.

A quadratic equation \$x^2+a_1x+a_0=0\$ is solved by the formula

\$x_(1,2) = -a_1/2 ± sqrt((a_1/2)^2-a_0\$

If the discriminant \$d = (a_1/2)^2-a_0 >= 0\$, the roots are real; if \$d < 0\$, the roots are complex, being \$u ± iv = -(a_1/2) ± i sqrt(-d)\$.

 

Program listing

program line description

P01 LBL P

Define the beginning of the polynomial root finder routine.

P02 INPUT F

Prompt for and store the order of the polynomial.

P03 STO i

Use order as loop counter.

 

I01 LBL I

Start prompting routine.

I02 INPUT(i)

Prompt for a coefficient.

I03 DSE i

Count down the input loop.

I04 GTO I

Repeat until done.

I05 RCL F

I06 STO i

Use order to select root finding routine.

I07 GTO(i)

Start root finding routine.

 

H01 LBL H

Evaluate polynomials using Horner’s method, and synthetically reduce the order of the polynomial using the root.

H02 RCL H

H03 STO i

Use pointer to polynomial as index.

H04 1

Starting value for Horner’s method.

 

J01 LBL J

Start the Horner’s method loop.

J02 ENTER

Save synthetic division coefficient.

J03 RCL× X

Multiply current sum by next power of x.

J04 RCL+(i)

Add new coefficient.

J05 DSE i

Count down the loop.

J06 GTO J

Repeat until done.

J07 RTN

 

S01 LBL S

Start solver setup routine.

S02 STO H

Store location of coefficients to use.

S03 250

S04 STO X

First initial guess.

S05 +/-

Second initial guess.

S06 FN= H

Specify routine to solve.

S07 SOLVE X

Solve for a real root.

S08 GTO H

Get synthetic division coefficients for next lower order polynomial.

S09 0

S10 ÷

Generate DIVIDE BY 0 error if no real root found.

 

Q01 LBL Q

Start quadratic solution routine.

Q02 x<>y

Exchange \$a_0\$ and \$a_1\$.

Q03 2

Q04 ÷

\$a_1//2\$.

Q05 +/-

\$-a_1//2\$.

Q06 ENTER

Q07 ENTER

Save \$-a_1//2\$.

Q08 STO F

Store real part if complex root.

Q09 x²

\$(a_1//2)^2\$.

Q10 R↑

\$a_0\$.

Q11 -

\$(a_1//2)^2-a_0\$.

Q12 CF 0

Initialize flag 0.

Q13 x<0?

Discriminant (\$d\$) < 0 ?

Q14 SF 0

Set flag 0 if \$d\$ < 0 (complex roots).

Q15 ABS

\$|d|\$.

Q16 SQRT

\$sqrt(|d|)\$.

Q17 STO G

Store imaginary part if complex root.

Q18 FS? 0

Complex roots?

Q19 RTN

Return if complex roots.

Q20 STO- F

Calculate \$-(a_1//2) - sqrt(|d|)\$.

Q21 R↓

Q22 STO+ G

Calculate \$-(a_1//2) + sqrt(|d|)\$.

Q23 RTN

 

B01 LBL B

Start second-order solution routine.

B02 RCL B

Get \$L\$.

B03 RCL A

Get \$M\$.

B04 GTO T

Calculate and display two roots.

 

C01 LBL C

Start third-order solution routine.

C02 3

Indicate cubic polynomial to be solved.

C03 XEQ S

Solve for one real root and put \$a_0\$ and \$a_1\$ for second-order polynomial on stack.

C04 R↓

Discard polynomial function value.

C05 XEQ Q

Solve remaining second-order polynomial and store roots.

C06 VIEW X

Display real root of cubic.

C07 GTO N

Display remaining roots.

 

E01 LBL E

Start fifth-order solution routine.

E02 5

Indicate fifth-order polynomial to be solved.

E03 XEQ S

Solve for one real root and put three synthetic division coefficients for fourth-order polynomial on stack.

E04 R↓

Discard polynomial function value.

E05 STO A

Store coefficient.

E06 R↓

E07 STO B

Store coefficient.

E08 R↓

E09 STO C

Store coeflicient.

E10 RCL E

E11 RCL+ X

Calculate \$a_3\$.

E12 STO D

Store \$a_3\$.

E13 VIEW X

Display real root of fifth-order polynomial.

 

D01 LBL D

Start fourth-order solution routine.

D02 4

D03 RCL× C

\$4a_2\$.

D04 RCL D

\$a_3\$.

D05 x²

\$a_3""^2\$.

D06 -

\$4a_2-a_3""^2\$.

D07 RCL× A

\$a_0(4a_2-a_3""^2 )\$.

D08 RCL B

\$a_1\$.

D09 x²

\$a_1""^2\$.

D10 -

\$b_0=a_0(4a_2-a_3""^2)-a_1""^2\$.

D11 STO E

Store \$b_0\$.

D12 RCL C

\$a_2\$.

D13 +/-

\$b_2=-a_2\$.

D14 STO G

Store \$b_2\$.

D15 RCL D

\$a_3\$.

D16 RCL× B

\$a_3a_1\$.

D17 4

D18 RCL× A

\$4a_0\$.

D19 -

\$b_1=a_3a_1-4a_0\$.

D20 STO F

Store \$b_1\$.

D21 4

To enter lines D21 and D22, press 4 SHOW 3.

D22 3

D23 10ˣ

D24 ÷

D25 7

D26 +

Create 7.004 as a pointer to the cubic coefficients.

D27 XEQ S

Solve for real root and put \$a_0\$ and \$a_1\$ for second-order polynomial on stack.

D28 R↓

Discard polynomial function value.

D29 XEQ Q

Solve for remaining roots of cubic and store roots.

D30 RCL X

Get real root of cubic.

D31 STO E

Store real root.

D32 FS? 0

Complex roots?

D33 GTO F

Calculate four roots of remaining fourth-order polynomial.

D34 RCL F

If not complex roots, determine largest real root \$y_0\$.

D35 x<y?

D36 x<>y

D37 RCL G

D38 x<y?

D39 x<>y

D40 STO E

Store largest real root of cubic.

 

F01 LBL F

Start fourth-order solution routine.

F02 2

F03 STO÷ D

\$J=a_3//2\$.

F04 STO÷ E

\$K=y_0//2\$.

F05 9

F06 10ˣ

F07 1/x

Create 10-9 as a lower bound for \$M^2\$.

F08 RCL E

\$K\$.

F09 x²

\$K^2\$.

F10 RCL- A

\$M^2=K^2-a_0\$.

F11 x<y?

F12 CLx

If \$M^2\$ < 10-9, use 0 for \$M^2\$.

F13 SQRT

\$M=sqrt(K^2-a_0)\$.

F14 STO A

Store \$M\$.

F15 RCL D

\$J\$.

F16 RCL× E

\$JK\$.

F17 RCL B

\$a_1\$.

F18 2

F19 ÷

\$a_1//2\$.

F20 -

\$JK-a_1//2\$.

F21 x=0?

F22 1

Use 1 if \$JK-a_1//2=0\$.

F23 STO B

Store 1 or \$JK-a_1//2\$.

F24 ABS

F25 STO÷ B

Calculate sign of \$C\$.

F26 RCL D

\$J\$.

F27 x²

\$J^2\$.

F28 RCL- C

\$J^2-a_2\$.

F29 RCL+ E

F30 RCL+ E

\$J^2-a_2+y_0\$.

F31 SQRT

\$C=sqrt(J^2-a_2+y_0)\$.

F32 STO× B

Store \$C\$ with proper sign.

F33 RCL D

\$J\$.

F34 RCL+ B

\$J+L\$.

F35 RCL E

\$K\$.

F36 RCL+ A

\$K+M\$.

F37 XEQ T

Calculate and display two roots of the fourth-order polynomial.

F38 RCL D

\$J\$.

F39 RCL- B

\$J-L\$.

F40 RCL E

\$K\$.

F41 RCL- A

\$K-M\$.

 

T01 LBL T

Start routine to calculate and display two roots.

T02 XEQ Q

Use quadratic routine to calculate two roots.

 

N01 LBL N

Start routine to display two real roots or two complex roots.

N02 RCL F

Get the first real root.

N03 STO X

Store the first real root.

N04 VIEW X

Display real root or real part of complex root.

N05 RCL G

Get the second real root or imaginary part of complex root.

N06 FS? 0

Were there any complex roots?

N07 GTO U

Display complex roots if any.

N08 STO X

Store second real root.

N09 VIEW X

Display second real root.

N10 RTN

Return to calling routine.

 

U01 LBL U

Start routine to display complex roots.

U02 STO i

Store the imaginary part of the first complex root.

U03 VIEW i

Display the imaginary part of the first complex root.

U04 VIEW X

Display the real part of the second complex root.

U05 RCL i

Get the imaginary part of the complex roots.

U06 +/-

Generate the imaginary part of the second complex root.

U07 STO i

Store the imaginary part of the second complex root.

U08 VIEW i

Display the imaginary part of the second complex root.

 

Flags used

Flag 0 is used to remember if the root is real or complex (that is, to remember the sign of \$d\$). If \$d\$ is negative, then flag 0 is set. Flag 0 is tested later in the program to assure that both the real and imaginary parts are displayed if necessary.

 

Notes

The program accommodates polynomials of order 2, 3, 4, and 5. It does not check if the order you enter is valid.

The program requires that the constant term \$a_0\$ is nonzero for these polynomials. (If \$a_0\$ is 0, then 0 is a real root. Reduce the polynomial by one order by factoring out x.)

The order and the coefficients are not preserved by the program.

Because of round-off error in numerical computations, the program may produce values that are not true roots of the polynomial. The only way to confirm the roots is to evaluate the polynomial manually to see if it is zero at the roots.

For a third- or higher-order polynomial, if SOLVE cannot find a real root, the error DIVIDE BY 0 is displayed.

Time and memory can be saved by omitting unnecessary routines. If not solving fifth-order polynomials, omit routine E. If solving fourth- or fifth-order polynomials, omit routines D, E, and F. If solving third-, fourth-, or fifth-order polynomials, omit routines C, D, E, and F.

 

Program usage

  1. Press XEQ [P] to start the polynomial root finder.

  2. Key in \$F\$, the order of the polynomial, and press R/S.

  3. At each prompt, key in the coefficient and press R/S. You’re not prompted for the highest-order coefficient — it’s assumed to be 1. You must enter 0 for coefficients that are 0. Coefficient A must not be 0. See table below.

  4. After you enter the coefficients, the first root is calculated. A real root is displayed as X=real value. A complex root is displayed as X=real part. (Complex roots always occur in pairs of the form \$u±iv\$, and are labeled in the output as X=real part and i=imaginary part, which you’ll see in the next step.)

  5. Press R/S repeatedly to see the other roots, or to see i=imaginary part, the imaginary part of a complex root. The order of the polynomial is same as the number of roots you get.

  6. For a new polynomial, go to step 1.

terms and coefficients

order

x5

x4

x3

x2

x

constant

5

1

\$E\$

\$D\$

\$C\$

\$B\$

\$A\$

4

1

\$D\$

\$C\$

\$B\$

\$A\$

3

1

\$C\$

\$B\$

\$A\$

2

1

\$B\$

\$A\$

 

Variables

\$A\$ through \$E\$

Coefficients of polynomial; scratch.

\$F\$

Order of polynomial; scratch.

\$G\$

Scratch.

\$H\$

Pointer to polynomial coefficients.

\$X\$

The value of a real root, or the real part of a complex root.

\$i\$

The imaginary part of a complex root; also used as an index variable.

 

Example

Find the roots of \$x^5 - x^4 - 101x^3 + 101x^2 + 100x - 100 = 0\$.

keystrokes x-register description

1.

XEQ [P]

F?value

Start polynomial root finder; prompt for order.

2.

5 R/S

E?value

Store 5 in \$F\$; prompt for \$E\$.

3.

1 +/– R/S

D?value

Store 1 in \$E\$; prompt for \$D\$.

4.

101 +/– R/S

C?value

Store –101 in \$D\$; prompt for \$C\$.

5.

101 R/S

B?value

Store 101 in \$C\$; prompt for \$B\$.

6.

100 R/S

A?value

Store 100 in \$B\$; prompt for \$A\$.

7.

100 +/– R/S

X=1.0000

Store —100 in \$A\$; calculate first root.

8.

R/S

X=1.0000

Calculate second root.

9.

R/S

X=10.0000

Calculate third root.

10.

R/S

X=⁻10.0000

Calculate fourth root.

11.

R/S

X=⁻1.0000

Calculate fifth root.

18. Statistics program

This chapter has 1 example program:

18.1. Normal and inverse-normal distributions

Ready-to-use Statefile direct download: https://technical.swissmicros.com/dm32/examples/STATE/NDIST.d32

Normal distribution is frequently used to model the behavior of random variation about a mean. This model assumes that the sample distribution is symmetric about the mean, M, with a standard deviation, S, and approximates the shape of the bell-shaped curve shown below. Given a value x, this program calculates the probability that a random selection from the sample data will have a higher value. This is known as the upper tail area, Q(x). This program also provides the inverse: given a value Q(x), the program calculates the corresponding value x.

prg normal dist
\$Q(x) = 0.5 - 1/(sigma sqrt(2×pi)) int_bar x^x e^(-((x-bar x) ÷ sigma)^2) dx\$

This program integrates the equation of the normal frequency curve. The inverse is obtained using Newton’s method to iteratively search for a value of x which yields the given probability Q(x).

 

Program listing

program line description

S01 LBL S

This routine initializes the standard-deviation program.

S02 0

Store default value for mean.

S03 STO M

S04 INPUT M

Prompt for and store mean, \$M\$.

S05 1

Store default value for standard deviation.

S06 STO S

S07 INPUT S

Prompt for and store standard deviation, \$S\$.

S08 RTN

Stop displaying value of standard deviation.

 

D01 LBL D

This routine calculates \$Q(X)\$ given \$X\$.

D02 INPUT X

Prompt for and store \$X\$.

D03 XEQ Q

Calculate upper tail area.

D04 STO Q

Store value in \$Q\$ so VIEW function can display it.

D05 VIEW Q

Display \$Q(X)\$.

D06 GTO D

Loop to calculate another \$Q(X)\$.

 

I01 LBL I

This routine calculates \$X\$ given \$Q(X)\$.

I02 INPUT Q

Prompt for and store \$Q(X)\$.

I03 RCL M

Recall the mean.

I04 STO X

Store the mean as the guess for \$X\$, called \$X_(guess)\$.

 

T01 LBL T

This label defines the start of the iterative loop.

T02 XEQ Q

Calculate \$(Q(X_(guess))-Q(X))\$.

T03 RCL– Q

T04 RCL X

T05 STO D

T06 R↓

T07 XEQ F

Calculate the derivative at \$X_(guess)\$.

T08 RCL÷ T

T09 ÷

Calculate the correction for \$X_(guess)\$.

T10 STO+ X

Add the correction to yield a new \$X_(guess)\$.

T11 ABS

T12 0.001

T13 x<y?

Test to see if the correction is significant.

T14 GTO T

Go back to start of loop if correction is significant. Continue if correction is not significant.

T15 RCL X

T16 VIEW X

Display the calculated value of \$X\$.

T17 GTO I

Loop to calculate another \$X\$.

 

Q01 LBL Q

This subroutine calculates the upper-tail area \$Q(X)\$.

Q02 RCL M

Recall the lower limit of integration.

Q03 RCL X

Recall the upper limit of integration.

Q04 FN= F

Select the function defined by LBL F for integration.

Q05 ∫FN d D

Integrate the normal function using the dummy variable \$D\$.

Q06 2

Q07 π

Q08 ×

Q09 SQRT

Q10 RCL× S

Calculate \$S×sqrt(2π)\$.

Q11 STO T

Store result temporarily for inverse routine.

Q12 ÷

Q13 +/–

Q14 0.5

Q15 +

Q16 RTN

 

F01 LBL F

Add half the area under the curve since we integrated using the mean as the lower limit.

F02 RCL D

Return to the calling routine.

F03 RCL– M

F04 RCL÷ S

This subroutine calculates the integrand for the normal function \$e^(-((X-M)÷S)^2÷2)\$.

F05 x²

F06 2

F07 ÷

F08 +/-

F09 eˣ

F10 RTN

Return to the calling routine.

 

Flags used

None.

 

Note

The accuracy of this program is dependent on the display setting. For inputs in the range between ±3 standard deviations, a display of four or more significant figures is adequate for most applications. At full precision, the input limit becomes ±5 standard deviations. Computation time is significantly less with a lower number of displayed digits.

If the inverse capability isn’t required, the inverse routine (in routines I and T) does not need to be keyed in.

 

Program usage

  1. Press XEQ [S].

  2. After the prompt for \$M\$, key in the population mean and press R/S. (If the mean is zero, just press R/S.)

  3. After the prompt for \$S\$, key in the population standard deviation and press R/S. (If the standard deviation is 1, just press R/S.)

  4. To calculate \$X\$ given \$Q(X)\$, skip to step 8 of these instructions.

  5. To calculate \$Q(X)\$ given \$X\$, press XEQ [D].

  6. After the prompt, key in the value of \$X\$ and press R/S. The result, \$Q(X)\$, is displayed.

  7. To calculate \$Q(X)\$ for a new \$X\$ with the same mean and standard deviation, press XEQ [D] and go to step 6.

  8. To calculate \$X\$ given \$Q(X)\$, press XEQ [I].

  9. After the prompt, key in the value of \$Q(X)\$ and press R/S. The result, \$X\$, is displayed.

  10. To calculate \$X\$ for a new \$Q(X)\$ with the same mean and standard deviation, press XEQ [I] and go to step 9.

 

Variables

\$D\$

Dummy variable of integration.

\$M\$

Population mean, default value zero.

\$Q\$

Probability corresponding to the upper-tail area.

\$S\$

Population standard deviation, default value of 1.

\$T\$

Variable used temporarily to pass the value \$S×sqrt(2π)\$ to the inverse program.

\$X\$

Input value that defines the left side of the upper-tail area.

 

Example: a smart date

A dating website lists around 12,000 possible dates in a reasonable distance. It allows filtering user profiles according to intelligence. The selected criterion is they must all have “3σ” intelligence, which means they are more intelligent than the available dates except for people more than three standard deviations above the mean.

How many profiles fall into the “3σ” band? Since this problem is stated in terms of standard deviations, the default values of zero for \$M\$ and 1 for \$S\$ are used.

keystrokes x-register description

1.

XEQ [S]

M?0.0000

start initialization routine

2.

R/S

S?1.0000

accept value of zero for \$M\$

3.

R/S

1.0000

accept value of 1 for \$S\$

4.

XEQ [D]

X?value

start distribution program, prompt for \$X\$

5.

3 R/S

Q=0.0014

enter 3 for \$X\$ and calculate \$Q(X)\$; display ratio of the population smarter than everyone within three standard deviations of the mean

6.

12000 ×

16.2059

multiply by the population; display the approximate number of dates exceeding the criteria

Let’s assume a reduced expectation and revise the criterion from “3σ” to “2σ”. Just press R/S to run the program again.

keystrokes x-register description

1.

R/S

X?3.0000

resume program

2.

2 R/S

Q=0.0228

enter 2 for \$X\$ and calculate \$Q(X)\$

3.

12000 ×

273.0014

multiply by the population; display the approximate number of dates exceeding the revised criteria

19. Miscellaneous programs and equations

This chapter has 1 example equation and 1 example program:

19.1. Time value of money

When provided with any combination of four out of the five values in the "Time Value of Money equation" (TVM), it becomes possible to solve for the fifth value. This equation is used across diverse financial scenarios, including consumer and home loans, as well as savings accounts.

Here is the TVM equation:

\$P [(1-(1+I//100)^-N)/(I//100)] + F (1+(I//100))^-N+B=0\$

The signs used for cash values (balance, B; payment, P; and future balance, F) align with the direction of cash movement. Positive sign pertains to money received, whereas negative sign signifies outgoing funds. It’s important to recognize that every problem can be examined from dual standpoints. The lender and the borrower perceive the same situation with signs reversed.

 

Equation entry

keystrokes x-register description

1.

EQN

EQN LIST TOP

Open the Equation list.

2.

RCL [P] × 100

P× 100_

Begin entering the equation.

3.

× ( 1

P×100×(1–█

4.

( 1 +

×100×(1–(1+█

5.

RCL [I] ÷ 100

–(1+I÷ 100_

6.

) yx

–(1+I÷100)^█

7.

RCL [N] )

+I÷100)^–N)█

8.

÷ RCL [I] +

100)^–N)÷I+█

9.

RCL [F] ×

0)^–N)÷I+F×█

10.

( 1 + RCL [I]

N)÷I+F×(1+I█

11.

÷ 100 )

F×(1+I÷100)█

12.

yx RCL [N]

1+I÷100)^–N█

13.

+ RCL [B]

I÷100)^–N+B█

14.

ENTER

P×100×(1–(1+

Terminate equation entry and save the equation to the list.

 

Note

The TVM equation requires that \$I\$ must be non-zero to avoid a DIVIDE BY 0 error. When solving for \$I\$ and its current value is uncertain, press 1 STO [I] before beginning the SOLVE calculation (SOLVE [I]). The order of value prompts depends upon the variable being solved for.

 

Equation usage with SOLVE

  1. If the first TVM calculation is to solve for interest rate, \$I\$, press 1 STO [I].

  2. Press EQN.

  3. Do one of the following:

    1. Press SOLVE [N] to calculate the number of compounding periods.

    2. Press SOLVE [I] to calculate periodic interest. For monthly payments, the result returned for \$I\$ is the monthly interest rate, \$i\$; press 12 × to see the annual interest rate.

    3. Press SOLVE [B] to calculate initial balance of a loan or savings account.

    4. Press SOLVE [P] to calculate periodic payment.

    5. Press SOLVE [F] calculate future value or balance of a loan.

  4. Key in the value of each variable when prompted for; press R/S to validate input each time.

  5. After pressing R/S for the last time, the value for the unknown variable is calculated and displayed.

  6. To calculate a new variable, or recalculate the same variable using different data, go back to step 2.

SOLVE works effectively in this application without initial guesses.

 

Variables

\$N\$

The number of compounding periods.

\$I\$

The periodic interest rate as a percentage. (For example, if the annual interest rate is 15% and there are 12 payments per year, the periodic interest rate, \$i\$, is 15÷12=1.25%.)

\$B\$

The initial balance of loan or savings account.

\$P\$

The amount of the periodic payment.

\$F\$

The future value of a savings account or balance of a loan.

 

Example, part 1

A customer finances the purchase of his new car with a 4-year (48-month) loan at 4.5% annual interest compounded monthly. The purchase price of the car is USD 25,900. His down payment is USD 8,000. What are the monthly payments?

keystrokes x-register description

1.

DISP FX 2

Set display format to FIX 2.

2.

EQN

P×100×(1–(1+

Open the Equation list (and navigate to TVM equation if needed).

3.

SOLVE [P]

I?value

Solve for \$P\$. Prompt for \$I\$.

4.

4.5 ENTER 12 ÷

I?0.38

Convert annual interest to equivalent monthly rate.

5.

R/S

N?value

Store 0.38 in \$I\$; prompt for \$N\$.

6.

48 R/S

F?value

Store 48 in \$N\$; prompt for \$F\$.

7.

0 R/S

B?value

Store 0 in \$F\$; prompt for \$B\$.

8.

25900 ENTER 8000

B?17+900.00

Calculate \$B\$, the beginning loan balance.

9.

R/S

P=⁻408.18

Store 17,900 in \$B\$; calculate monthly payment \$P\$.

Since the problem is seen from the borrower’s perspective, the answer of USD 408.18 is negative. Money received by the borrower is positive (as the beginning loan balance), while money paid out is negative.

 

Example, part 2

What interest rate would reduce monthly payment by USD 20?

keystrokes x-register description

1.

EQN

P×100×(1–(1+

Open the Equation list (and navigate to TVM equation if needed).

2.

SOLVE [I]

P?⁻408.18

Solve for \$I\$. Prompt for \$P\$.

3.

RND

P?⁻408.18

Truncate the number to 2 decimal places.

4.

20 +

P?⁻388.18

Remove USD 20 from the monthly payment.

5.

R/S

N?48.00

Store –388.18 in \$P\$; prompt for \$N\$.

6.

R/S

F?0.00

Store 48 in \$N\$; prompt for \$F\$.

7.

R/S

B?17+900.00

Store 0 in \$F\$; prompt for \$B\$.

8.

R/S

I=0.16

Store 17,900 in \$B\$; calculate new monthly interest \$I\$.

9.

12 ×

1.98

Calculate new annual interest \$I\$.

 

Example, part 3

Keeping the calculated interest rate, let’s assume the car is to be sold in two years. How much money will the borrower still owe at that time? In other words: what is the future balance in 24 months?

keystrokes x-register description

1.

EQN

P×100×(1–(1+

Open the Equation list (and navigate to TVM equation if needed).

2.

SOLVE [F]

P?⁻388.18

Solve for \$F\$. Prompt for \$P\$.

3.

R/S

I?0.16

Store –388.18 in \$P\$; prompt for \$I\$.

4.

R/S

N?48.00

Store 0.16 in \$I\$; prompt for \$N\$.

5.

24 R/S

B?17+900.00

Store 24 in \$N\$; prompt for \$B\$.

6.

R/S

F=⁻9+126.97

Store 17,900 in \$B\$; calculate new future balance \$F\$. The negative number indicates the money is owed, from the borrower’s perspective.

7.

DISP FX 4

Set display format to FIX 4.

19.2. Prime number generator

Ready-to-use Statefile direct download: https://technical.swissmicros.com/dm32/examples/STATE/PRIME.d32

The program supports integers exceeding 3 as input. Should the provided number qualify as a prime number (meaning it can’t be evenly divided by integers except for 1 and itself), the program will output the entered value. However, if the input doesn’t qualify as a prime number, the program will return the first prime number surpassing the input value.

The program detects non-prime numbers through a comprehensive examination of all potential factors. If a number doesn’t qualify as prime, the program increments it by 2 (ensuring it remains an odd value) and assesses whether it has discovered a prime number. This iterative procedure persists until a prime number is successfully identified.

prg prime flowchart

Program listing

program line description

Y01 LBL Y

This routine displays prime number \$P\$.

Y02 VIEW P

 

Z01 LBL Z

This routine calculates \$P + 2\$.

Z02 2

Z03 RCL+ P

 

P01 LBL P

This routine stores the input value for \$P\$.

P02 STO P

P03 2

P04 ÷

P05 FP

P06 0

P07 x=y?

Tests for even input.

P08 1

P09 STO+ P

Increments \$P\$ if an even number has been input.

P10 3

Stores 3 in test divisor, \$D\$.

P11 STO D

 

X01 LBL X

This routine tests \$P\$ to see if it is prime.

X02 RCL P

X03 RCL÷ D

X04 FP

Finds the fractional part of \$P ÷ D\$.

X05 x=0?

Tests if remainder is zero (number not prime if true).

X06 GTO Z

If the number is not prime, tries next possibility.

X07 RCL P

X08 SQRT

X09 RCL D

X10 x>y?

Tests to see whether all possible factors have been tried.

X11 GTO Y

If all factors have been tried, branches to the display routine.

X12 2

Calculates the next possible factor, \$D + 2\$.

X13 STO+ D

X14 GTO X

Branches to test potential prime with new factor.

Flags used

None.

Program usage

  1. Key in a positive integer greater than 3.

  2. Press XEQ [P] to start the program. Prime number, \$P\$ will be displayed.

  3. To see the next prime number, press R/S.

Variables

\$P\$

Prime value and potential prime values.

\$D\$

Divisor used to test the current value of \$P\$.

Note

No test is performed to ensure that input is greater than 3.

Example usage

Is 127 prime? Which is the next prime number?

keystrokes x-register description

1.

127

127_

key in number 127

2.

XEQ [P]

P=127.0000

127 is indeed prime

3.

R/S

P=131.0000

next prime number is 131

20. Calculator State

A State (Calculator State) is the set of data in memory defining the state of the calculator at any given time, together with everything it contains:

While Extended registers (index 100 up to 999) are part of the calculator State, Global registers (index -100 down to -999) aren’t. Global registers reside in a region of calculator RAM independent from the current State. This means that they remain untouched when another State is loaded, or activated from the Available States list (see Multi-State), and they are not included in the Statefile when saving the State.

20.1. State VS Statefile

The complete set of data defining the calculator comes in two forms:

  • a State: the data lives in work memory and is used for calculations and number manipulations in real-time,

  • a Statefile: the same set of data stored as a text file on the internal USB disk, in folder STATE. It is the “backed up” version of a State.

The DM32 can handle several States opened in memory; the calculator’s display and keypad can be immediately switched to any of those opened States to start (or continue) working with it. This feature is called Multi-State and is covered later in this chapter.

20.2. Saving and loading a State

The current, or active, calculator State can be saved to a Statefile on the internal USB disk to be loaded later, restoring the calculator to a particular context.

20.2.1. Save State

  1. Press SETUP.

  2. Select 1. File.

  3. Select 2. Save State.

  4. In the dialog which appears, use the up/down navigation keys to highlight either <New File> or one of the Statefiles and press ENTER. From there two options are available:

    1. If <New File> is selected, a dialog opens to prompt for the name of the new file. Use the letter keys [A] to [Z] to type the name. Space characters aren’t allowed, use the undescore _ (press √x) soft-key instead. Confirm with R/S.

    2. If one of the Statefiles is selected, the calculator prompts for confirmation that the file can be overwritten. Pressing ENTER overwrites the file.

Press C at any time to cancel and step back to the previous screen.

About filename length limits, please see DMCP5 and filenames.

20.2.2. Load State

A State can be loaded to restore the calculator to that definite State.

  1. Press SETUP.

  2. Select 1. File.

  3. Select 1. Load State.

  4. In the dialog which appears, use the up/down navigation keys to highlight the desired Statefile and press ENTER.

  5. A warning appears; the data from the Statefile to be loaded is about to replace the calculator State. The user should save the State to a Statefile first if it must be kept for future use.

  6. Press ENTER to confirm. The calculator is restored to the condition contained in the Statefile.

Press C at any time to cancel and step back to the previous screen.

The illustration below shows how Statefiles and State relate to each other.

states

Statefiles from the internet can be copied to the internal USB disk. This manual has example sections Mathematics programs, Statistics program, and Miscellaneous programs and equations, which all provide links to Statefiles containing already-written and ready-to-use programs and equations.

20.3. Multi-State

The DM32 offers the Multi-State functionality. Several calculator States can be available simultaneously in memory. These Available States populate the Available States list. From there, the user activates one of them for the calculator to work with, a bit like selecting a tab in a web browser. There is always at least one State in the list. When there is only one State in the list, it is the Active State.

Another way to represent Multi-State is to consider each Available State like a virtual calculator in the background; activating one State is like bringing the corresponding calculator to the foreground.

Different States can be used to arrange data and operations in the DM32. For instance, a group of equations useful for electricity problems can be grouped in a dedicated State. Or a State could hold a group of variables in relation to a particular subject. Another State could hold a collection of financial calculation programs. Any combination and arrangement is possible and limited almost only by the user’s imagination.

Operations executed on the calculator only affect the active State. To modifiy or use data from another Available State, it has to be activated first.

The illustration below illustrates the Multi-State functionality.

states available

The functionality of Multi-State is described below as a fictive step-by-step example. The shown steps are:

This is followed by additional Multi-Sate information:

20.3.1. Open and close the Available States list

Open the Available States list with F4.

By default the only State present is called New.

dmcp states list

The maximum number of Available States is 128. At the bottom of the display is a series of soft-keys:

label function

New

This adds a blank State, called New, to the list and activates it.

Load

Creates a State from the Statefile specified in the Load Calculator State dialog. This opened State is immediately activated.

Save

Saves the currently highlighted State to a Statefile on the USB disk.

Info

Displays meta data about the currently highlighted State.

Del

Removes the highlighted State from the Available States list.

Pressing C closes the list and returns to the stack display.

The diagram below, and subsequent illustrations in this chapter, show a stylized view of the contents of the Available States list on the left, and folder /STATE of the internal USB disk on the right, side-by-side. The present situation assumes a default Available States list and a couple of Statefiles on the internal USB disk:

state default

20.3.2. Add a State to the Available States list

Call the Available States list with F4. From here, there are two ways to add a State to the list:

  • Load a State
    state open  
    Use soft-key Load. The calculator shows the contents of folder /STATE on the USB disk. One of the Statefiles can be highlighted using up/down navigation keys. The size for each is displayed in bytes.
    dmcp states list load
     
    Press ENTER to open the State. If the Statefile has no dependencies, it is immediately added to the Available States list and activated.
    dmcp states list loaded
     
    Duplicate Available States are not allowed. If the Statefile to be loaded resolves to the same name as one of the Available States, load operation is interrupted and the calculator shows an error screen:
    dupe load
    The offending State must be saved under a different name first.  

  • Create a new State
    state new  
    Use soft-key New. This adds a blank State, called New, to the list and activates it. Because the Available States list already contains a State called New, a digit is appended to the newly created State, making it New2.
    dmcp states list new
     

When using command Load from the File menu, the Active State is replaced with the one to load. When using the Load command described above, that State is added to the Available States list and immediately activated.

20.3.3. Save a State from the Available States list

state save  

  1. Call the Available States list with F4.

  2. Highlight the State to be saved with the up/down navigation keys.
    dmcp states list new
     

  3. Use soft-key Save. In the dialog which appears, use the up/down navigation keys to highlight either <New File> or one of the existing Statefiles and press ENTER. If the Active State has been previously saved to a Statefile, that Statefile is automatically highlighted. Thus:

    1. If updating the State, simply press ENTER and confirm overwrite with ENTER.

    2. If <New File> is selected, a dialog opens to prompt for the name of the new Statefile. Use the letter keys [A] to [Z] to type the name. Use      to toggle between lowercase, uppercase and number entry. Space characters aren’t allowed, use the undescore _ (press √x) soft-key instead. Confirm with R/S.
      dmcp states list save  

    3. If one of the already existing Statefiles is selected, the calculator prompts for confirmation that the file can be overwritten. Pressing ENTER overwrites the file.
      dmcp states list overwrite  

Press C at any time to cancel and step back to the previous screen.  
 

Duplicate Available States are not allowed. If the entered name for the Statefile to be saved resolves to the same name as another of the Available States, save operation is interrupted and the calculator shows an error screen:
dupe save
Exception to this is when re-saving the Active State to the same Statefile (updating the Statefile), which produces no error.
About filename length limits, please see DMCP5 and filenames.

20.3.4. Reading Available State information

The Available States list includes soft key Info which brings up the State Info screen:

The screen gives additional information about the State name:

the State name as it appears in the Available States list

20.3.5. Activate a State from the Available States list

state activate  

  1. Call the Available States list with F4.

  2. Highlight the State to activate with up/down navigation keys.
    dmcp states list switch
     

  3. Press ENTER.

  4. The calculator returns to Calculator mode. The name of the active State is shown in the status bar at the top of the display.
    dmcp states list activated
     
    Since the stack and Global registers are shared between States in the Available States list, the both these memory regions are untouched.

Pending operations (like digit-entry, program entry or pending prompt) are cancelled when activating a State.

20.3.6. Delete a State

state close  

  1. Call the Available States list with F4.

  2. Highlight the State to be deleted with the up/down navigation keys.
    dmcp states list switch
     

  3. Use soft-key Del.
    dmcp states list delete
     

  4. Press ENTER to confirm (or C to cancel).
    dmcp states list deleted
     

The State is removed from the Available States list. Statefiles on the internal USB disk are untouched.

20.3.7. Load Statefile dependencies

When loading a State using Load from the Available States list, the calculator detects Remote XEQ instructions in the selected State’s program memory and asks whether dependent States (targeted by Remote XEQ instructions) should be added to the Available States list as well. As an example, when loading Statefile areas.d32 containing Remote XEQ instructions targeting Statefiles circles.d32 and squares.d32, upon pressing Load the following dialog opens:

dep load 1

The dialog shows the number of dependent Statefiles and soft-keys Yes, Always, Never and No. Here is what the options do:

  • Yes and Always load dependencies, including nested dependencies.

  • Never and No load highlighted Statefile only.

  • Always and Never update setting Load Dependencies to Always and Never, respectively.

If Always or Never have been selected by mistake, the automatic display of this options screen is disabled, which means the Load Dependencies feature stops asking what to do. It can be restored in the DM32 Setup Settings menu.

If a dependent State resolves to the same name as one already present in the Available States list, it is ignored upon dependency loading.

Loading a State from the File menu does not load dependent States. Only Load from the Available States list does.

20.3.8. Contents of a blank State

When creating a new State with function New from the Available States list, the added State has the following defaults:

memory region status of New State

stack registers

shared; ported from the State active at execution of New

variable registers

all clear

Extended registers

all clear

flags

all clear

angular mode

set to DEG

radix mark

set to period

display format

set to FIX 4

equation memory

all clear

program memory

all clear

20.3.9. Exchange Statefiles with a computer

*.d32 Statefiles found on the internet, or previously extracted from the DM32, can be copied to the /STATE folder of the internal USB disk from a computer. Conversely, Statefiles stored in the DM32 can be copied to a computer. See Activate USB Disk on how to connect the DM32 to a computer.

20.3.10. Passing data between Available States

All Available States share two memory regions:

This means that switching States by activating a different State from the Available States list will not affect the contents of either of these two regions. This can be used to pass data from one Available State to another.

While stack registers are written to the Statefile when saved, indirect-only Global registers are not. See Structure of a Statefile for details about the contents of a Statefile.
Loading a Statefile from the File menu or the Available States list replaces the stack with that from the Statefile.

20.3.11. Reset all States

The file menu has a function to wipe all States from memory.

  1. Press SETUP.

  2. Select 1. File.

  3. Select 3. Load Clean State.

  4. A warning appears; the calculator is about to delete all Available States and replace them with a single blank State called “New”. User should save important States to Statefiles first if they must be kept for future use.

  5. Press ENTER to confirm. The Available States list is now reset and contains a single blank State.

20.4. Structure of a Statefile

Statefiles stored on the internal disk in folder /STATE are ASCII text files with extension .d32. They can be opened, modified and saved for use by the DM32 from any general computer text editor. Statefiles hold the entire contents of calculator memory (except Global registers). Since this includes equations and programs, it is possible to review and modify programs and/or equations stored in a Statefile without the need for DM32-specific software.

Statefiles consist of keywords and values, one of each per line. Keywords are attached to categories of calculator memory, which are:

The DM32 automatically groups keywords by category in a Statefile, separates categories with a blank line and adds a comment line at the beginning of each category for identification. Here is an example Statefile:

# STACK
SX: 3.141592653589793238462643383279503
SY: 65

# REGS
RR: 12.5
R100: 1000
R101: 256

# FLAGS
F10
F11

# MODE
MTRIG: RAD
MFMT: FIX 3
FN= B

# EQUATION LIST
EQNPTR: 1
EQN
 A = \pi; \mul; SQ( R )
 C = \pi; \mul; 2 \mul; R
EQNEND

# PROGRAM
PTR: 0
PGM
  INPUT R
  RCL R
  2
  \mul;
  \pi;
  \mul;
  RTN
PGMEND

Lines starting with a number sign “#” are ignored by the calculator.

Below is a description the above example Statefile, category by category. To understand how the different keywords work and what they mean, see Statefile syntax further in this chapter. To understand what character codes like \pi; are, see Statefile functions in equations and programs.

  • # STACK: the two lines there show that stack x- and y-registers hold values pi and 65. The absence of other stack values means that they equal zero.

  • # REGS: variable R holds value 12.5. Indirect-only registers number 100 and 101 hold values 1000 and 256. All other variables equal zero.

  • # FLAGS: flags 10 and 11 are set. Any unmentioned flag is clear.

  • # MODE: this Statefile sets the angular mode to radians (MTRIG: RAD) and the display format to FIX 3 (MFMT: FIX 3). It also defines label B as the current integration program.

  • # EQUATION LIST: the list of equations holds one equation per line and is delimited by keywords EQN and EQNEND. EQNPTR: 1 means that the currently selected equation is the first in the list. This Statefile contains two equations:

    • A = π × R²

    • C = π × 2 × R

  • # PROGRAM: program memory is shown, one instruction per line, and delimited by keywords PGM and PGMEND. PTR: 0 means that the program pointer sits on the first line of program memory PRGM TOP.

Comments in a Statefile may be added manually with a computer text editor by starting a line with number sign “#”. It can make programs in Statefiles easier to read and understand. However, any such comment is lost when the Statefile is subsequently saved from the calculator using F4 Save or SETUP 1. File 2. Save State.

20.5. Statefile syntax

Each line in a Statefile holds one case-sensitive record in one of the above categories. Each record comes in the form of either

  • a keyword with an assigned value, or

  • a calculator function or number when the line represents an equation or an instruction from program memory.

The keywords are formed with a 1-uppercase-letter prefix defining its category (with an exception for the FN= keyword). Options which follow the prefix are appended without a space and are specific to the category. Values are usually separated from options by a colon and a space.

Equations and program instructions use the same function names as can be found in the table of section Appendix D: Functions index, in column “name in equation or program”, with exceptions as described in section Statefile functions in equations and programs below.

Equation list and program memory use special keywords to delimit the beginning and end of their respective listing.

Here are keywords broken down by prefix and options:

category prefix options value example

1.

stack values

S

  • X: (x-register)

  • Y: (y-register)

  • Z: (z-register)

  • T: (t-register)

  • L: (LASTx-register)

decimal value (cannot be written as a fraction)

SY: 1.2345678

2.

registers

R

variable name from A to Z and i

decimal value (cannot be written as a fraction)

RQ: 6000

Extended register number from 100 to 999

decimal value (cannot be written as a fraction)

R345: 1.41421356

3.

flags

F

none

integer from 0 to 11
according to flag number
(directly appended to prefix)

F3

4.

mode

M

FMT: (display format)

one of the options below

  • FIX n

  • SCI n

  • ENG n

  • ALL

MFMT: SCI 3

TRIG: (angular mode)

one of the options below

  • DEG

  • RAD

  • GRAD

MTRIG: RAD

/C:

decimal value to determine maximum fraction denominator

M/C: 16

DOTINV

when present, radix mark is set to comma ,

MDOTINV

none

FN=

integration program label A to Z and i

FN= B

5.

equations

E

QN
[…​]
QNEND

keywords to delimit beginning and end of the Equation list

QNPTR:

integer for the currently selected equation in the Equation list

EQNPTR: 3

6.

programs

P

GM
[…​]
GMEND

keywords to delimit beginning and end of program memory

TR:

integer for the current program pointer position

PTR: 27

20.5.1. Exhaustive list of valid Statefile keywords and options

this keyword…​ designates or activates:

SX:

x-register

SY:

y-register

SZ:

z-register

ST:

t-register

SL:

LASTx-register

RA: to RZ: and Ri:

variables A to Z and i

R100: to R999:

Extended registers 100 to 999

F1 to F11

flags 0 to 11

MFMT: FIX

FIX display format

MFMT: SCI

SCI display format

MFMT: ENG

ENG display format

MFMT: ALL

ALL display format

MTRIG: DEG

degrees angular mode

MTRIG: RAD

radians angular mode

MTRIG: GRAD

gradians angular mode

M/C:

maximum fraction denominator

MDOTINV

radix mark (set to comma when present)

FN=

currently selected integration program

EQN

beginning of Equation list

EQNEND

end of Equation list

EQNPTR:

currently selected equation

PGM

beginning of program memory

PGMEND

end of program memory

PTR:

current position of program pointer

There is no dedicated keyword to control Fraction display; this is enabled by setting flag 7 with keyword F7.

20.6. Statefile functions in equations and programs

Names of functions in Statefiles can be found in the table of section Appendix D: Functions index, in column “name in equation or program”. There are exceptions to this though. To preserve conformity with the ASCII standard, some characters are expressed either as codes between a backslash and a semicolon, or as a 1- or 2-character shortcut in the ASCII range. Below is a list of those characters and the matching code and shortcut for each.

20.6.1. Statefile characters ASCII conversion table

character colloquial designation code shortcut

²

superscript 2

\sqr;

q

ˣ

superscript x

\powx;

a

̂x

x-hat

\xhat;

g

̂y

y-hat

\yhat;

h

x-bar

\xbar;

u

y-bar

\ybar;

v

radical (only for x-th root)

\sqrt;

l

σ

lowercase sigma

\sig;

o

Σ

uppercase sigma

\Sig;

z

arrow up

\up;

t

arrow down

\down;

k

π

pi

\pi;

p

integration symbol

\integ;

|

not equal

\neq;

#

less or equal

\le;

le

greater or equal

\ge;

ge

×

multiply

\mul;

*

÷

divide

\div;

:

negative number

\neg;

~

uppercase theta

\theta;

f

arrow right

\rarr;

j

°

degree

\deg;

'

( )

bold parentheses for indirect address (i)

\blpar; \brpar;

{ }

20.6.2. Statefile function names ASCII conversion table

The following is a list of all functions names using such special characters in Statefiles, the valid Statefile spellings for each, and the corresponding keypad press(es). The functions are sorted in the same order as in the table of section Appendix D: Functions index.

function code short code keypad call

space [1]

_

_

[SPACE]

\neg; (make number negative)

~

+/–

×

\mul;

*

×

÷

\div;

:

÷

10ˣ

10\powx;

10a

10ˣ

π

\pi;

p

π

Σ+

\Sig;+

z+

Σ+

Σ–

\Sig;-

z-

Σ–

Σx

\Sig;x

zx

SUMS x

Σx²

\Sig;x\sqr;

zxq

SUMS x²

Σxy

\Sig;xy

zxy

SUMS xy

Σy

\Sig;y

zy

SUMS y

Σy²

\Sig;y\sqr;

zyq

SUMS y²

σx

\sig;x

ox

s,σ σ_x_

σy

\sig;y

oy

s,σ σ_y_

θ,r→y,x

\theta;,r\rarr;y,x

f,rjy,x

y,x

∫FN d

\integ;FN d label

|FN d label

∫FN d variable

→°C

\rarr;\deg;C

j’C

→°C

CLΣ

CL\Sig;

CLz

CLEAR Σ

→CM

\rarr;CM [2]

jCM

→cm

CMPLX×

CMPLX\mul;

CMPLX*

CMPLX ×

CMPLX÷

CMPLX\div;

CMPLX:

CMPLX ÷

CMPLXeˣ

CMPLXe\powx;

CMPLXea

CMPLX

CMPLXyˣ

CMPLXy\powx;

CMPLXya

CMPLX

→DEG

\rarr;DEG [2]

jDEG

→DEG

eˣ

e\powx;

ea

→°F

\rarr;\deg;F [2]

j’F

→°F

→GAL

\rarr;GAL [2]

jGAL

→gal

→HMS

\rarr;HMS [2]

jHMS

→HMS

→HR

\rarr;HR [2]

jHR

→HR

(i)

\blpar;i\brpar;

{i}

RCL [(i)]

→IN

\rarr;IN [2]

jIN

→in

→KG

\rarr;KG [2]

jKG

→kg

→L

\rarr;L [2]

jL

→l

→LB

\rarr;LB [2]

jLB

→lb

→RAD

\rarr;RAD [2]

jRAD

→RAD

RCL×

RCL\mul;

RCL*

RCL × variable

RCL÷

RCL\div;

RCL:

RCL ÷ variable

R↓

R\down;

Rk

R↓

R↑

R\up;

Rt

R↑

STO×

STO\mul;

STO*

STO × variable

STO÷

STO\div;

STO:

STO ÷ variable

x²

x\sqr; [2]

xq [2]

x²

ˣ√y

\powx;\sqrt;y [2]

aly [2]

ˣ√y

\xbar;

u

,

̂x

\xhat;

g

L.R. ̂x

x̄w

\xbar;w

uw

, x̄w

xy?

x\neq;y?

x#y?

x?y

xy?

x\le;y?

x[y?

x?y

xy?

x\ge;y?

x]y?

x?y

x≠0?

x\neq;0?

x#0?

x?0

x≤0?

x\le;0?

x[0?

x?0

x≥0?

x\ge;0?

x]0?

x?0

\ybar;

v

,

̂y

\yhat;

h

L.R. ̂y

y,x→θ,r

y,x\rarr;\theta;,r

y,xjf,r

→θ,r

yˣ

y\powx; [3]

ya [3]

yˣ

[1] Used in equations to separate arguments of a 2-operand function, like ˣ√y. For instance, number \$root(3)(27)\$ translates to XROOT( 3 _ 27 ). Other example: for a probability calculation PROB Cn,r of combining 5 items at a time from a pool of 15, correct spelling is Cn,r( 15 _ 5 ).

[2] For use as RPN program instruction. Equations use prefix form with parentheses, i.e. for number \$25^2\$ in an equation, correct spelling is SQ( 25 ). For a conversion of 12 kilograms to pounds (12 →lb), correct spelling is \rarr;LB( 12 ), or jLB( 12 ). See Equations syntax.

[3] For use as RPN program instruction. Equations use infix character ^. To represent \$10^6\$, correct spelling is 10 ^ 6.

20.6.3. Fractions in Statefiles

Fractions that are part of a program are stored in Statefiles in the same form as they are entered in the calculator. This means that, for instance, number 1 2/3 is represented with the following entry in a Statefile: 1.2.3.

20.7. Syntax of equations in Statefiles

In a Statefile, each line between keywords EQN and EQNEND represents an equation from the Equation list of the corresponding active State. Equations in a Statefile must be written according to the following rules:

  • Every term of the equation (variables, operands, operators, parentheses, equal sign) is separated from its neighbor(s) by a space.

  • Functions are written as found in the table of section Appendix D: Functions index, in column “name in equation or program”, with a caveat:

  • Be aware that some functions have a prefix form for equations which differs from their postfix version used for RPN program instructions. Look for notes in Appendix D: Functions index.

20.7.1. Examples of equations in Statefiles

Here are a few examples of equations:

textbook Statefile code form Statefile 1-char. shortcut form on calculator

\$A = (pi × d^2)/4\$

A = ( \pi; \mul; SQ( D ) ) \div; 4

A = ( p * SQ( D ) ) : 4

A=(π×SQ(D))÷4

\$root(3)((R×T)/100)\$

XROOT( 3 _ R \mul; T \div; 100 )

XROOT( 3 _ R * T : 100 )

XROOT(3 R×T÷100)

\$V(r)= -e^2/r\$

V \mul; R = - ( SQ( E ) \div; R )

V * R = - ( SQ( E ) : R )

V×R=–(SQ(E)÷R)

\$S = T 1/sqrt(1-v^2/c^2)\$

S = T \mul; INV( SQRT( 1 - ( SQ( V ) \div; SQ( C ) ) ) )

S = T * INV( SQRT( 1 - ( SQ( V ) : SQ( C ) ) ) )

S=T×INV(SQRT(1–(SQ(V)÷SQ(C))))

21. DM32 Setup

To display the DM32 Setup menu, press SETUP. A list appears:

Every selection advances the display one step down the menu hierarchy (or toggles a checkbox). To go back a step, press C or key. When at topmost level, either of these keys exits the Setup menu.

21.1. Setup → File

set file

It is possible to save/load complete Calculator State to/from a Statefile. For details about States, see Calculator State.

Default save/load directory is /STATE. Last saved/loaded file is taken as Active and is re-loaded after calculator RESET (either due to RESET button press on the back of the unit or firmware update).

21.1.1. States

Load State

Loads calculator state from selected Statefile.

Save State

Saves current calculator state to specified Statefile.

Load Clean State

Completely clears calculator state. Deletes all States from the Available States list.

For a detailed explanation about States and Multi-State, see Calculator State.

21.1.2. Activate USB Disk

Used to copy files from/to a host computer — e.g. backup/restore the calculator State Files from /STATE directory.

In this manual, the USB Disk is sometimes referred to as “internal disk”.

  1. Connect the calculator to a computer using a USB cable,

  2. select option Activate USB Disk,

  3. the DM32’s flash disk should be visible on the computer,

  4. read and/or write files,

  5. 'eject device' on the host machine,

  6. the calculator should end USB disk mode automatically if correctly ejected by OS. USB disk mode can be ended manually by pressing C on the calculator, but all data must be flushed to disk first.

The last two points 'eject device' and 'press C on calculator' (if it doesn’t end automatically) are important to avoid unsaved data and possible FAT disk corruption.
The DM32 follows the USB 2.0 specification. The host computer must be capable of handling this type of connection.

21.1.3. Show Disk Info

Displays information about the USB Disk.

21.2. Setup → Settings

set set

21.2.1. Set Time

To set time and time format.

A note about RTC (Real-Time Clock) correction
The onboard real-time clock can be corrected. To do this, the ppm drift of the calculator clock must first be measured and calculated.

Use the following steps to apply clock frequency correction.

  1. Calculate correction factor \$C\$ which best matches required ppm correction \$P\$:
    \$C = 2^20 P /(10^6 + P)\$

  2. Resulting value \$C\$ has to be an integer and \$-511 ≤ C ≤ 512\$.

  3. Create file /rtccalib.cfg in root directory of calculator internal USB disk and write value \$C\$ there.

  4. Once the RTC correction is active, the ppm value is written in the Settings menu at the end of line Set Time >.

The following expressions evaluate a reasonably accurate approximation of correction factor \$C\$ when ppm value \$P\$ is known, or vice-versa:

  • \$C = 1.04858 × P\$

  • \$P = 0.953674 × C\$

21.2.2. Set Date

To set date and date format.

21.2.3. Load Dependencies

This setting determines what happens when loading dependencies. Press 3 (or use navigation keys to highlight the setting and press ENTER) to cycle through the options:

  • Ask: the “Load Statefile Dependencies” screen shows up if these conditions are met:

    • a State with dependencies is added to the Available States list

    • and at least one of the added State’s dependencies name cannot be found among Available States.

  • Always: added State’s dependencies are added without further notice.

  • Never: only the selected State is added without further notice.

If the “Load Statefile Dependencies” screen has stopped showing up when loading a State with dependencies, setting this value to Ask brings it back.

21.2.4. Stack Font

Cycles through and previews available DM32 fonts. These are:

  • Legacy dot-matrix:

    • segmented
      stack font 0

    • full strokes
      stack font 1

  • SwissKeys:

    • slashed zero
      stack font 2

    • dotted zero
      stack font 3

    • void zero
      stack font 4

These settings are automatically saved into /config.txt on change. Therefore, user settings should be preserved after calculator RESET.

21.2.5. Configuration file 'config.txt'

As soon as one setting is changed from default, settings are saved at the root of the internal USB disk in a text file with name config.txt. In the file, settings are defined with the following keywords and values:

keyword value meaning

FONT

0

Legacy dot-matrix font, segmented

1

Legacy dot-matrix font, full strokes

2

SwissKeys, slashed zero

3

SwissKeys, dotted zero

4

SwissKeys, void zero

CLK24

0

12-hour time format (“5:30 PM”)

1

24-hour time format (“17:30”)

DATEFMT

MDY

month-day-year date format

DMY

day-month-year date format

YMD

year-month-day date format

Example contents of a config.txt file:

FONT 2
CLK24 0
DATEFMT YMD

21.3. Setup → System

As actions available in this menu can be destructive, entering it opens a warning dialog.

set sys 1

Select 2. Enter System Menu to go past it.

set sys 2

21.3.1. Flash firmware from FAT

The calculator software is divided in two main parts:
  • an Operating System (DMCP) which is common to all SwissMicros vertical platforms

  • a calculator program that is executed by the OS

Typical firmware file name looks like

DMCP_flash_3.23_DM32S-1.46.bin

where

DMCP   - OS name
flash  - target area for flashing (CPU flash)
3.23   - OS version
DM32S  - program name (preloaded to OS)
1.46   - program version

21.3.2. Bootloader

Activates bootloader mode for firmware flashing. Once bootloader mode entered, DM32 firmware can be flashed. See Firmware update chapter for more information.

Press the RESET button on the back of the calculator if you activate Bootloader mode accidentally.

21.3.3. Program Info

Information about the current program running on the DMCP OS.

21.3.4. Reset to DMCP menu

Resets the calculator to the OS menu. Useful mainly to load a different calculator program.

Program Info

Displays information about the currently loaded program.

Run program

Run the currently loaded program.

Load program

Loads and runs a calculator program from the USB disk. Valid calculator programs bear the .pg5 extension.

Load QSPI from FAT

TBW

Settings

Calls the Setup menu's Settings section.

Activate USB Disk

Calls the Setup menu's File section.

Enter system menu

Returns to the System menu.

The only way to exit the DMCP menu is to either select Run Program or perform a hard RESET.

21.3.5. Format FAT Disk

Formats the FAT disk.

Destroys all FAT disk contents!

If the internal USB disk (“FAT disk”) gets corrupted, which can typically happen when the USB cable is unplugged without “ejecting” the device beforehand, or with an unknowingly bad or loose USB connection, using the Format FAT Disk function will return it to a good condition. But it will also destroy all data on the disk:

  • onboard help file

  • off-images

  • screenshots

  • statefiles

Which is why backing up the contents of the calculator is always the better option. To restore the onboard help file, download the latest version at: https://technical.swissmicros.com/dm32/fat/HELP/dm32help.html and place a copy in a folder called HELP at the root of the internal USB disk.

21.3.6. FAT Disk Media Test

Low-level FAT disk test.

Destroys all FAT disk contents!

21.3.7. Power OFF mode: n

Diagnostics function.

21.3.8. Self Test

KBD Test

To test proper contact of all keys. User input required. Exit by pressing      and simultaneously.

LCD Test

Automated test of global and partial display refresh. Returns to the menu selection automatically when done.

IR Test

Sends automated test message out the IR port. Returns to the menu selection automatically when done.

BEEP Test

Plays a melody through the buzzer. Can be interrupted with C.

Diagnostics

Live view of various system hardware variables. For control and debugging purposes only. Exit with C.

21.4. Setup → About

Displays version information for currently running DMCP and calculator program. Any key exits.

22. Firmware Update

Please remember it is always wise to make FAT disk backups periodically and especially before any update.
The latest firmware version is available at https://technical.swissmicros.com/dm32/firmware/

For quick update instructions, please follow Quick Update Guide.

The preferred firmware update method is by copying firmware file to calculator FAT disk. See Quick Update Guide for update procedure.

Firmware update from FAT disk is implemented in main firmware, so it could be unavailable if the main firmware is corrupted. In such a case, another method of update based on internal CPU flashing routine should be used. This method requires the calculator to be switched in so called 'Bootloader mode'. Once activated, the internal bootloader exposes standard DFU interface and can be programmed by any DFU programming software.

Following sections cover the use of two programs able to use this DFU interface:

Availability of the particular update method on mainstream operating systems outlines following table:

FAT disk[1] dm_tool dfu-util[2]

Windows

Linux i686

Linux x86_64

macOS

[1] FAT disk update was made available starting with DMCP version 3.5; therefore, a calculator with an earlier firmware version must be updated with one of the other methods.

[2] macOS users can get dfu-util via Homebrew.

22.1. Quick Update Guide (FAT disk update)

Here we will update DMCP system and DM32 program at once using combined flashing file.

Prerequisites

DMCP5_flash_x.xx_DM32-y.yy.bin - Complete DM32 firmware file e.g. DMCP5_flash_3.50t25_DM32-2.08.bin

Steps

  1. Activate USB disk from SETUP → File → Activate USB Disk or alternatively from DMCP System menu.

  2. Connect USB cable from DM32 to PC/Mac computer.

  3. Copy the DMCP5_flash_x.xx_DM32-y.yy.bin file from the PC/Mac computer to root folder of calculator disk.

  4. Eject (safely remove) the calculator disk from PC/Mac computer. Please, be patient this can take some time. Do not unplug the cable, even after the calculator’s USB disk has been successfully ejected by the OS, as USB power is required for the rest of the procedure.

  5. If calculator does not detect OS ejection, shut down USB connection by pressing C. New firmware file is detected and the calculator prompts for update. Confirm it immediately with ENTER or cancel by pressing EXIT to activate flashing process later using Flash firmware from FAT either from DM32 program SETUP → System or directly from DMCP System menu Enter System Menu.

  6. Flash progress is displayed from 0 to 100%. An automatic verification pass follows.

  7. Once finished, the calculator resets and should restart to updated DM32.

Any State which hasn’t been saved to a Statefile prior to updating is lost.

22.2. Bootloader mode activation

Bootloader mode can be activated from main Setup menu: SETUP → System → Bootloader or by using RESET and PGM button.

The sequence of entering bootloader mode using RESET and PGM button is:

  • Press and hold PGM button

  • Press and release the RESET button

  • Release the PGM button

The calculator backplate only has one hole to access the RESET button. Therefore the backplate must be removed to access both the RESET and PGM buttons.

See section Battery on how to take the backplate apart.

22.3. FW Update Using dm_tool

The latest version of dm_tool can be downloaded from the Tools web page.

22.3.1. Prerequisites for Windows

22.3.2. Prerequisites for Linux

USB device access rights: this configuration is optional.

Allow access to the DFU device for users in plugdev group by running as root:

cd /etc/udev/rules.d/
cat << OI > 49-stm32-dfuse.rules
# This is udev rules file (place in /etc/udev/rules.d)
# Makes STM32 DfuSe device accessible to the "plugdev" group

ACTION=="add", SUBSYSTEM=="usb", ATTRS{idVendor}=="0483", ATTRS{idProduct}=="df11", MODE="664", GROUP="plugdev"
OI
udevadm control --reload-rules

Then add users to plugdev group.

22.3.3. Launching dm_tool

Switch the calculator to bootloader mode

From menu or by RESET+PGM buttons (see Bootloader mode activation).

Connect the calculator to the PC

Be sure the libusb driver is installed if used in Windows (http://technical.swissmicros.com/doc/libusb_install/libusb_install.html).

Launch dm_tool

It can be launched by clicking on the exe file or from command line with firmware filename as argument.

If everything works well and the calculator was connected before launching dm_tool, then the message on the right side of [Program] button should show device number. If it shows "No DFU capable devices found (Click to refresh)" try to click at the message and it should display the ID of connected device after refresh and

Memory layout:
    0x8000000-0x80fffff:  size 1024kB = 512*2kB pages

in the text area.

If the message "No DFU capable devices found" still remains there something is wrong with libusb driver installation or connection to the calculator or the calculator isn’t in bootloader mode.

Finally press the [Program] button to flash new firmware. When the update is completed, you can close dm_tool, then Press [ON] to launch the new f/w.

22.4. FW Update Using dfu-util

macOS users can get dfu-util via Homebrew
Linux users (and possibly macOS users too) can avoid sudo use by setting appropriate user rights for DFU interface, see user rights configuration for Linux.

Note that dfu-util is command line utility launched from a terminal application and controlled by commands from the console. For new users, here are some tutorials on how to use command-line interfaces:

Proceed with the following steps:

Switch the calculator to bootloader mode

From menu or by RESET+PGM buttons (see Bootloader mode activation).

Connect the calculator to the computer

List information about connected DFU device using console command sudo dfu-util -l

Sample output of this command (from macOS)

$ sudo dfu-util -l
Password:
dfu-util 0.9

Copyright 2005-2009 Weston Schmidt, Harald Welte and OpenMoko Inc.
Copyright 2010-2016 Tormod Volden and Stefan Schmidt
This program is Free Software and has ABSOLUTELY NO WARRANTY
Please report bugs to http://sourceforge.net/p/dfu-util/tickets/

Deducing device DFU version from functional descriptor length
Found Runtime: [05ac:828b] ver=0149, devnum=6, cfg=1, intf=3, path="29-1.8.1.3", alt=0, name="UNKNOWN", serial="UNKNOWN"
Found DFU: [0483:df11] ver=2200, devnum=14, cfg=1, intf=0, path="20-4", alt=2, name="@OTP Memory /0x1FFF7000/01*0001Ke", serial="207B35994E34"
Found DFU: [0483:df11] ver=2200, devnum=14, cfg=1, intf=0, path="20-4", alt=1, name="@Option Bytes  /0x1FFF7800/01*040 e/0x1FFFF800/01*040 e", serial="207B35994E34"
Found DFU: [0483:df11] ver=2200, devnum=14, cfg=1, intf=0, path="20-4", alt=0, name="@Internal Flash  /0x08000000/512*0002Kg", serial="207B35994E34"

Where lines Found DFU: [0483:df11] indicate that calculator is correctly connected to the computer and switched into bootloader mode.

Prepare firmware file

Download the latest firmware file from https://technical.swissmicros.com/dm32/firmware/ and ensure it is accessible from current directory in console e.g. by ls -l DMCP5_flash_3.50t25_DM32-2.08.bin.

Alternatively, download firmware file directly to current directory using command (edit to use correct firmware file name according to before-mentioned page)

curl -O https://technical.swissmicros.com/dm32/firmware/DMCP5_flash_3.50t25_DM32-2.08.bin
Launch dfu-util command

Start flashing using command (edit to use correct firmware file name)

sudo dfu-util -D DMCP5_flash_3.50t25_DM32-2.08.bin -d 0483:df11 -a "@Internal Flash  /0x08000000/512*0002Kg" -s 0x8000000

Please, be patient, as the operation takes some time (up to a few minutes).

Press RESET button after dfu-util finishes the flashing.

Example output of dfu-util

$ dfu-util -D DMCP5_flash_3.50t25_DM32-2.08.bin -d 0483:df11 -a "@Internal Flash  /0x08000000/512*0002Kg" -s 0x8000000
dfu-util 0.9

Copyright 2005-2009 Weston Schmidt, Harald Welte and OpenMoko Inc.
Copyright 2010-2016 Tormod Volden and Stefan Schmidt
This program is Free Software and has ABSOLUTELY NO WARRANTY
Please report bugs to http://sourceforge.net/p/dfu-util/tickets/

dfu-util: Invalid DFU suffix signature
dfu-util: A valid DFU suffix will be required in a future dfu-util release!!!
Opening DFU capable USB device...
ID 0483:df11
Run-time device DFU version 011a
Claiming USB DFU Interface...
Setting Alternate Setting # 0 ...
Determining device status: state = dfuERROR, status = 10
dfuERROR, clearing status
Determining device status: state = dfuIDLE, status = 0
dfuIDLE, continuing
DFU mode device DFU version 011a
Device returned transfer size 2048
DfuSe interface name: "Internal Flash  "
Downloading to address = 0x08000000, size = 756288
Download	[=========================] 100%       756288 bytes
Download done.
File downloaded successfully

real	1m55.929s
user	0m0.044s
sys	0m0.048s

23. Appendix A: Hardware reference

23.1. DM32 hardware specifications

Specification Details

Construction

Case made from stainless steel, matte black Physical Vapour Deposition (PVD) coated and laser engraved

Software

Custom software running on SwissMicros Operating System (DMCP)

Floating point standard

IEEE 754-2008, 128-bit floating point precision implementation with 128-bit transcendental function support

ISO conformity

ISO/IEC TR 24732

Processor

Ultra low power Arm Cortex-M33 160 MHz

Flash memory

64 Mbit external flash

Display type

Monochromatic high contrast (14:1) transflective memory LCD display

Display resolution

400 × 240 px

Display active area

58.8 × 35.3 mm

Display dot pitch

147 × 147 µm

Connectivity (PC)

USB-C port, connects as USB mass storage device

Connectivity (IR)

IR Transmitter compatible with the original HP-82240A/B printer

Battery type

1 × CR2032 lithium coin cell, 3V[1]

Battery life

Up to 3 years

Size

77 × 144 × 12 mm

Weight

180 g

Warranty

5 years

[1] The battery isn’t rechargeable. See Battery chapter below for battery replacement and further info.

23.2. Battery

The DM32 uses a standard, non-rechargeable CR2032 battery. SwissMicros recommends using a reputable brand battery. It is easy to replace and only requires a Phillips screwdriver. Here are the steps to do it.

  • Make sure you keep all your programs and memory by saving a state file from the File menu.

  • Lay the unit on a soft, flat surface with the backplate facing up.
    Battery change step 1

  • Remove the Phillips screws at the top of the case (2×).
    Battery change step 1

  • Lift the top edge of the backplate about 10° or 12mm or ½in.
    Battery change step 1

  • Slide the backplate backwards.
    Battery change step 1

  • Use a soft, non-conductive material, like a toothpick or a plastic spudger, to push the dead battery out of its compartment.
    Battery change step 1

Slide in a fresh battery. The positive terminal faces up and away from the PCB. Follow the above steps backwards until the calculator is closed. Do not over-torque the screws.

23.3. Disassembly

The DM32 PCB can be detached from the keypad/display assembly.

The display is connected to the PCB via a flexible flat cable at the top of the unit. This connection is fragile and must be broken loose before any attempt to disassemble.

To disassemble, follow all the steps but the last one under Battery. From there:

  • With a non-conductive, non-abrasive tool, like a toothpick or a plastic spudger, gently push open the tray-like lock on the flexible flat cable connector at the top of the unit.
    Battery change step 1

  • With the gate open, pull the flexible flat cable out of the connector.
    Battery change step 1

  • With the cable loose, remove the wide, flathead Phillips screws securing the PCB on the sides (2×).
    Battery change step 1

  • Lift the PCB from the top about 1cm, or ½in.
    Battery change step 1

  • Pull the PCB upwards to clear the hooks at the bottom.
    Battery change step 1

  • The PCB should now be disconnected from the keypad/display assembly.
    Battery change step 1

Any attempt to further disassemble, or modify, the components shown in the diagram will invalidate your warranty.

23.4. USB connectivity/flash disk

The USB-C port on the top edge of the unit transports both power and data (USB 2.0 communication standard).

Power

When connected to an USB port delivering power, the calculator uses this source.

Data

Connecting to a computer allows for moving data from and to the calculator. See Activate USB Disk for more info.

The calculator has no charging circuitry. The USB-C connector cannot therefore recharge the battery. The battery inside the calculator is not rechargeable. See Battery for more detail.
usb port

23.5. Enhancements over HP-32SII

item SwissMicros DM32 HP-32SII

CPU

Arm Cortex-M33 @ 160 MHz

HP Saturn (Sacajawea) @ 640 kHz

display

4-line, 12 characters by line, 400 × 240 px, monochromatic memory LCD

1-line, 12 characters by line, 5 × 7 segments per character, dot matrix LCD

display active area

58.8 × 35.3 mm

57.8 × 13.7 mm

software

upgradeable

hard-coded in ROM

fonts

2 fonts with variants for up to 5 options

1 dot matrix font

I/O

USB 2.0 data transfer (USB-C connector)

N/A

data backup

backup of entire calculator memory (except Global registers) as editable text file

N/A (batteries removed = complete loss of memory)

memory feature

Multi-State, “virtual calculators” to switch calculators on the fly

N/A

memory

442 Kilobytes

384 bytes

registers

33 base registers, additional 900 Extended and 900 Global registers, addressed indirectly

33 registers

precision

34 digit, exponent ±6145

12 digit, exponent ±499

debugging

step-into, step-over, step-out and Debug view

single-step execution (SST)

storage

64 MBit internal flash disk

N/A

construction

stainless steel shell, Phillips screws in threaded brass inserts

hot melt hold-down posts, can only be destructively taken apart

power source(s)

1 × CR2032 lithium coin cell (3V) or USB-C (5V)

3 × LR44 coin cells

size

77 × 144 × 12 mm

80 × 148 × 15 mm

23.6. Behavior differences with HP-32SII

While HP-32SII documentation may be valid in many cases, the DM32 is a distinct machine and has a few significant differences in behavior.

domain description

memory representation

Due to the processing core and memory type in the DM32 and how software is implemented, no fixed memory representation is used. It is subject to change at any time for optimization or functionality addition. For these reasons, it is impossible to definitively describe memory requirements for variables and program or equation terms like they have been on the HP-32SII.

memory reporting

Values shown when invoking the MEM menu with key MEM are somewhat different. The total amount of memory left is shown in kilobytes. Memory used by program labels is shown in bytes. Also bear in mind that States currently populating the Available States list also use calculator memory.

checksums

On the HP-32SII, checksums are algorithmically-generated chains of characters derived from larger sets of data. Since every program or equation generates its own, unique checksum, this information can be used to ensure correct entry of examples manually keyed in from documentation. Checksums have been left out of the DM32 altogether because:

  • as a consequence of how data is represented in the DM32’s memory, checksums would differ from what they are on the HP-32SII;

  • moreover, data representation in the DM32’s memory could change in the future for optimization or functionality addition, which could possibly affect the generation of checksums;

  • Statefiles copied from a computer can directly feed the calculator with correct program and equation examples; programs entered manually on the calculator can be extracted from Statefiles to be checked on a computer.

Therefore, using SHOW (which can display checksums on the HP-32SII) on the DM32 has the following effects in specific modes:

fractions

Certain conditions will show different fraction reductions compared to the HP-32SII. For example, with flags 8 and 9 set, key in 16 /c 8.999 ENTER. The DM32 shows 9 0/16, while the HP-32SII shows 8 16/16.

integration

Due to higher internal precision, algorithm and implementation, integration results may differ.

function preview

Like on the HP-32SII, holding a key displays the corresponding internal function name (as can be found in the table of section Appendix D: Functions index, in column “name in equation or program”) after 0.25 second. On the DM32 though, holding it further turns the message to NULL after 2.5 seconds. At this point, function call is cancelled and releasing the key has no effect.

24. Appendix B: Memory

24.1. Available memory

The DM32 offers 442K of work memory which holds

Inactive States (in the Available States list, called with F4) consume memory.

To consult the status of memory, see Memory (MEM) menu.

24.2. Variables / memory registers

The DM32 has 33 memory registers and 1800 indirect-only registers:

register # contents

1 to 26

variables A-Z

27

indirect addressing variable i

28 to 33

statistics registers

100 to 999

Extended registers

–100 to –999

Global registers

Although variable names use latin letters just like program labels, they have no connection whatsoever. Variable B is separate from program label B. In the same vein, stack registers x, y, z and t are separate from variables of the same name.

To obtain a general view of variables in the calculator, see Memory (MEM) menu.

24.3. Memory (MEM) menu

The MEM menu shows information about memory usage in the DM32. To open the MEM menu, press MEM. The display shows:

mem

Value on the left is the amount of work memory left.

24.4. Clearing functions

The calculator generally does not prompt for confirmation; deletion is immediate and cannot be undone.

24.4.1. Clearing in Calculator mode

If digit-entry is not complete (_ symbol), clears the rightmost digit.
If entry is complete, sets x-register to zero and disables stack lift.
Also clears messages.

C

Immediately sets (clears) the x-register to zero, whether digit-entry is active or not.
Cancels the current situation: a menu, a message, a prompt or a catalog, and closes the Equation list.

CLEAR

Brings up the CLEAR menu.
x clears the x-register to zero like or C. This is useful as it can be added as a program instruction.
VARS clears all variables (stores value zero in every one of them).
ALL clears all stack registers, variables, equations and programs. Σ clears statistics registers.

24.4.2. Clearing in the Equation list

Clearing keys have dedicated functions when calculator is in the Equation list (EQN).

Begins editing the selected equation; cursor appears at the end of the line. Every subsequent press deletes the rightmost character.

C

Exits the Equation list immediately, even when equation entry is active (cursor on).

CLEAR

If equation entry is active (cursor on), brings up message CLEAR EQN?. Select Y or N with 1/x or Σ+. The entire equation is deleted.
If equation entry is not active (only viewing equations), the entire equation is deleted immediately.

24.4.3. Clearing in Program mode

Clearing keys have dedicated functions when calculator is in Program mode (PRGM).

C

Always exits Program mode.
If digit-entry is active (cursor _ visible), saves the program line with the digits already keyed in before exiting.

Deletes program line at program pointer.
If digit-entry is active (cursor _ visible), deletes the rightmost digit.
If the program line contains an equation, begins editing the equation.
If the equation is being edited (cursor visible), deletes the rightmost character.

CLEAR

Brings up the same CLEAR menu as in Calculator mode, but function ALL is replaced with PGM, which clears the program memory completely. All programs are lost.
If the current program line contains an equation, PGM is replaced with EQN which deletes the program line.

CLEAR x

Inserts a program instruction to clear the x-register.

MEM PGM CLEAR

Clears a specific program (label) from memory. After MEM PGM, use or to navigate the list of program labels and press CLEAR to delete every program line bearing the selected label from program memory (i.e. the entire program or routine).

24.4.4. Clearing memory

To clear most of memory, use CLEAR ALL Y. Here is a list of exactly what this resets.

setting/object

CLEAR ALL

angular mode

unchanged

radix mark

unchanged

display format

unchanged

denominator (/c)

unchanged

number base

unchanged

flags

unchanged

fraction display

unchanged

random number seed

unchanged

stack lift

enabled

stack

cleared (set to zero)

variables

cleared (set to zero)

Extended_ registers

cleared (set to zero)

Global registers

unchanged

Equation list

cleared

program memory

cleared

FN= label

null

current equation

EQN LIST TOP

program pointer

PRGM TOP

system time and date

unchanged

CLEAR ALL Y only clears memory for the Active State.

24.4.5. Delete all States

To delete all States from the Available States list, use Load Clean State from the DM32 Setup File menu.

24.4.6. Hard RESET

The printed circuit board has a hard RESET button accessible through a hole in the backplate. By gently inserting a thin object, like a pin or an open paperclip, it is possible to press this button through the hole.

reset hole

This will reset the system and then reload the Available States list and the active State as they were last saved to the internal disk. If one of the States to reload isn’t available from the internal disk, an error message appears after RESET, and the calculator falls back to another State.

24.5. DMCP5 and filenames

The supported characters for filenames in DMCP5 are:

  • uppercase latin letters A to Z

  • lowercase latin letters a to z

  • digits 0 to 9

  • underscore _

Here are a few length limits to consider:

  • maximum file pathname length supported by DMCP5 is 127 characters (above this limit the system isn’t able to handle files);

  • maximum Statefile pathname length for after-reset load: 55 characters (above this limit the statefile will be not reloaded after RESET);

  • maximum Statefile name length (truncated otherwise): 31 characters (this is the file name without an extension used for state name).

Maximum filename length (including extension) which can be entered from the onboard file dialog as new file is 28 characters.

25. Appendix C: Messages

A message appears on the display when particular conditions are met. A warning annunciator turns on to call attention to the message. Some messages will remain on the display until cleared. Pressing or C clears a message; pressing any other key clears the message and executes that key’s function.

message meaning

∫FN ACTIVE

The running program attempted to select a program label (FN= label) while an integration calculation was running.

∫(∫FN)

The running program attempted to integrate a program (∫FN d variable) while another integration calculation was running.

∫(SOLVE)

The running program attempted to solve a program while an integration calculation was running.

ALL VARS=0

No variables in memory (displayed by variables catalog MEM VAR). Exits the catalog.

CALCULATING

Function is being executed, please wait.

CLR EQN? Y N

Confirm deletion of equation being edited; occurs only when pressing CLEAR during equation entry.

CLR PGMS? Y N

Confirm deletion of all programs; occurs only when pressing CLEAR PGM in Program mode.

DIVIDE BY 0

Attempted division by zero (also appears when pressing %CHG if y-register is zero).

DUPLICAT. LBL

Attempted to enter a label already used by another program or routine.

EQN LIST TOP

Reached “top” of equation memory, at which point the list of equations wraps around.

INTEGRATING

Integral is being calculated; please wait.

INTERRUPTED

A running SOLVE or ∫FN function has been interrupted by C or R/S.

INVALID DATA

Data error:

  • in combinations or permutations, attempted to calculate with:

    • r > n

    • non-integer r or n

    • n ≥ 1034

  • in trigonometric or hyperbolic functions, attempted to calculate:

    • TAN with x an odd multiple of 90°

    • ACOS or ASIN with x < –1 or x > 1

    • HYP ATAN with x ≤ –1 or x ≥ 1

    • HYP ACOS with x < 1

INVALID EQN

Syntax error detected in equation during evaluation, SOLVE or ∫FN.

INVALID x!

Attempted factorial or gamma operation with x as negative integer.

INVALID

Exponentiation error:

  • attempted to raise 0 to the 0th power or to a negative power

  • attempted to raise a negative number to a non-integer power

  • attempted to raise complex number (0 + i0) to a number with a negative real part

INVALID (i)

Attempted an indirect address operation with invalid number in index register (|i| ≥ 34 or 0 ≤ |i| < 1).

LOG(0)

Attempted logarithm of zero or (0 + i0).

LOG(NEG)

Attempted logarithm of a negative number.

MEMORY CLEAR

All user memory has been cleared.

MEMORY FULL

Attempted operation with insufficient memory.

NO

Conditional test returned false (only occurs when conditional test is invoked from the keypad).

NONEXISTENT

Attempted to refer to nonexistent program label or line number with GTO, GTO , GTO XEQ, XEQ or FN=, regardless of whether the nonexistent program label is referred to from the keypad (manually) or by a program instruction.
In the context of a Remote XEQ, attempted to refer to nonexistent program label or State.

NO LABELS

No program labels in memory (displayed by programs catalog MEM PGM). Exits the catalog.

NO ROOT FND

Function SOLVE cannot find a root using the current initial guesses. Operation SOLVE called from a program line does not trigger this error; instead, in this condition, the program pointer skips the next program line (the line immediately follwing the SOLVE variable instruction).

OVERFLOW

The magnitude of the result is too large.
The calculator returns 9.999999999999999999999999999999999 × 106144.
Flag 6 is automatically set. If flag 5 is set, this condition additionally halts the running program and leaves the message on display until a key is pressed.

PRGM TOP

Reached “top” of program memory, at which point program lines wrap around.

RUNNING

A program is running (other than a SOLVE or ∫FN routine).

SELECT FN

Attempted to execute SOLVE variable or ∫FN d variable without a selected program label with FN=; only happens after SOLVE of ∫FN is invoked after MEMORY CLEAR, or if current label no longer exists.

SOLVE ACTIVE

The running program attempted to select a program label (FN= label) while a SOLVE operation was running.

SOLVE(SOLVE)

The running program attempted to solve a program while a SOLVE operation was running.

SOLVE(∫FN)

The running program attempted to integrate a program while a SOLVE operation was running.

SOLVING

An equation or program is being solved for its root; please wait.

SQRT(NEG)

Attempted to calculate the square root of a negative number.

STAT ERROR

Statistics error:

  • attempted to do a statistics calculation with n = 0

  • attempted to calculate sx, sy, , , m, r or b with n = 1

  • attempted to calculate r, or x̄w with x-data only (all y-values = 0)

  • attempted to calculate , , r, m or b with all x-values equal

TOO BIG

Magnitude of the number too large for conversion to HEX, OCT or BIN base. The number must be in the range –34,359,738,368 ≤ n ≤ 34,359,738,367.

XEQ OVERFLOW

The running program attempted a 16th call to XEQ. Up to 15 subroutines can be nested. Functions SOLVE and ∫FN use one nesting level and will trigger this error.

YES

Conditional test returned true (only occurs when conditional test is invoked from the keypad).

26. Appendix D: Functions index

All calculator functions are listed below in alphabetical order, with the keystrokes to invoke them and a description. The order is based on function names as they appear in programs and equations (and not necessarily as they do on keys). Non-programmable functions are simply shown as keystrokes. Special characters (Greek or non-letter) are listed first, except for functions with an initial arrow, like →RAD. The first column contains color bullets:

  • function can be used in equations,

  • function appears only in equations,

  • function saves contents of x-register to LASTx.

name in equation or program keystroke description

+/–

+/–

Changes the sign of a number.

+

+

Returns y + x.

-

Returns yx.

×

×

Returns y × x.

÷

÷

Returns y ÷ x.

^

Indicates an exponent.

Deletes the last digit keyed in;
clears x;
clears a menu;
erases last function keyed in an equation;
starts equation editing;
deletes a program step.

Displays previous entry in variables or programs catalogs;
moves to previous equation in Equation list;
moves program pointer to previous step.

Displays next entry in variables or programs catalogs;
moves to next equation in Equation list;
moves program pointer to next line (during program entry) executes the current program line (only during program entry).

1/x

1/x

Reciprocal.

10x

10x

Common exponential. Returns 10 raised to the x power.

%

%

Percent. Returns (y × x) ÷ 100.

%CHG

%CHG

Percent change. Returns (xy)(100 ÷ y).

π

π

Returns the approximation 3.141592653589793238462643383279503 (34 digits).

Σ+

Σ

Accumulates (y,x) into statistics registers.

Σ–

Σ–

Removes (y,x) from statistics registers.

Σx

SUMS x

Returns the sum of X-values.

Σx²

SUMS x²

Returns the sum of squares of X-values.

Σxy

SUMS xy

Returns the sum of products of X- and Y-values.

Σy

SUMS y

Returns the sum of Y-values.

Σy²

SUMS y²

Returns the sum of squares of Y-values.

σx

s,σ σx

Returns population standard deviation of X-values: √(Σ(xīx)2 ÷ n).

σy

s,σ σy

Returns population standard deviation of Y-values: √(Σ(yi )2 ÷ n).

θ,r→y,x

y,x

Polar to rectangular coordinates. Converts (r,θ) to (x,y).

∫FN d variable

→∫ ∫FN d variable

Integrates the displayed equation or the program selected by FN=, using lower limit of the variable of integration in the y-register and upper limit of the variable of integration in the x-register.

(

(

Open parenthesis. Starts a quantity associated with a function in an equation.

)

)

Close parenthesis. Ends a quantity associated with a function in an equation.

A through Z

RCL [letter] or STO [letter]

Value of named variable; insert letter. (In equation mode.)

ABS

PARTS ABS

Absolute value. Returns |x|.

ACOS

ACOS

Arc cosine. Returns cos–1 x.

ACOSH

HYP ACOS

Hyperbolic arc cosine. Returns cosh–1 x.

ALOG

10x

Common exponential. Returns 10 raised to the specified power (antilogarithm).

ALL

DISP ALL

Selects display of all significant digits.

ASIN

ASIN

Arc sine. Returns sin–1 x.

ASINH

HYP ASIN

Hyperbolic arc sine. Returns sinh–1 x.

ATAN

ATAN

Arc tangent. Returns tan–1 x.

ATANH

HYP ATAN

Hyperbolic arc tangent. Returns tanh–1 x.

b

L.R. b

Returns the y-intercept of the regression line.

BASE

Displays the base menu.

BIN

BASE BN

Selects binary (base-2) mode.

C

Turns on calculator; clears x; clears messages and prompts; cancels menus; cancels catalogs; cancels equation entry; cancels program entry; halts execution of an equation; halts a running program.

/c

/c

Denominator. Sets denominator limit for displayed fractions to x. If x=1, displays current /c value.

→°C

→°C

Converts °F to °C. Returns (x–32) ÷ 1.8.

CF n

FLAGS CF n

Clears flag n (0 ≤ n ≤ 11).

CLEAR

Displays menu to clear numbers or parts of memory; clears selected variable or program from MEM catalog; clears selected equation.

CLEAR ALL

Clears all stored data, equations, and programs. Flags, display and fraction format and radix configuration remain untouched.

CLEAR PGM

Clears all programs (calculator in Program mode).

CLEAR EQN

Clears the displayed equation (calculator in Program mode).

CLΣ

CLEAR Σ

Clears statistics registers.

CLVARS

CLEAR VARS

Clears all variables to zero.

CLx

CLEAR x

Clears the x-register to zero.

→CM

→cm

Converts inches to centimeters. Returns 2.54x.

CMPLX

Displays the CMPLX_ prefix for complex functions.

CMPLX+/–

CMPLX +/–

Complex change sign. Returns –(zx + izy).

CMPLX+

CMPLX +

Complex addition. Returns (z1x + iz1y) + (z2x + iz2y).

CMPLX–

CMPLX

Complex subtraction. Returns (z1x + iz1y) – (z2x + iz2y).

CMPLX×

CMPLX ×

Complex multipliction. Returns (z1x + iz1y) × (z2x + iz2y).

CMPLX÷

CMPLX ÷

Complex division. Returns (z1x + iz1y) ÷ (z2x + iz2y).

CMPLX1/x

CMPLX 1/x

Complex reciprocal. Returns 1/(zx + izy).

CMPLXCOS

CMPLX COS

Complex cosine. Returns cos (zx + izy).

CMPLXeˣ

CMPLX

Complex natural exponential. Returns e(zx + izy).

CMPLXLN

CMPLX LN

Complex natural log. Returns loge (zx + izy).

CMPLXSIN

CMPLX SIN

Complex sine. Returns sin (zx + izy).

CMPLXTAN

CMPLX TAN

Complex tangent. Returns tan (zx + izy).

CMPLXyˣ

CMPLX

Complex power. Returns (z1x + iz1y)(z2x + iz2y).

Cn,r

PROB Cn,r

Combinations of n items taken r at a time. Returns n! ÷ (r! (n–r)!).

COS

COS

Cosine. Returns cos x.

COSH

HYP COS

Hyperbolic cosine. Returns cosh x.

DEC

BASE DEC

Selects decimal mode.

DEG

MODES DG

Selects degrees angular mode.

→DEG

→DEG

Radians to degrees. Returns (360/2π)x.

DISP

Displays menu to set the display format.

DSE variable

DSE variable

Decrement, skip if equal or less. For control number ccccccc.fffii stored in a variable, subtracts ii (in increment value) from ccccccc (counter value) and, if the result ≤ fff (final value), skips the next program line.

E

Begins entry of exponents and adds “E” to the number being entered. Indicates that a power of 10 follows.

ENG n

DISP EN

Selects engineering display format with n digits following the first digit (0 ≤ n ≤ 11).

ENTER

Separates two numbers keyed in sequentially; completes equation entry; evaluates the displayed equation (and stores result if appropriate).

ENTER

ENTER

Copies x into the y-register, lifts y into the z-register, lifts z into the t-register, and loses t. (In Program mode.)

EQN

Opens the Equation list.

ex

Natural exponential. Raises e to the power of x-register.

EXP

Natural exponential. Returns e raised to the specified power. (In equation mode.)

→°F

→°F

Converts °C to °F. Returns 1.8x + 32.

FDISP

Toggles fraction-display mode.

FIX n

FDISP FX n

Selects fixed display with n decimal places (0 ≤ n ≤ 11).

FLAGS

Displays the menu to set, clear, and test flags.

FN= label

FN=

Selects labeled program as the current function (used by SOLVE and ∫FN).

FP

PARTS FP

Fractional part of x.

FS? n

FLAGS FS? n

If flag n (0 ≤ n ≤ 11) is set, executes the next program line; if flag n is clear, skips the next program line.

→GAL

→gal

Converts liters to gallons. Returns 0.2641720523581484153798999216091625x.

GRAD

MODES GR

Sets gradians angular mode.

GTO label

GTO label

Sets the program pointer to first line of program label in program memory.

GTO . label nn

Sets program pointer to line 0 ≤ nn ≤ 99 of program label.

GTO . .

Sets program pointer to PRGM TOP.

GTO XEQ [LETTER] nnnn

Sets program pointer to any labeled line number.

GTO [LETTER] nnnn

Sets program pointer to any unlabeled line number.

HEX

BASE HEX

Selects hexadecimal (base-16) mode.

HYP

Displays the HYP_ prefix for hyperbolic functions.

→HMS

→HMS

Hours to hours, minutes, seconds. Converts x from a decimal fraction to hours-minutes-seconds format.

→HR

→HR

Hours, minutes, seconds to hours. Converts x from hours-minutes-seconds format to a decimal fraction.

i

RCL [i] or STO [i]

Indirect. Value of variable i.

(i)

RCL [(i)] or STO [(i)]

Indirect. Value of variable whose letter corresponds to the numeric value stored in variable i.

→IN

→in

Converts centimeters to inches. Returns x ÷ 2.54.

INPUT variable

INPUT variable

Recalls the variable to the x-register, displays the variable’s name and value, and halts program execution.
Pressing R/S (to resume program execution) or (to execute the current program line) stores input in the variable. (Used only in programs.)

INV

1/x

Reciprocal of argument.

IP

PARTS IP

Integer part of x.

ISG variable

ISG variable

Increment, Skip if Greater. For control number ccccccc.fffii stored in variable, adds ii (increment value) to ccccccc (counter value) and, if the result > fff (final value), skips the next program line.

→KG

→kg

Converts pounds to kilograms. Returns 0.45359237x.

→L

→l

Converts gallons to liters. Returns 3.785411784x.

LASTx

LASTx

Returns number stored in the LASTx register.

→LB

→lb

Converts kilograms to pounds. Returns x ÷ 0.45359237.

LBL label

LBL label

Labels a program with a single letter for reference by the XEQ, GTO, or FN= operations. (Used only in programs.)

LN

LN

Natural logarithm. Returns loge x.

LOG

LOG

Common logarithm. Returns log10 x.

L.R.

Displays menu for linear regression.

m

L.R. m

Returns the slope of the regression line: FORMULA

MEM

Displays the amount of available memory and the catalog menu.

MEM PGM

Begins catalog of programs.

MEM VAR

Begins catalog of variables.

MODES

Displays menu to set angular modes and the radix (. or , ).

n

SUMS n

Returns the number of sets of data points.

OCT

BASE OC

Selects octal (base-8) mode.

OFF

Turns the calculator off.

PARTS

Displays the menu for selecting parts of numbers.

Pn,r

PROB Pn,r

Permutations of n items taken r at a time. Returns n! ÷ (nr)!.

PRGM

Activates or cancels (toggles) Program mode.

PROB

Displays the menu for probability functions.

PSE

PSE

Pause. Halts program execution briefly to display x, variable, or equation, then resumes. (Used only in programs.)

r

L.R. r

Returns the correlation coefficient between the X- and Y-values: FORMULA

RAD

MODES RAD

Selects radians angular mode.

→RAD

→RAD

Degrees to radians. Returns (2π/360)x.

RADIX,

MODES ,

Selects the comma as the radix mark (decimal point).

RADIX.

MODES .

Selects the period as the radix mark (decimal point).

RANDOM

PROB R

Returns a random number in the range O through 1.

RCL variable

RCL variable

Recall. Copies variable into the x-register.

RCL+ variable

RCL + variable

Returns x + variable.

RCL- variable

RCL variable

Returns x - variable.

RCL× variable

RCL × variable

Returns x × variable.

RCL÷ variable

RCL ÷ variable

Returns x ÷ variable.

RND

RND

Rounds x to n decimal places in FIX n display mode; to n + 1 significant digits in SCI n or ENG n display mode; or to decimal number closest to displayed fraction in fraction-display mode.

RTN

RTN

Return. Marks the end of a program; the program pointer returns to the top or to the calling routine.

R↓

R↓

Roll down. Moves t to the z-register, z to the y-register, y to the x-register, and x to the t-register.

R↑

R↑

Roll up. Moves t to the x-register, z to the t-register, y to the z-register, and x to the y-register.

s,σ

Displays the standard-deviation menu.

SCI n

DISP SC n

Selects Scientific display with n decimal places (0 ≤ n ≤ 11).

SCRL

Scroll. Enables and disables scrolling of equations in Equation and Program modes.

SEED

PROB SD

Restarts the random-number sequence with the seed |x|.

SF n

FLAGS SF n

Sets flag n (0 ≤ n ≤ 11).

SHOW

Shows the full mantissa (all 12 digits) of x (or the number in the current program line); while in the Equation list, displays the complete equation with a smaller font; while in Program mode, shows complete contents of line at the pointer.

SIN

SIN

Sine. Returns sin x.

SINH

HYP SIN

Hyperbolic sine. Returns sinh x.

SOLVE variable

SOLVE variable

Solves the displayed equation or the program selected by FN=, using initial estimates in variable and x.

[SPACE]

R/S inserts a blank space character during equation entry.

SQ

x²

Square of argument.

SQRT

√x

Square root of x.

STO variable

STO variable

Store. Copies x into variable.

STO+ variable

STO + variable

Stores variable + x into variable.

STO– variable

STO variable

Stores variable – x into variable.

STO× variable

STO × variable

Stores variable × x into variable.

STO÷ variable

STO ÷ variable

Stores variable ÷ x into variable.

STOP

R/S

Run/stop. Begins program execution at the current program line; stops a running program and displays the x-register.

SUMS

Displays the summation menu.

sx

s,σ sx

Returns sample standard deviation of x-values: FORMULA

sy

s,σ sy

Returns sample standard deviation of y-values: FORMULA

TAN

TAN

Tangent. Returns tan x.

TANH

HYP TAN

Hyperbolic tangent. Returns tanh x.

VIEW variable

VIEW variable

Displays the labeled contents of variable without recalling the value to the stack.

XEQ

Evaluates the displayed equation.

XEQ label

XEQ label

Executes the program identified by label.

XEQ label:_State_

XEQ State label

Remotely executes the program identified by label from State.

x²

x2

Square of x.

ˣ√y

ˣ√y

The xth root of y.

,

Returns the mean of X values: Σxi ÷ n.

̂x

L.R. ̂x

Given a Y-value in the x-register, returns the X-estimate based on the regression line: ̂x = (Y – b) ÷ m.

x!

x!

Factorial (or gamma). Returns (x)(x–1)…(2)(1), or Γ(x+1).

XROOT

xy

The argument1 root of argument2.

x̄w

, x̄w

Returns weighted mean of x values: (Σyixi) ÷ Σyi.

,

Displays the mean (arithmetic average) menu.

x<> variable

x variable

Exchanges x with a variable.

x<>y

xy

Moves x to the y-register and y to the x-register.

x?y

Displays the “x?y” comparison tests menu.

xy?

x?y

If xy, executes next program line; if x=y, skips the next program line.

xy?

x?y

If xy, executes next program line; if x>y, skips next program line.

x<y?

x?y <

If x<y, executes next program line; if xy, skips next program line.

x>y?

x?y >

If x>y, executes next program line; if xy, skips next program line.

xy?

x?y

If xy, executes next program line; if x<y, skips the next program line.

x=y?

x?y =

If x=y, executes next program line; if xy, skips next program line.

x?0

Displays the “x?0” comparison tests menu.

x≠0?

x?0

If x≠0, executes next program line; if x=0, skips the next program line.

x≤0

x?0

If x≤0, executes next program line; if x>0, skips next program line.

x<0

x?0 <